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Manual for Corporate RecruitmentContents I. Preface 1. Why this book? 2. What does it contain? II. Selection Procedures of MNC’s III. Importance of Aptitude in Recruitment Process IV. Patterns of various MNC Aptitude Papers V. Quantitative Aptitude 1. Percentages a. Percentage change b. Percentage difference c. Multiple percentage changes 2. Profit & Loss a. Discounts b. % Profit c. % Loss 3. Averages and Ages 4. Ratios and Proportions a. Partnerships b. Mixtures & Allegations 5. Test on chapters 1 to 4 6. Solutions for the test 7. Time and Distance a. Trains b. Boats & Streams c. Races 8. Time and Work a. Work & Wages b. Pipes & Cisterns 9. Mensuration a. Areas b. Volumes c. Basics of Geometry 10. Test on chapters 6 to 9 11. Solutions for the test 12. Interest a. Simple Interest b. Compound Interest 13. Clocks 14. Calendars 15. Probability a. Playing Cards b. Dices c. Coloured Balls 16. Test on chapters 10 to 13 17. Solutions for the test 18. Comprehensive Test on Quantitative Aptitude 19. Solutions for the test VI. Logical Aptitude 1. Blood Relations 2. Directions 3. Coding & Decoding 4. Series a. Letter Series b. Number Series c. Odd Man Out Series 5. Test on chapters 1 to 4 6. Solutions for the test 7. Analytical Reasoning a. Arrangements b. Comparisons c. Selections d. Family Based Problems e. Intersection Type 8. Critical Reasoning 9. Test on chapters 7 to 8 10. Solutions for the test 11. Cubes a. Counting the cubes b. Painting with equal cuttings c. Painting with inequal cuttings d. Miscellaneous 12. Logical Deductions 13. Test on chapters 11 to 12 14. Solutions for the test 15. Data Interpretation 16. Data Sufficiency 17. Venn Diagrams 18. Test on chapters 15 to 17 19. Solutions for the test 20. Comprehensive Test on Logical Aptitude 21. Solutions for the test VII. Verbal Aptitude 1. Reading Comprehension 2. Vocabulary Test 3. Sentence Completion a. Prepositions b. Adverbs c. Conjunctions d. Verb Forms 4. Sentence Correction Preface The book is mainly targeted to provide the graduates, who are looking for their placements in companies from various sectors, with the most comprehensive book that can help them prepare to crack the aptitude tests. The approach of the book is different from other aptitude and reasoning books available in the market in a way that it concentrates more on the logic behind the problems rather on the formulae to solve them. There had been a necessity for a book that can serve the needs of the graduates seeking their placements and this book can provide the best solution. It is designed in such a way that all the concepts required to be prepared in by the students to crack the aptitude test conducted by the companies are discussed in detail with required synopsis and examples. The following are the topics that will be covered in this book: I. Selection Processes of various MNC’s: This makes the students aware of the recruitment processes of various MNC‟s with detailed description of all the rounds of selection and the qualities that the candidate has to develop to pass it. II. Quantitative Aptitude: This section deals with all the topics related with arithmetic problems, the logics behind each concept and applying the logics for solving the problems. All the exercises and the tests are provided with solutions to help the readers check their approaches to the problems. III. Logical Aptitude: This section deals with problems related with Logical and Analytical reasoning, explaining all the concepts with vivid logics behind them. All the problems and the tests are provided with solutions to help the reader to understand better. IV. Verbal Aptitude: This section deals with testing the reader on his knowledge of English language and this is one of the sections in the aptitude section of the test conducted by the companies. It will help the readers to improve their vocabulary, comprehension, functional grammar and sentence structures. Outstanding Features: 1. Every concept is explained more clearly with logic behind the concept, without the usage of numerous formulae. This provides the readers with a better level of understanding over the topics. 2. Every logic is strengthened by solved examples, exercises, tests and solutions to ensure that the reader gets all the required inputs at the required level of complexity. 3. The CD contains Diagnostic Tests, Vocabulary Building List and Practice Papers with real-time difficulty to provide the user with extra benefits. In all, there is a guarantee that this book will be a very helpful and effective tool for the job-seekers by providing them with all the inputs and guiding them towards their placement in the companies. Recruitment Patterns of various MNC’s Various MNC‟s have different patterns for recruitment but the skeletal structure of the patterns is commonly aid to be as follows: Round I: Written test on aptitude Round II: Written test on technical knowledge Round III: Group Discussion Round IV: Technical Interview Round V: HR Interview So unless you prove yourself in aptitude test you will never get a chance to prove any other expertise you possess in other aspects. This is the reason why aptitude is considered the most important factor by the aspirants of various MNC recruitments. Importance of aptitude in recruitment process Aptitude test is the first round of recruitment process for any company in any sector like Banking, Software, Insurance, Pharmaceutics etc. All the graduates with 60% or above are eligible for the recruitment process and everyone is tested on the same grounds of aptitude. This gives us the clear idea that the companies are giving aptitude more importance than the academic percentages. What is aptitude? Aptitude literally means a natural talent. It is something that comes with us by our birth. But it is to be explored and developed within by us and that can be achieved by understanding and practicing the concepts of aptitude. The candidates with good aptitude skills are considered better than others because they are fast at their mind and good at problem solving skills. Thus aptitude has become the most important soft skill these days. Why aptitude? Even if the candidate is good at academics and communication skills, he will not get a chance to prove them unless he passes through the initial round of aptitude testing. So we can conclude that without appropriate levels of aptitude an aspirant can never achieve success in the recruitment process of any corporate sector company. This book helps all the aspirants in clearly understanding the concepts of aptitude that are required for the recruitment processes of various companies. For further practice on these concepts covered in the book you can refer to the books on aptitude by Pearson Education like Test of reasoning and general intelligence by Showick Thorpe and Quantitative Techniques by Khattar. QUANTITATIVE APTITUDE Percentages Understanding Percentages: The word percent can be understood as follows: Per cent => for every 100. So, when percentage is calculated for any value, it means that that you calculate the value for every 100 of the reference value. Why Percentage? Percentage is a concept evolved so that there can be a uniform platform for comparison of various things. (Since each value is taken to a common platform of 100.) Eg: To compare three different students depending on the marks they scored we cannot directly compare their marks until we know the maximum marks for which they took the test. But by calculating percentages they can directly be compared with one another. Before going deeper into the concept of percentage, let u have a look at some basics and tips for faster calculations: Calculation of Percentage: Percentage = (Value / Total value) X 100 Eg: 50 is what % of 200? Soln: Percentage = (50/200) X 100 = 25%. Calculation of Value: Value = (Percentage/100) X total value Eg: What is 20% of 200? Soln: Value = (20/100) X 200 Note: Percentage is denoted by “%”, which means “/100”. Eg: What is the decimal notation for 35%? Soln: 35% = 35/100 = 0.35. For faster calculations we can convert the percentages or decimal equivalents into their respective fraction notations. Percentages – Fractions Conversions: The following is a table showing the conversions of percentages and decimals into fractions: Percentage Decimal Fraction 10% 0.1 1/10 12.5% 0.125 1/8 16.66% 0.1666 1/6 20% 0.2 1/5 25% 0.25 1/4 30% 0.3 3/10 33.33% 0.3333 1/3 40% 0.4 2/5 50% 0.5 1/2 60% 0.6 3/5 62.5% 0.625 5/8 66.66% 0.6666 2/3 70% 0.7 7/10 75% 0.75 3/4 80% 0.8 4/5 83.33% 0.8333 5/6 90% 0.9 9/10 100% 1.0 1 Similarly we can go for converting decimals more than 1 from the knowledge of the above cited conversions as follows: We know that 12.5% = 0.125 = 1/8 Then, 1.125 = [8(1)+1]/8 = 9/8 (i.e., the denominator will add to numerator once, denominator remaining the same. Also, 2.125 = [8(2)+1]/8 = 17/8 (here the denominator is added to numerator twice) 3.125 = [8(3)+1]/8 = 25/8 and so on. Thus we can derive the fractions for decimals more than 1 by using those les than 1. We will see how use of fractions will reduce the time for calculations: Eg: What is 62.5% of 320? Soln: Value = (5/8) X 320 (since 62.5% = 5/8) = 200. Percentage Change: A change can be of two types – an increase or a decrease. When a value is changed from initial value to a final value, % change = (Difference between initial and final value/initial value) X 100 Eg: If 20 changes to 40, what is the % increase? Soln: % increase = (40-20)/20 X 100 = 100%. Note: 1. If a value is doubled the percentage increase is 100. 2. If a value is tripled, the percentage change is 200 and so on. Percentage Difference: % Difference = (Difference between values/value compared with) X 100. Eg: By what percent is 40 more than 30? Soln: % difference = (40-30)/30 X 100 = 33.33% (Here 40 is compared with 30. So 30 is taken as denominator) Eg: By what % is 60 more than 30? Soln: % difference = (60-30)/30 X 100 = 100%. (Here is 60 is compared with 30.) Hint: To calculate percentage difference the value that occurs after the word “than” in the question can directly be used as the denominator in the formula. Important Points to Note: 1. When any value increases by a. 10%, it becomes 1.1 times of itself. (since 100+10 = 110% = 1.1) b. 20%, it becomes 1.2 times of itself. c. 36%, it becomes 1.36 times of itself. d. 4%, it becomes 1.04 times of itself. Thus we can see the effects on the values due to various percentage increases. 2. When any value decreases by a. 10%, it becomes 0.9 times of itself. (Since 100-10 = 90% = 0.9) b. 20%, it becomes 0.8 times of itself c. 36%, it becomes 0.64 times of itself d. 4%, it becomes 0.96 times of itself. Thus we can see the effects on a value due to various percentage decreases. Note: 1. When a value is multiplied by a decimal more than 1 it will be increased and when multiplied by less than 1 it will be decreased. 2. The percentage increase or decrease depends on the decimal multiplied. Eg: 0.7 => 30% decrease, 0.67 => 33% decrease, 0. 956 => 4.4% decrease and so on. Eg: When the actual value is x, find the value when it is 30% decreased. Soln: 30% decrease => 0.7 x. Eg: A value after an increase of 20% became 600. What is the value? Soln: 1.2x = 600 (since 20% increase)  x = 500. Eg: If 600 is decrease by 20%, what is the new value? Soln: new value = 0.8 X 600 = 480. (Since 20% decrease) Thus depending on the decimal we can decide the % change and vice versa. Eg: When a value is increased by 20%, by what percent should it be reduced to get the actual value? Soln: (It is equivalent to 1.2 reduced to 1 and we can use % decrease formula) % decrease = (1.2 – 1)/1.2 X 100 = 16.66%. 3. When a value is subjected multiple changes, the overall effect of all the changes can be obtained by multiplying all the individual factors of the changes. Eg: The population of a town increased by 10%, 20% and then decreased by 30%. The new population is what % of the original? Soln: The overall effect = 1.1 X 1.2 X 0.7 (Since 10%, 20% increase and 30% decrease) = 0.924 = 92.4%. Eg: Two successive discounts of 10% and 20% are equal to a single discount of ___ Soln: Discount is same as decrease of price. So, decrease = 0.9 X 0.8 = 0.72 => 28% decrease (Since only 72% is remaining). Exercise: 1. If 20% of 40% of a = 25% of a% of b, then what is b? a. 8/5 b. 16/25 c. 8/25 d. None 2. By what % is 200 more than 50? a. 100 b. 200 c. 300 d. None 3. A value changes from 30 to 80. What is the percentage change? a. 125 b. 166.66 c. 156 d. None 4. The population of a city is increased by 30% and thus became 78000. What is the original population? a. 76000 b. 64200 c. 60000 d. None 5. In a theatre, the number of seats is increased by 20% and the price per ticket is increased by 10% but the public response decreased by 30%. What is the net effect on the economy of the theatre? a.10% rise b. 7% fall c. 7% rise d. None 6. A saves 20% of his income. His income is increased by 20% and so he increased his expenditure by 30%. What is the percentage change in his savings? a. 20% fall b. 4% fall c. 20% rise d. 4% rise 7. The price of petrol is increased by 25%. By what percent the consumption be reduced to make the expenditure remain the same? a. 25% b. 33.33% c. 20% d. None 8. The side of a square is increased by 20%. The percentage change in its area is ___ a. 20% b. 44% c. 36% d. None 9. If the length of a rectangle is increased by 33.33%, by what percentage should the breadth be reduced to make the area same? a. 20% b. 33.33% c. 25% d. None 10. In an election between two candidates, A and B, A secured 56% of the votes and won by 48000 votes. Find the total number of votes polled if 20% of the votes were declared invalid. a. 500000 b. 400000 c. 600000 d. None 11. A reduction of 10% in price of sugar enables a housewife to buy 5 kg more for Rs. 300/-. Find the reduced price per kg of sugar. a. 5/- b. 4.5/- c. 6/- d. None 12. From a 20lt solution of alt and water with 20% salt, 2lt of water is evaporated. Find the new % concentration of salt. a. 20% b. 23% c. 25% d. None 13. In a list of weights of candidates appearing for police selections, the weight of A is marked as 58 kg instead of 46.4 kg. Find the percentage of correction required. a. 30 b. 20 c. 24 d. None 14. A person spends 20% of his income on rent, 20% of the rest on food, 10% of the remaining on clothes and 10% on groceries. If he is left with Rs. 9520/- find his income. a. 10000/- b. 15000/- c. 20000/- d. None 15. A shopkeeper offers three successive discounts of 10%, 20% and 30% to a customer. If the actual price of the item is Rs. 10000, find the price the custome has to pay to the shopkeeper. a. 5040/- b. 4000/- c. 6000/- d. None 16. If 10lt solution of water and alcohol containing 10% alcohol is to be made 20% alcohol solution, find the volume of alcohol to be added. a. 1 lt b. 1.25 lt c. 1.5 lt d. 2 lt 17. A is twice B and B is 200% more than C. By what percent is A more than C? a. 400 b. 600 c. 500 d. 200 18. In an examination, a student secures 40% and fails by 10 marks. If he scored 50%, he would pass by 15 marks. Find the minimum marks required to pass the exam. a. 250 b. 100 c. 110 d. 125 19. If A is 20% taller than B, by what percent is B shorter than A? a. 20% b. 25% c. 16.66% d. None 20. The population of a town increases at a rate of 10% for every year. If the present population is 12100, find the population two years ago. a. 11000 b. 9800 c. 10000 d. 10120 21. A solution of salt and water contains 15% salt. If 30 lt water is evaporated from the solution the concentration becomes 20% salt. Find the original volume of the liquid before water evaporated. a. 100 lt b. 120 lt c. 200 lt d. None 22. If 240 lt of oil is poured into a tank, it is still 20% empty. How much more oil is to be poured to fill the tank? a. 300 lt b. 60 lt c. 120 lt d. None 23. A and B were hired for the same salary. A got two 40% hikes whereas B got a 90% hike. What is the percentage difference in the hikes thay got? a. 16% b. 6% c. 10% d. 8% 24. The population of a town doubled every 5 years from 1960 to 1975. What is the percentage increase in population in this period? a. 800 b. 400 c. 700 d. 600 25. In a test of 80 questions, Jyothsna answered 75% of the first 60 questions correctly. What % of the remaining questions she has to answer correctly so that she can secure an overall percentage of 80 in the test? a. 80% b. 90% c. 85% D. 95% Solutions: 1. 1/5 X 2/5 X a = ¼ X a X b => b = 8/25 2. % difference = (200-50)/50 X 100 = 300 % 3. % increase = (80-30)/30 X 100 = 166.66 % 4. 1.3 x = 78000 => x = 60000. 5. Net effect = 1.2 X 1.1 X 0.7 = 0.924 => 7.6% decrease. 6. Let I be the income. Expenditure = 0.8I Savings = 0.2I => 20% New income = 1.2I (since 20% rise) New expenditure = (0.8I) X 1.3 (Since 30% rise) = 1.04I So, new savings = 1.2I – 1.04I = 0.16I => 16% (So income decreased form 20% to 16%) % decrease = (20-16)/20 X 100 = 20%. 7. It is equivalent to 1.25 decreased to 1. % decrease = (1.25-1)/1.25 X 100 = 20% 8. % change in area = 1.2 X 1.2 (since area = side X side) = 1.44 => 44%. 9. It is equivalent to 1.25 decreased to 1. So 20% decrease. 10. Valid Votes: A got 56% => B got 44% Difference = 12% = 48000 So, 100% = 400000. These are valid votes. But valid votes are only 80% of total votes. So, 80% of total votes = 400000 => total votes = 500000 11. Total money = Rs. 300. Saving of the lady = 10% of 300 = 30/- With 30/- she bought 5 kg sugar => each kg costs Rs. 6/- 12. In 20lt, salt = 20% => 4 lt. New volume = 18 lt (2 lt evaporated) So, new % = 4/18 X 100 = 22.22% 13. % correction = (58-46.4)/58 X 100 = 20% 14. Three successive decreases of 20%, 20% and 10% => 0.8 X 0.8 X 0.9 = 0.576 Again 10% decrease => 0.576 – 0.1 = 0.476. So, 0.476 x = 9520 => x = 20000. 15. Total discount = 0.9 X 0.8 X 0.7 = 0.504 of actual price. So, price = 0.504 X 10000 = 5040. 16. In 10 lt, alcohol is 10% = 1 lt. Let x lt alcohol is added. So, (1+x)/(10+x) = 20% = 1/5 => x = 1.25 lt. 17. A = 2B and B = 3C (ince 200% more)  A = 6C => 500 % more. 18. 50% of max marks – 40% of max marks = 25  max marks = 250 Pass marks = 40% of max + 10 => 100 + 10 = 110. 19. A = 1.2 B => B = A/1.2 => 0.8333A => 16.66%. (OR) Decrease from 1.2 to 1 => 16.66%. 20. 1.1 X 1.1 X x = 12100 => x = 10000. 21. Salt = 15% of x = 0.15x (x = volume of solution) Now, 0.15x/(x-30) = 20% = 1/5 (since 30 lt evaporated)  x = 120 lt 22. 20% empty => 80 % full = 240 lt => 20% = 60 lt 23. A => 1.4 X 1.4 = 1.96 B => 1.9 => 6% difference. 24. From 1960 to 1975, in 15 years population doubled every 5 yrs => three times So, 2 X 2 X 2 = 8 times => 700% more. 25. [(75% X 60) + (x% X 20)] / 80 = 80% => x = 95. (since required is 80%) (OR) 60 out of 80 is 3/4. So, (3/4 X 75) + (1/4 X x) = 80 => x =95. Profit and Loss What is Profit? When a person does a business transaction and gets more than what he had invested, then he is said to have profit. The profit he gets will be equal to the additional money he gets other than his investment. So profit can be understood as the extra money one gets other than what he had invested. Eg: A person bought an article for Rs. 100 and sold it for Rs. 120. Then he got Rs. 20 extra and so his profit is Rs. 20. What is Loss? When a person gets an amount less than what he had invested, then he is said to have a loss. The loss will be equal to the deficit he got than the investment. Eg: A person bought an article at Rs. 100 and sold it for Rs. 90. Then he got a deficit of Rs. 10 and so his loss is Rs. 10. Cost Price (CP): The money that the trader puts in his business is called Cost Price. The price at which the articles are bought is called Cost Price. In other words, Cost Price is nothing but the investment in the business. Selling Price (SP): The price at which the articles are sold is called the Selling Price. The money that the trader gets from the business is called Selling Price. In other words, Selling Price is nothing but the returns from a business. Marked/Market/List Price (MP): The price that a trader marks or lists his articles to is called the Marked Price. This is the only price known to the customer. Discount: The waiver of cost from the Marked Price that the trader allows a customer is called Discount. Note: 1. Profit or loss percentage is to be applied always to the Cost Price only. 2. Discount percentage is to be applied always to the Marked Price only. Relationship Among CP, SP and MP: A trader adds his profit to the investment and sells it at that increased price. Also he allows a discount on Marked Price and sells at the discounted price. So, we can say that, o SP = CP + Profit. (CP applied with profit is SP) o SP = MP – Discount. (MP applied with discount is SP) Understanding Profit and Loss: So, by now we came to know that if CP is increased and sold it would result in profit and vice versa. Also whatever increase is applied to CP, that increase itself is the profit. For Rs. 10 profit, CP is to be increased by RS. 10 and the increased price becomes SP. For 10% profit, CP is to be increased by 10% and it is the SP. (From previous chapter we know that any value increased by 10% becomes 1.1 times.) So, for 10% profit, CP increased by 10% => 1.1CP = SP. o SP = 1.1CP => SP/CP = 1.1 => 10% profit o SP = 1.07CP => SP/CP = 1.07 => 7% profit o SP = 1.545CP => SP/CP = 1.545 => 54.5% profit and so on. Similarly, o SP = 0.9CP => SP/CP = 0.9 => 10% loss (Since 10% decrease) o SP = 0.76CP => SP/CP = 0.76 => 24% loss and so on. So, to calculate profit % or loss %, it is enough for us to find the ratio of SP to CP. Note: 1. If SP/CP > 1, it indicates profit. 2. If SP/CP < 1, it indicates loss. Multiple Profits or losses: A trader may sometimes have multiple profits or losses simultaneously. This is equivalent to having multiple changes and so all individual changes are to be multiplied to get the overall effect. Examples: 1. A trader uses a 800gm weight instead of 1 kg. Find his profit %. Soln: (He is buying 800 gm but selling 1000 gm. So, CP is for 800 gm and SP is for 1000 gm.) SP/CP = 1000/800 = 1.25 => 25% profit. 2. A trader uses 1 kg weight for 800 gm and increases the price by 20%. Find his profit/loss %. Soln: 1 kg weight for 800 gm => loss (decrease) => 800/1000 = 0.8 20% increase in price => profit (increase) => 1.2 So, net effect = (0.8) X (1.2) = 0.96 => 4% loss. 3. A milk vendor mixes water to milk such that he gains 25%. Find the percentage of water in the mixture. Soln: To gain 25%, the volume has to be increased by 25%. So, for 1 lt of milk, 0.25 lt of water is added => total volume = 1.25 lt % of water = 0.25 / 1.25 X 100 = 20%. 4. A trader bought an item for Rs. 200. If he wants a profit of 22%, at what price must he sell it? Soln: CP=200, Profit = 22%. So, SP = 1.22CP = 1.22 X 200 = 244/-. 5. A person buys an item at Rs. 120 and sells to another at a profit of 25%. If the second person sells the item to another at Rs. 180, what is the profit % of the second person? Soln: SP of 1 st person = CP of 2 nd person = 1.25 X 120 = 150. SP of 2 nd person = 180. Profit % = SP/CP = 180/150 = 1.2 => 20%. 6. A milk vendor mixes water to 20 lt of milk such that the ratio of milk and water is 4:3. He sold the mixture at Rs. 12 per liter but bought the milk at Rs. 10 per liter. Find the profit % of the vendor. Soln: milk : water = 4:3 => he bought 4 parts (milk) but sold 7 parts (mixture) CP = 10 and SP = 12. So, profit % = (SP/CP) X (SP/CP) = (7/4) X (12/10) = 2.1 => 110% gain. 7. A trader buys some apples at a price of 10 apples for Rs. 8 and sold them at a price of 8 apples for Rs. 10. Find his profit or loss %. Soln: He bought 10 apples for Rs. 8 and sold 8 apples for Rs. 10 => clearly got profit  SP > CP => (SP/CP) X (SP/CP) = (10/8) X (10/8) = 100/64 = 1.5625 => 56.25 % gain. 8. A trader allows a discount of 25% on his articles but wants to gain 50% gain. How many times the CP should be marked on the items? Soln: CP applied with profit = MP applied with discount = SP  1.5CP = 0.75MP (since 50% gain and 25% discount) => MP = 2CP. 9. By selling an item at a price a trader gains 40%. What is the profit / loss % if the item is sold at half the price? Soln: SP =1.4CP => (SP/2) = 0.7CP => 30% loss. 10. A trader gets a profit of 25% on an article. If he buys the article at 10% lesser price and sells it for Rs. 2 less, he still gets 25% profit. Find the actual CP of the article. Soln: 25% gain => SP = 1.25CP…..1. Now, CP is 10% less => 0.9CP and SP is Rs. 2 less => (SP-2). Still, profit is 25% => (SP-2)=1.25(0.9CP) , where SP = 1.25CP (From 1)  CP = Rs. 16. 11. A trader gets a discount of 20% from the dealer and marks it at 20% more price then the actual MP to the customer. Find his overall gain %. Soln: Let MP be the price on the item. Then, CP=0.8MP (20% discount) and SP = 1.2MP. So, gain => SP/CP = 1.2/0.8 = 1.5 => 50%. 12. A trader allows a discount of 20% to the customer after marking the item up by 25%. Find his gain/loss% if he is given a commission of 20% of the MP by the dealer. Soln: Trader‟s SP = 0.8 X (1.25MP) = MP (since 20% discount on 25% raised price) Trader‟s CP = 0.8 MP (20% commission) So, gain = SP/CP = MP/0.8MP = 1.25 => 25%. Exercise: 1. The profit obtained by selling an article for Rs.56 is the same as the loss obtained by selling it for Rs.42. What is the cost price of the article? 1) Rs.40 2) Rs.50 3) Rs.49 4) None of these 2. A dealer professes to sell his goods at cost price and uses an 880gm weight instead of a kg. What is his percentage of gain? 1) 13.13% 2) 13.33% 3) 13.36% 4) 13.63% 3. P sold an article for Rs.1,080 thereby losing 10% Q sold another article for Rs.1,800 at a loss of 10%. Who incurred a greater loss? 1) P 2) Q 3) Cannot say 4) Both have equal 4. Swapna bought 15 apples for Rs.10 and sold them at the rate of 12 apples for Rs.12. What is the percentage of profit made by her? 1) 100% 2) 150% 3) 125% 4) None of these 5. By selling some cloth at the cost price a merchant still gained 19 1 /21%. How much less cloth does he measure for a meter? 1) 15cm 2) 16cm 3) 20cm 4) None of these 6. 30% loss on cost price in what percent loss on selling price? 1) 30% 2) 20% 3) 15% 4) None of these 7. Arun purchased a house for Rs.75,000 and a site for Rs.15,000 respectively, if he sold the house for Rs.83,000 and the site for Rs.10,000, then find the resultant percentage of gain? 1) 3% 2) 3 1 /3% 3) 30% 4) 33 1 /3% 8. The manufacturing cost of a watch is Rs.180 and the transportation lost is Rs.500 for 100 watches. What will be the selling price if it is sold at 20% gains 1) Rs.222 2) Rs.216 3) Rs.221 4) Rs.220 9. A person, by selling an article at three-fourths of the list price incurs a loss of 20%. Find the profit percentage if he sells at the list price? 1) 25% 2) 6.66% 3) 11 1 /9% 4) None of these 10. A sells an article to B at a gain of 20%. B sells is to C at a gain of 25% and C in turn sells is to D at a loss of 33 1 /3%. If D paid Rs.1,000 for it, then what is the cost price of A. 1) Rs.1,000 2) Rs.2,000 3) Rs.3,000 4) Rs.4,000 11. Ajay had purchased a second hand scooter for 18,000 and spent Rs.1,800 for repairs. After one year he wanted to sell the scooter. At what price should he sell it to gain 11 1 /9%, if 9 1 /11% is to be deducted at the end of every year on account of deprecation? 1) Rs.18,000 2) Rs.19,800 3) Rs.20,000 4) Rs.22,500 12. After getting three equal successive discount percentages over a marked price of Rs.1,000 a customer has to pay 729 for an article. What is the rate of each of the successive discounts? 1) 10% 2) 20% 3) 30% 4) 40% 13. One-fifth of the cost price, one-seventh of the marked price and one-sixth of the selling price are all equal. What is the gain or loss to the trader? 1) 20%gain 2) 16 2 /3% loss 3) 14 2 /7%gain 4) 10%loss 14. Due to a slump in the market, A, while selling 12 apples to B, allows him to count them as 9. But due to an overnight demand A is forced to buy them back at the same rate as he sold and allows B to count 9 apples as 12. What is overall gain percentage of B 1) 77 7 /9% 2) 75% 3) 50% 4) 66 2 /3% 15. A trader offers to give two articles free for every 10 articles I purchase. I get a total of 10 articles free for my purchase and I sell them all at a rate such that I get back my investment from the sale of just 10 of the articles. What is my overall percentage of profit 1) 100% 2) 150% 3) 500% 4) 250% 16. A mechanic purchases a cooler for Rs.32,000 and incurs Rs.13,000 on installation and repairs. After one year he sold it for Rs.40,000. What is the profit or loss percentage, if the deprecation rate of the machine is 20% p.a? 1) 8 1 /3% 2) 12 1 /12% 3) 16 1 /4% 4) 11 1 /9% 17. Ramya bought a certain number of apples at 6 apples for Rs.10 and sold them at 4 apples for Rs.10. Find the number of apples she bought if total gain is Rs.60 1) 30 2) 31 3) 62 4) None of these 18. 5kg of ghee was bought by Venu for Rs.300. One kg becomes spoilt. He sells the remaining in such a way that on the whole he incurs a loss of 10%. At what price per kg does he sell the ghee? 1) Rs.46.25 2) Rs.45.70 3) Rs.46.60 4) Rs.67.50 19. A trader professes to lose 10% in selling 2kgs of rice. He uses 2 weighing stones, each of which is marked 1kg but weighs less. If the percentage of profit is 2 6 /7% and one of the two stones weighs only 800 gm, how much does the second stone weigh 1) 800gm 2) 850gm 3) 900gm 4) 950gm 20. A girl sold her pen for Rs.39 and got a percentage of profit numerically equal to the cost price. The cost price of that pen is.. 1) Rs.25 2) Rs.20 3) Rs.30 4) None of these 21. A person loses 10% on one investment but gains 20% on another. If the ratio of the investments is 3:4, what is the percentage of gain or loss on the two investments taken together? 1) 6 1 /8% 2) 7 1 /7% 3) 11 1 /9% 4) None of these 22. A trader professes to sell all articles at a loss of 25%, but sells three-fifth of them at again of 25% and the remaining at a loss of 25%. What is his overall percentage of gain or loss 1) 5% loss 2) 10% gain 3) 5% gain 4) No loss, No gain 23. A man sells an article at a profit of 20%. If he had bought it at 10% less and sold it for Rs.18 more, he would have gained 40%. Find the cost price of the article. 1) Rs.500 2) Rs.300 3) Rs.400 4) Rs.550 24. An article was sold at a profit of 20%. If both cost price and selling price are Rs.100 less each, then magnitude of the percentage of profit would have been 4 percentage points more than that in the first case. Then the cost price is 1) Rs.500 2) Rs.600 3) Rs.800 4) None of these 25. A man bought 2 articles at the same price and sells them together at 30% gain. Had he bought the first article at 20% less and the second article at 10% more and then sold them together for Rs.48 less, he would have gained 20% on the whole. What is the total cost of 2 articles? 1) Rs.200 2) Rs.300 3) Rs.400 4) Rs.500 26. A trader marks up the price of the product by 40%. If the discount is increased from 15% to 25%, his profit comes down by Rs.42. What is the cost price? 1) Rs.150 2) Rs.200 3) Rs.250 4) Rs.300 27. The catalogue price of an article is Rs.15,000. If the discount is increased from 15% to 20%, then profit falls from 27.5% to 20%. Find the cost price of the article? 1) Rs.12,000 2) Rs.10,000 3) Rs.12,250 4) Rs.12,750 28. The marked price of an article is Rs.300. If the selling price is 50% more than the amount of discount allowed, find the selling price 1) Rs.180 2) Rs.150 3) Rs.200 4) Rs.175 29. The cost of an apple is 33 1 /3% less than the cost of 1 mango. If a man sells four apples at the cost price of 5 mangoes, what is his percentage of profit? 1) 75% 2) 81% 3) 87.5% 4) 90% 30. A merchant professed to sell 20 articles at a loss which is equals to the cost price of 2 articles but sold 18 articles at the cost price of 20 articles. What is the gain percent? 1) 19 1 /11% 2) 10% 3) 11 1 /9% 4) 0% 31. The percentage by which the marked price exceeds the cost price of an article and the percentage of discount allowed on the article are in the ratio of 3:2. If it is sold at the cost price, what is the percentage of discount allowed? 1) 20% 2) 25% 3) 33 1 /3% 4) 50% 32. The purchase prices of three articles are in the ratio 3:4:5 the first one is sold at a profit of 10% and the second at a loss of 7.5%. If the overall percentage of profit or loss of the first two articles is the same as the percentage profit or loss of all the articles taken together, what is the percentage of profit or loss in the case of the third article? 1) 8.75 2) 1.25 3) 0 4) Can‟t be determined. 33. A dishonest oil merchant claims that he gets a profit of only 5% but he gives only one litre of oil instead of 1kg. If 1.25 litre of oil weighs 1kg what is his overall percentage of profit? 1) 31.25% 2) 25% 3) 26% 4) None of these 34. A fruit vendor sells mangoes and bananas and gets equal revenue from each. He gets a profit of 20% on each mango and a profit of 25% on each banana. If the ratio of the number of bananas sold to the number of mangoes sold is 4:1, what is the ratio of the cost price of a banana to that of a mango? 1) 1:5 2) 6:25 3) 2:9 4) Can‟t be determined. 35. A trader buys 150 pens for Rs.1,000 and he marks each of them at Rs.10. He gives a discount of 20% on each pen and he gives 1 pen free on bulk purchases of 9 pens. What is his minimum possible overall percentage of profit? 1) 8% 2) 10% 3) 20% 4) 5% 36. A trader gives a discount on an article such that the profit as a percent of marked price is the same as the discount as a percent of cost price. What is the ratio of the actual profit percentage to the actual discount percentage an the article? 1) 4:1 2) 2:1 3) 1:2 4) Can‟t be determined. 37. The cost price of a computer is Rs.1,000 less then the selling price of a television and the selling price of the computer is 30% more than the cost price of the television. If the selling price of the computer is 4% more than the selling price of the television, what is the percentage of profit on selling the television? 1) 20% 2) 25% 3) 16 2 /3% 4) Can‟t be determined. 38. The marked prices of two articles are in the ratio of 1:2, their discount percentages are also in the ratio of 1:2 and the profit they get is also in the ratio of 1:2. What is the ratio of their cost price? 1) 1:2 2) 5:8 3) 2:5 4) Can‟t be determined. 39. A trader purchases two watches. He marks the first one up by Rs.200 over the cost price and gives a discount of 20% on it. The second one he marks up by 50% and gives a discount of Rs.160. If he gains 15% on both the watches put together and 8% on the first alone, what is the percentage of profit on the second watch? 1) 21% 2) 22% 3) 18.5% 4) Can‟t be determined. 40. Javed sells 2,000 mangoes in a week. He recovers his total cost by selling first 1,200 Mangoes. He sells the next 300 Mangoes for a loss of 20% and he sells the last 500 Mangoes for a loss of 40%. What is his overall percentage of profit? 1) 45% 2) 35% 3) 27% 4) 12.5% Solutions: 1. Profit at a price = loss at other price => CP must be numerically between those prices  CP = (56+42)/2 = Rs. 49. 2. Gain % = 1000/880 => 1. 1363 => 13.63% 3. For P, SP=1080 and loss=10% => CP = 1080/0.9 =1200 => loss = 1200-1080 = 120. For Q, SP=1800 and loss=10% => CP = 1800/0.9 = 2000 => loss = 2000-1800 = 200. 4. She got profit => profit % = 15/10 X 12/12 = 1.5 => 50%. 5. Profit % = 19 1/21 => 1.19047. Let he measure x cm for 100 cm. Then, 100/x = 1.19047 => x=84 cm So he measures 16 cm less for every meter. 6. Loss = 30% on CP i.e., 0.3CP => SP = 0.7CP Loss % on SP = loss/SP X 100 = 0.3CP/0.7CP X 100 = 42.85%. 7. Total CP = 90000 & total SP = 93000 => gain = SP/CP = 93000/90000 =1.0333 = 3.33% 8. Total cost of a watch = 180 + (500/100) = 185. Gain = 20% => SP = 1.2CP = 1.2 X 185 = 222 9. 0.75 MP = 0.8 CP (since 20% loss) So, MP = 1.0666CP => 6.66% gain 10. 1.2 X 1.25 X 0.6666 X CP = 1000 => CP = 1000 (profits of 20%, 25% & loss of 33.33%) 11. Total CP=18000+1800 = 19800. Depreciation = 9.09% and gain = 11.11% => SP = (0.9091)X(1.1111)X19800 = 20000. 12. Let „f‟ be the factor of discount => 1000 X f X f X f = 729 => f = 0.9 => 10% decrease. 13. CP/5 = SP/6 => SP/CP=1.2 => 20% gain. 14. In two transactions B is gaining => SP > CP for B in two transactions. So, gain% = 12/9 X 12/9 = 1.7777 => 77.77%. 15. 2 articles free for every 10 articles bought. So 10 free articles => 50 articles bought. Money of 60 articles (10 articles free) is obtained by selling only 10 articles. So SP of 10 articles = CP of 60 articles => SP/CP = 6 => 500% gain. 16. Total CP = 45000. Depreciation = 20% =>new CP = 0.8 X 45000 = 36000. SP = 40000 => SP/CP = 40/36 = 1.1111 => 11.11% gain 17. CP => 6 apples for Rs. 10. SP => 4 apples for Rs. 10 => 6 apples for Rs. 15 So, for 6 apples, gain is Rs.5 => Rs. 60 gain requires 72 apples. 18. CP of 5 kg ghee = 300. Loss = 10% => SP = 0.9 CP = 270. For Rs. 270, 4 kg are sold  SP for 1 kg = 270/4 =Rs. 67.5 19. Let w be the weight of the second stone. Now, 0.9 X (1000/800) X (1000/w) = 1.0285 (since profit is 2.85%)  w = 900 gm (nearly) 20. SP = 39. Profit % = CP. CP + (CP% of CP) = SP => CP = 30/-. 21. ratio = 3:4 => investments are 3/7 and 4/7. Overall loss/gain % = (3/7)(-10) + (4/7)(20) = 50/7 = 7 1/7 %. 22. 3/5 th are sold at gain of 25% and 2/5 th are sold at loss of 25%. First, (3/5 X 25 – 2/5 X 25) = 5% gain. 23. 20% gain => SP = 1.2 CP. New CP = 0.9 CP and New SP = SP + 18 => 1.2CP+18. 40% gain => new SP = 1.4 X new CP => (1.2CP+18) = 1.4(0.9CP) => CP = 300. 24. 20% gain => SP = 1.2CP. New CP = CP – 100 and new SP = SP -100 & 24% gain => new SP=1.4 X new CP  CP – 100 = 1.4 ( 1.2CP – 100) => CP = 600. 25. Let each article costs x => Total CP = 2x and SP = 1.3 X 2x = 2.6x. New total CP = 0.8x + 1.1x = 1.9x, New SP = SP – 48 = 2.6x – 48 and gain = 20% So, 2.6x – 48 = 1.2 X 1.9x => 2x = 300. 26. MP = 1.4CP. Also 10% change is discount => Rs. 42 gain => 10% of 1.4CP = 42  CP = 300. 27. MP = 15000. 5% change in discount i.e., 5% of MP = 7.5 % of CP (profit change) So, CP = 5/7.5 X MP = 10000. 28. MP = 300. SP = 1.5 X discount. Now, SP = MP – discount => SP = 180. 29. CP of apple = 0.6666 X CP of mango…….1 Man sold 4 apples for CP of 5 mangoes => his CP = 4 X CP of apple And his SP = 5 X CP of mango. So, SP/CP = (5XCP of mango)/(4XCP of apple) = 1.875 => 87.5%. 30. SP of 18 articles = CP of 20 articles => SP/CP = 20/18 = 1.1111 => 11.11% gain 31. If CP is raised by 3x %, the discount should be 2x %. Also, after discount SP=CP => increase of 3x% X decrease of 2x%. From inspection, 33.33% discount => 50% increase (since 3:2) and 1.5 X 0.6666 = 1. 32. CP of first two articles are in ration of 3:4. So for 2 articles, gain/loss % = (3/7)X10 – (4/7)X7.5 = 0. So, overall profit/loss% = 0 => (3/12)X10 – (4/12)X7.5 + (5/12)x = 0 => x=0%. 33. Overall profit = 1.05 X (1.25/1) = 1.3125 => 31.25% gain 34. For mango, SP = 1.2 CPm and for banana SP = 1.25 CPb. Revenue from mango = revenue from banana => 1.2 CPm = 4 X 1.25 CPb (since they are sold in ratio of 1:4) So, CPb/CPm = 6:25. 35. 150 pens for Rs.1000 => total CP = 1000. 1 pen free for every 9 pens => he can sell 135 pens (for least possible profit) SP of each pen = 10 and discount = 20% => SP = 8. Total SP = 135 X 8 = 1080 => SP/CP = 1080/1000 = 1.08 => 8%. 36. Profit% of MP = discount% of CP => profit%/discount% cant be determined without the values of MP and CP. 37. CP computer = SP TV – 1000 and SP computer = 1.3 X CP TV. SP Computer = 1.04 SP TV => 1.3 CP TV = 1.04 SP TV => SP/CP = 1.25 => 25% gain. 38. Without the knowledge of atleast on of the prices the ratio of CP‟s cant be determined. 39. MP1 = CP1 + 200 and discount = 20%.Also MP2 = 1.5CP2 and discount = Rs. 160. Also SP1/CP1 = 8% gain. With this information it can‟t be said what is the profit % on 2 nd watch. 40. 300 sold at loss of 20% and 500 old at a loss of 40% => loss% = (3/8)X20 + (5/8)X40 = 32.5 => loss factor = 0.675 Already he got a gain by SP of 1200 = CP of 2000. So overall profit % = (2000/1200) X 0.675 = 1.125 => 12.5% gain. Averages and Ages What is average? The concept of average is equal distribution of the overall value among all the things or persons present there. So the formula for finding the average is as follows: Average, A = Total of all things, T / Number of things, N Therefore, Total, T = AN If any person joins a group with more value than the average of the group then the overall average increases. This is because the value in excess than the average will also be distributed equally among all the members. Similarly when any value less than the average joins the group the overall group decreases as the deficit is divided equally among all the people present there. Example: Consider three people A, B and C with total of Rs. 30/-. Their average becomes Rs. 10/- for each. If another person D joins them with Rs. 50/- then he has Rs. 40/- more than actual average of Rs. 10/-. So this Rs. 40/- will get distributed among those four and each gets Rs. 10/-. Thus the average becomes Rs. 20/- each. Example: The average age of a class of 30 students is 12. If the teacher is also included the average becomes 13 years. Find the teacher‟s age. Soln: When the teacher is included there are totally 31 members in the class and the average is increased by 1 year. This means that everyone got 1 extra year after distributing the extra years of the teacher. So extra years of the teacher are as follow: 31x1=31 years. Age of the teacher = actual avg + extra years = 12 + 31 = 43 years. Exercise: 1. The average of 13 papers is 40. The average of the first 7 papers is 42 and of the last seven papers is 35. Find the marks obtained in the 7 th paper? (A) 23 (B) 38 (C) 19 (D) None of these 2. The average age of the Indian cricket team playing the Nagpur test is 30. The average age of 5 of the players is 27 and that of another set of 5 players, totally different from the first five, is 29. If it is the captain who was not included in either of these two groups, then find the age of the captain. (A) 75 (B) 55 (C) 50 (D) Cannot be determined 3. A bus goes to Ranchi from Patna at the rate of 60 km per hour. Another bus leaves Ranchi for Patna at the same times as the first bus at the rate of 70 km per hour. Find the average speed for the journeys of the two buses combined if it is known that the distance from Ranchi to Patna is 420 kilometers. (A) 64.615 kmph (B) 64.5 kmph (C) 63.823 kmph (D) 64.82 kmph 4. A train travels 8 km in the first quarter of an hour, 6 km in the second quarter and 40 km in the third quarter. Find the average speed of the train per hour over the entire journey. (A) 72 km/h (B) 18 km/h (C) 77.33 km/h (D) 78.5 km/h 5. The average weight of 6 men is 68.5 kg. If I is known that Ram and Tram weigh 60 kg each, find the average weight of the others. (A) 72.75 kg (B) 75 kg (C) 78 kg (D) None of these 6. The average score of a class of 40 students is 52. What will be the average score of the rest of the students if the average score of 10 of the students is 61. (A) 50 (B) 47 (C) 48 (D) 49 7. The average age of 80 students of IIM, Bangalore of the 1995 batch is 22 years. What will be the new average if we include the 20 faculty members whose average age is 37 years? (A) 32 years (B) 24 years (C) 25 years (D) None of these 8. Out of the three numbers, the first is twice the second and three times the third. The average of the three numbers is 88. The smallest number is (A) 72 (B) 36 (C) 42 (D) 48 9. The sum of three numbers is 98. If the ratio between the first and second is 2 : 3 and that between the second and the third is 5 : 8, then the second number is (A) 30 (B) 20 (C) 58 (D) 48 10. The average height of 30 girls out of a class of 40 is 160 cm and that of the remaining girls is 156 cm. The average height of the whole class is (A) 158 cm (B) 158.5 cm (C) 159 cm (D) 157 cm 11. The average weight of 6 persons is increased by 2.5 kg when one of them whose weight is 50 kg is replaced by a new man. The weight of the new man is (A) i 65 kg (B) 75 kg (C) 76 kg (D) 60 kg 12. The average age of A, B C and D five years ago was 45 years. By including X, the present average age of all the five is 49 years. The present age of X is (A) 64 years (B) 48 years (C) 45 years (D) 40 years 11 13. The average salary of 20 workers in an office is Rs. 1900 per month. If the manager‟s salary is added, the average salary becomes Rs. 2000 per month. What is the manager‟s annual salary? (A) Rs. 24, 000 (B) Rs. 25,200 (C) Rs. 45,600 (D) None of these 14. The average weight of a class of 40 students is 40 kg. If the weight of the teacher be included, the average weight increases by 500 gm. The weight of the teacher is (A) 40.5 kg (B) 60 kg (C) 62 kg (D) 60.5 kg 15. In a Infosys test, a student scores 2 marks for every correct answer and loses 0.5 marks for every wrong answer. A student attempts all the 100 questions and scores 120 marks. The number of questions he answered correctly was (A) 50 (B) 45 (C) 60 (D) 68 16. The average of the first ten natural numbers is (A) 5 (B) 5.5 (C) 6.5 (D) 6 17. The average of the first ten whole numbers is (A) 4.5 (B) 5 (C) 5.5 (D) 4 18. The average of the first ten even numbers is (A) 18 (B) 22 (C) 9 (D) 11 19. The average weight of a class of 30 students is 40 kg. If, however, the weight of the teacher is included, the average become 41 kg. The weight of the teacher is (A) 31 kg (B) 62 kg (C) 71 kg (D) 70 kg 20. 30 oranges and 75 apples were purchased for Rs. 510. If the price per apple was Rs. 2, then the average price of oranges was (A) Rs. 12 (B) Rs. 14 (C) Rs. 10 (D) Rs. 15 21. A batsman made an average of 40 runs in 4 innings, but in the fifth inning, he was out on zero. What is the average after fifth innings? (A) 32 (B) 22 (C) 38 (D) 49 22. The average weight of a school of 40 teachers is 80 kg. If, however, the weight of the principle be included, the average decreases by 1 kg. What is the weight of the principal? (A) 109 kg (B) 29 kg (C) 39 kg (D) None of these 23. The average age of Ram and Shyam is 20 years. Their average age 5 years hence will be (A) 25 years (B) 22 years (C) 21 years (D) 20 years 24. The average of 20 results is 30 and that of 30 more results is 20. For all the results taken together, the average is (A) 25 (B) 50 (C) 12 (D) 24 25. The average of 5 consecutive numbers is 18. The highest of these numbers will be (A) 24 (B) 18 (C) 20 (D) 22 26. Three years ago, the average age of a family of 5 members was 17 years. A baby having been born, the average of the family is the same today. What is the age of the baby? (A) 1 years (B) 2 years (C) 6 months (D) 9 months 27. Varun average daily expenditure is Rs. 10 during May, Rs. 14 during June and Rs. 15 during July. His approximate daily expenditure for the 3 months is (A) Rs. 13 approximately (B) Rs. 12 (C) Rs. 12 approximately (D) Rs. 10 28. A ship sails out to a mark at the rate of 15 km per hour and sails back at the rate of 20 km/h. What is its average rate of sailing? (A) 16.85 km (B) 17.14 km (C) 17.85 km (D) 18 km 29. The average temperature on Monday, Tuesday and Wednesday was 41 0 C and on Tuesday, Wednesday and Thursday it was 40 0 C. If on Thursday it was exactly 39 0 C, then on Monday, the temperature was (A) 42 0 C (B) 46 0 C (C) 23 0 C (D) 26 0 C 30. The average of 20 results is 30 out of which the first 10 results are having an average of 10. The average of the rest 10 results is (A) 50 (B) 40 (C) 20 (D) 25 31. ten years ago, Mohan was thrice as old as Ram was but 10 years hence, he will be only twice as old. Find Mohan‟s present age. a) 60 years b) 80 years c) 70 years d) 76 years 32. The ages of Ram and Shyam differ by 16 years. Six years ago, Mohan‟s age was thrice as that of Ram‟s, find their present ages. a) 14 years, 30 years b) 12 years, 28 years c) 16 years, 34 years d) 18 years, 38 years 33. 15 years hence, Rohit will be just four times as old as he was 15 years ago. How old is Rohit at present? a) 20 b) 25 c) 30 d) 35 34. A man‟s age is 125% of what it was 10 years ago, but 83 1/3 % of what it will be after ten 10 years. What is his present age? a) 45 years b) 50 years c) 55 years d) 60 years 35. If twice the son‟s age in years be added to the father‟s age, the sum is 70 and if twice the father‟s age is added to the son‟s age, the sum is 95. Father‟s age is a) 40 years b) 35 years c) 42 years d) 45years 36. Three years ago, the average age of a family of 5 members was 17. A baby having been born the average age of the family is the same today? What is the age of the child? a) 3 years b) 5 years c) 2years d) 1 year 37. The ratio of A‟s and B‟s ages is 4:5 If the difference between the present age of A and the age of B 5 years hence is 3, then what is the total of present ages of A and B? a) 68 years b) 72 years c) 76 years d) 64 years 38. The ages of A and B are in the ratio of 6:5 and sum of their ages is 44 years. The ratio of their ages after 8 years will be a) 4 : 5 b) 3 : 4 c) 3 : 7 d) 8 : 7 39. 5 years ago, the combined age of my mother and mine was 40 years. Now, the ratio of our age is 4:1. How old is my mother? (A) 10 (B) 40 (C) 60 (D) 20 (E) 50 40. Honey was twice as old as Vani 10 years ago. How old is Vani today if Honey will be 40 years old 10 years hence? a) 20 b) 25 c) 15 d) 35 e) 30 41. One year ago, a mother was 4 times older to her son. After 6 years, her age become more than double her son‟s age by 5 years. The present ratio of their age will be? a.13 : 12 b.11 : 13 c.3 : 1 d.25 : 7 e.4 : 3 42. Vandana‟s mother is twice as old as her brother. She is 5 years younger to her brother but 3 years older to her sister. If her sister is 12 years of age, how old is her mother? a.30 b.35 c.45 d.40 e.50 43. Sonu is 4 years younger Manu while Dolly is four years younger to Sumit but 1/5 times as old as Sonu. If Sumit is eight years old, how many times as old is Manu as Dolly? a.3 b.½ c.2 d.1 e.¼ 44. Our mother is 3 times as old as my brother and I am 1/3 rd times older than my brother. If 4 years ago I was as old as my brother today, what is the age of my mother. a.40 b.36 c.44 d.42 e.48 45. Ruchi‟s age was double that of Niti 2 years ago. If Ruchi was 2 years older to Niti then, try to guess how old she is today. a.6 b.4 c.8 d.2 e.20 46. If we add the age of three brothers Sunil, Sanjay and Sonu, then it becomes 60 years today. If 6 years ago the Sonu was of half the age of Sanjay and 1/3 rd to the age of Sunil, then find out the present age of Sanjay. a.14 b.15 c.16 d.18 e.24 47. Sonu‟s age is 2/3 rd of Manu‟s. After 5 years Sonu will be 45 years old. Manu‟s present age is a.55 b.56 c.58 d.60 e.64 48. Ratio of Sonu‟s age to Manu‟s is equal to 4:3. If Sonu will be 26 years old after 6 years, the present age of Manu is a.11 b. 15 c.14 d.17 e.13 49. Binny is born on 1 st October. He is younger to Sunny by one week and two days. If on 1 st October it was a Saturday, then Sunny‟s birthday will come on which day this year? (A) Wednesday (B) Thursday (C) Monday (D) Saturday (E) Sunday 50. Binny is half as old as Sunny. Chinky is twice old as Sunny. How many times is Chinky as old as Binny? (A) 6 (B) 4 (C) 8 (D) 3 (E) 2 Ratios and Proportions What is a ratio? A ratio is a representation of distribution of a value present among the persons present and is shown as follows: If a total is divided among A, B and C such that A got 4 parts, B got 5 parts and C got 6 parts then it is represented in ratio as A:B:C = 4:5:6. So, 4:5:6 means that the total value is divided into 4+5+6 = 15 equal parts and then distributed as per the ratio. Example 1: Divide Rs. 580 between A and B in the ratio of 14:15. Soln: A:B = 14:15 => 580 is divided into 29 equal parts => each part = Rs. 20. So A‟s share = 14 parts = 14 x 20 = Rs. 280 B‟s share = 15 parts = Rs. 300. Example 2: If A:B = 2:3 and B:C = 4:5 then find A:B:C. Soln: To combine two ratios the proportions common for them shall be in equal parts. Here the common proportion is B for the given ratios. Making B equal in both ratios they become 8:12 and 12:15 => A:B:C = 8:12:15. Example 3: Three numbers are in the ratio of 3: 4 : 8 and the sum of these numbers is 975. Find the three numbers. Soln: Let the numbers be 3x, 4x and 8x. Then their sum = 3x+4x+8x = 15x = 975 => x = 65. So the numbers are 3x = 195, 4x = 260 and 8x = 520. Example 4: Two numbers are in the ratio of 4 : 5. If the difference between these numbers is 24, then find the numbers. Soln: Let the numbers be 4x and 5x. Their difference = 5x – 4x = x = 24 (given). So the numbers are 4x = 96 and 5x = 120. Example 5: Given two numbers are in the ratio of 3 : 4. If 8 is added to each of them, their ratio is changed to 5 : 6. Find two numbers. Soln: Let the numbers be a and b. A:B = 3:4 => A / B = 3 / 4. Also, (A+8) / (B+8) = 5 / 6. Solving we get, A=12 and B = 16 Example 6: A garrison has provisions for 120 soldiers for 240 days. After 180 days 60 more soldiers will join the group. For how many more days will the provisions last? Soln: Actually after 180 days, If 120 members are there provisions come for 60 more days (since total 240 days) But now 180 members are there. So number of days = (120/180) X 60 = 40 days. Example 7: If 24 men working for 12 hrs a day can do a work in 16 days, in how many days can 8 men working 6 hrs a day do it? Soln: 24 men – 12 hrs – 16 days 8 men – 6 hrs - ? days (n) n =16 X (12 / 6) X (24 / 8) ( since no of hrs reduced no of days has to increase and no of men reduced also increases no of days i.e., inverse proportional) => n = 96 days. EXERCISE 1. Divide Rs.1870 into three parts in such a way that half of the first part, one-third of the second part and one-sixth of the third part are equal. 1. 241, 343, 245 2. 400, 800, 670 3. 470, 640, 1160 4. None 2. Divide Rs.500 among A, B, C and D so that A and B together get thrice as much as C and D together, B gets four times of what C gets and C gets 1.5 times as much as D. Now the amount C gets? 1. 300 2. 75 3. 125 4. None 3. If 4 examiners can examine a certain number of answer books in 8 days by working 5 hours a day, for how many hours a day would 2 examiners have to work in order to examine twice the number of answer books in 20 days. 1. 6 2. 1/2 3. 8 4. 9 4. In a mixture of 40 liters, the ratio of milk and water is 4:1. How much water much be added to this mixture so that the ratio of milk and water becomes 2:3 1. 20 litres 2. 32 litres 3. 40 litres 4. 30 litres 5. If three numbers are in the ratio of 1:2:3 and half the sum is 18, then the ratio of squares of the numbers is: 1. 6:12:13 2. 1:2:4 3. 36:144:324 4. None 6. The ratio between two numbers is 3:4 and their LCM is 180. the first number is: 1. 60 2. 45 3. 15 4. 20 7. A and B are tow alloys of argentums and brass prepared by mixing metals in proportions 7:2 and 7:11 respectively. If equal quantities of the two alloys are melted to form a third alloy C, the proportion of argentums and brass in C will be: 1. 5:9 2. 5:7 3. 7:5 4. 9:5 8. If 30 men working 7 hours a day can do a piece of work in 18 days, in how many days will 21 men working 8 hours a day do the same work? 1. 24 days 2. 22.5 days 3. 30 days 4. 45 days 9. The incomes of A and B are in the ratio 3:2 and their expenditure are in the ratio 5:3. If each saves Rs.1000, then, A‟s income is 1. 3000/- 2. 4000/- 3. 6000/- 4. 9000/- 10. If the ratio of sines of angles of a triangle is 1:1:\2, then the ratio of square of the greatest side to sum of the squares of other two sides is 1. 3:4 2. 2:1 3. 1:1 4. Can‟t say 11. Divide Rs.680 among A, B and C such that A gets 2/3 of what B gets and B gets 1/4 th of what C gets. Now the share of C is? 1. 480/- 2. 300/- 3. 420/- 4. None 12. A, B, C enter into a partnership. A contributes one-third of the whole capital while B contributes as much as A and C together contribute. If the profit at the end of the year is Rs.84, 000, how much would each received? 1. 24,000, 20,000, 40,000 2. 28,000, 42,000, 14,000 3. 28,000, 42,000, 10,000 4. 28,000, 14,000, 42,000 13. The students in three batches at AMS Careers are in the ratio 2:3:5. If 20 students are increased in each batch, the ratio changes to 4:5:7. the total number of students in the three batches before the increases were 1. 10 2. 90 3. 100 4. 150 14. The speeds of three cars are in the ratio 2:3:4. The ratio between the times taken by these cars to travel the same distance is 1. 2:3:4 2. 4:3:2 3. 4:3:6 4. 6:4:3 15. Rs.2250 is divided among three friends Amar, Bijoy and Chandra in such a way that 1/6 th of Amar‟s share, 1/4 th of Bijoy‟s share and 2/5 th of Chandra‟s share are equal. Find Amar‟s share. 1. 720/- 2.1080/- 3. 450/- 4. 1240/- 16. After an increment of 7 in both the numerator and denominator, a fraction changes to ¾. Find the original fraction. 1. 5/12 2. 7/9 3. 2/5 4. 3/8 17. The difference between two positive numbers is 10 and the ratio between them is 5:3. Find the product of the two numbers. 1. 375 2. 175 3. 275 4. 125 18. If 30 oxen can plough 1/7 th of a field in 2 days, how many days will 18 oxen take to do the remaining work? 1. 30 days 2. 20 days 3. 15 days 4. 18 days 19. A cat takes 5 leaps for every 4 leaps of a dog, but 3 leaps of the dog are equal to 4 leaps of the cat. What is the ratio of the speed of the cat to that of the dog? 1. 11:15 2. 15:11 3. 16:15 4. 15:16 20. The present ratio of ages of A and B is 4:5. 18 years ago, this ratio was 11:16. Find the sum total of their present ages. 1. 90 years 2. 105 years 3. 110 years 4. 80 years 21. Three men rent a farm for Rs.7000 per annum. A puts 110 cows in the farm for 3 months, B puts 110 cows for 6 months and C puts 440 cows for 3 months. What percentage of the total expenditure should A pay? 1. 20% 2. 14.28% 3. 16.66% 4. 11.01% 22. 10 students can do a job in 8 days, but on the starting day, two of them informed that they are not coming. By what fraction will the number of day required for doing the whole work get increased? 1. 4/5 2. 3/8 3. 3/4 4. 1/4 23. A dishonest milkman mixed 1 liter of water for every 3 liters of milk and thus make up 36 liters of milk. If he now adds 15 liters of milk to the mixture, find the ratio of milk and water in the new mixture. 1. 12:5 2. 14:3 3. 7:2 4. 9:4 24. Rs.3000 is distributed among A, B and C such that A gets 2/3 rd of what B and C together get and C gets ½ of what A and B together get. Find C‟s share 1. 750/- 2. 1000/- 3. 800/- 4. 1200/- 25. If the ratio of the ages of Maya and Chhaya is 6:5 at present, and fifteen years from now, the ratio will get changed to 9:8, then find Maya‟s present age. 1. 24 years 2. 30 years 3. 18 years 4. 33 years 26. If Rs.58 is divided among 150 children such that each girl and each boy gets 25 p and 50 p respectively. Then how many girls are there? 1. 52 2. 54 3. 68 4. 62 5 27. If 391 bananas were distributed among three monkeys in the ratio ½:2/3:3/4, how many bananas did the first monkey get? 1. 102 2. 108 3. 112 4. 104 28. A mixture contains milk and water in the ratio 5:1. On adding 5 liters of water, the ratio of milk to water becomes 5:2. the quantity of milk in the mixture is: 1. 16 litres 2. 25 litres 3. 32.5 litres 4. 22.75 litres 29. A beggar had ten paise, twenty paise and one rupee coins in the ratio 10:17:7 respectively at the end of day. If that day he earned a total of Rs.57, how many twenty paise coins did he have? 1. 114 2. 171 3. 95 4. 85 30. Vijay has coins of the denomination of Re.1, 50 p and 25 p in the ratio of 12:10:7. The total worth of the coins he has is Rs.75. Find the number of 25 p coins that Vijay has 1. 48 2. 72 3. 60 4. None Comprehensive Test – I (Chapters 1 – 4) 1. 25% of a number subtracted form itself gives 120. The number is a. 125 b. 135 c. 140 d. 160 2. If x is 80 % of y, then what % of x is y? a. 20 b. 90 c. 120 d. 125 3. A man spends 30% of his income on rent, 20% on food, 20% on miscellaneous items and saves Rs. 1050. His total salary is a. 3740 b. 3750 c. 3500 d. 3510 4. A‟s income is 25% less than that of B. By what % is B‟s income more than that of A? a. 75 b. 25 c. 33.33 d. 66 5. In an election 10 % of the votes were invalid. 40% of the votes were for A and the rest to B. B won with a majority of 243 votes, the total number of votes polled is a. 1250 b. 1350 c. 1155 d. None 6. In a class there were 80 boys and 70 girls. If 25% of boys and 30% of girls passed in an exam find the fail % of the class. a. 27 b. 72.66 c. 27.5 d. 72.5 7. A person‟s salary was increased by 25% in one year. In the next year it increased by 50%. What is the % increase in the salary? a. 87.5 b. 75 c. 37.5 d. None 8. A man scores 42.5% and failed by 5 marks in an exam. If he scored 52.5% he would pass by 15 marks. Find the minimum marks to pass. a. 200 b. 100 c. 90 d. 80 9. A trader bought some oranges. 4% of them were spoiled, 10% of remaining rotten and he sold 90 % of the good ones. If 540 oranges were left the number of oranges he bought was a. 6000 b. 6250 c. 6500 d. 6750 10. The population of a city was 9000. If the male population increased by 15% and the female population increased by 16% the total population increased by 1390. The number of men were a. 4000 b. 4250 c. 4750 d. 5000 11. By selling an article for Rs. 1000 the person loses 20%. At what price it has to be sold to gain 30%? a. 1500 b. 1625 c. 1675 d. 1680 12. SP of 4 articles is equal to CP of 3 articles. The % of gain or loss is a. 25 b. 50 c. 75 d. 80 13. A man bought 60 apples for Rs. 100 and 40 other apples for Rs. 50. How many apples has he to sell for Rs. 120 to gain 25%? a. 10 b. 64 c. 88 d. 90 14. X sold 3/5 th of his goods at 50 % gain. If he sells the remaining at CP find the overall profit %. a. 10 b. 25 c. 30 d. 40 15. A radio was sold for 18% profit. If it were sold for Rs. 30 more a profit of 20% would have gained. Find the CP. a. 1000 b. 1200 c. 1500 d. 1800 16. A shopkeeper had calculated profit % on SP and announced it as 40%. His actual profit % is a. 60 b. 66.5 c. 66.66 d. 66.33 17. The price of an article increased by 20% and later decreased by 20%. If present value is Rs. 480 the original price is a. 480 b. 490 c. 500 d. 520 18. Due to increase in price of eggs by 20% two eggs less were available for Rs. 20. The present price of eggs per dozen is a. 24 b. 20 c. 25 d. 18 19. After two successive discounts on list price of Rs. 5000 an article was sold for Rs. 3600. If the first discount was 20% the second discount is a. 5% b. 10% c. 15% d. 20% 20. Kiran bought a radio on 15% discount. If he got a discount of 18% he would save Rs. 63. The SP is a. 1785 b. 1722 c. 1745 d. 1740 21. A shopkeeper buys toffees at rate of 40 for Rs. 5 and sells at rate of 50 for Rs. 10. The profit % is a. 60 b. 50 c. 25 d. 30 22. A man sells his articles at 5% above CP. If he had bought them for 5% lesser price and sold them for Rs. 2 less, he wiuld have gained 10%. The CP of the articles is a. 500 b. 360 c. 425 d. 400 23. The marked price of a table is Rs. 1200, 20% above CP. It is sold at a discount of 10%. The profit % is a. 10 b. 8 c. 7.5 d. 6 24. The average monthly salary of 20 employes is Rs. 1500. If the manager‟s salary is added the average becomes Rs. 1600. The manager‟s salary is a. 3500 b. 3600 c. 3800 d. 3900 25. Of the three numbers the first is twice the second and half of the third. Their average is 56. Find the smallest number. 26. a. 20 27. 22 28. 24 29. 26 26. A batsman scores 64 runs in his 16 th innings and increases his average by 3. His average after 16 th innings is a. 18 b. 17 c. 19 d. 16 27. 12 yrs ago, the average age of a husband and his wife was 20yrs. The average age is same today, they having two children. What is the present age of the youngest child if children differ in age by 2yrs? a. 6 b. 5 c. 8 d. 7 28. The average age of jawans in army of 40 is reduced by 1yr when 10 men with average 20 yrs are replaced by 10 new men. Find the average age of the new men? a. 14 b. 15 c. 16 d. 17 29. The average weight of 8men in increased by 2 kg when one of them with weight of 50kg is replaced by a new man. The weight of the new man is a. 60 b. 65 c. 63 d. 66 30. The average age of husband, wife and their child 3yrs ago was 27yrs and that of the wife and the child 5yrs ago was 20yrs. The present age of the husband is a. 40 b. 30 c. 33 d. 43 Time and Distance Speed: We have the relation between speed, time and distance as follows: Speed = distance / time. So the distance covered in unit time is called speed. This forms the basis for Time and Distance. It can be re-written as Distance = Speed X Time or Time = Distance / Speed. Units of Speed: The units of speed are kmph (km per hour) or m / s. 1 kmph = 5 / 18 m / s 1 m / s = 18 / 5 kmph Average Speed: When the travel comprises of various speeds then the concept of average speed is to be applied. Average Speed = Total distance covered / Total time of travel Note: In the total time above, the time of rest is not considered. Example 1: If a car travels along four sides of a square at 100 kmph, 200 kmph, 300 kmph and 400 kmph find its average speed. Soln: Average Speed = Total distance / Total time. Let each side of square be x km. Then the total distance = 4x km. The total time is sum of individual times taken to cover each side. To cover x km at 100 kmph, time = x / 100. For the second side time = x / 200. Using this we can write average speed = 4x / (x/100 + x/200 + x/300 + x/400) = 192 kmph. Example 2: A man if travels at 5/6 th of his actual speed takes 10 min more to travel a distance. Find his usual time. Soln: Let s be the actual speed and t be the actual time of the man. Now the speed is (5/6)s and time is (t+10) min. But the distance remains the same. So distance 1 = distance 2 => s X t = (5/6)s X (t+10) => t = 50 min. Example 3: If a person walks at 30 kmph he is 10 min late to his office. If he travels at 40 kmph then he reaches to his office 5 min early. Find the distance to his office. Soln: Let the distance to his office be d. The difference between the two timings is given as 15 min = 1 / 4 hr. Now if d km are covered at 30 kmph then time = d/30. Similarly second time = d/40. So, d/30 – d/40 = 1 / 4 => d = 30 km. Note: When two objects move with speeds s1 and s2 a. In opposite directions their combined speed = s1 + s2 b. In same direction their combined speed = s1 ~ s2. Example 4: Two people start moving from the same point at the same time at 30 kmph and 40 kmph in opposite directions. Find the distance between them after 3 hrs. Soln: Speed = 30 + 40 = 70 kmph (since in opposite directions) Time = 3 hrs So distance = speed X time = 70 X 3 = 210 km. Example 5: A starts from X to Y at 6 am at 40 kmph and at the same time B starts from Y to X at 50 kmph. When will they meet if X and Y are 360 km apart? Soln: Distance = 360 km Speed = 40 + 50 = 90 kmph. Time = distance / speed = 360 / 90 = 4hrs from 6 am => 10 am. Example 6: A starts from X to Y at 6 am at a speed of 50 kmph. After two hours B starts from Y to X at 60 kmph. When will they meet if X and Y are 430 km apart? Soln: By the time B started A traveled for 2 hrs => 2 X 50 = 100 km. So at 8 am, distance = 430 – 100 = 330 km Speed = 50 + 60 = 110 kmph. Time = distance / speed = 330 / 110 = 3 hrs from 8 am => 11 am. Note: When a train crosses a negligible length object (man / pole / tree) the distance that it has to travel is its own length. When a train has to cross a lengthy object (train / bridge / platform) the distance it has to travel is the sum of its length and the length of the object. Example 7: If a train traveling at 40 kmph crosses another train of length 100m traveling at 14 kmph in opposite direction in 30 s find the length of the train. Soln: Let length of train be d. Distance to be covered = d + 100. Speed = 40 + 14 = 54 kmph = 54 X 5 / 18 = 15 m / s Time = 30 s. Distance = speed X time => d+100 = 15 X 30 => d = 350 m. Note: If a man rows a boat along the stream flowing at speed S2 then it is termed downstream speed and is given by S down = S1 + S2 , where S1 is speed of boat in still water. If a man rows a boat opposite to the stream flowing at S2 then it is termed upstream and is given by S up = S1 – S2. Exercise: 1. A car moves at a speed of 80km/hr. What is the speed of the car in meters per second? 1) 9 2 12 2) 9 2 22 3) 9 1 20 4) 2 9 21 2. If a man can cover 12 meters in one second, how many kilo meters can be cover in 3 hours 45 minutes? 1) 168 km 2) 162 km 3) 150 km 4) 156 km 3. If a man running at 15 kmph. Crosses a bridge in 5 minutes, then the length of the bridge is 1) 1230 m 2) 1240 m 3) 1250 m 4) 1220 m 4. Walking at th 4 3 of his usual speed a man is late by 2 hours 30 minutes. The usual time would have been 1) 2 1 7 hrs 2) 2 1 3 hrs 3) 4 1 3 hrs 4) 8 7 hrs 5. In a 1 km race, A beats B by 100 m and C by 150 m. In a 2700 m race, by how many meters does B beat C? 1) 100 m 2) 120 m 3) 150 m 4) 180 m 6. Traveling at a speed of 8 kmph a student reaches school from his house 10 minutes early. If he travels at 6 kmph, he is late by 20 minutes. Find the distance between the school and the house. 1) 12 km 2) 1 km 3) 10 km 4) 13 km 7. A man takes 5 hours 45 minutes in walking to a certain place and riding back. He could have gained 2 hours by riding both ways. The time he would take to walk both ways is _________ 1) 12 hrs 2) 11 hrs 45minutes 3) 7 hrs 45 minutes 4) 3 hrs 8. The ratio between rates of walking of two persons is 3:4. If the time taken by nd 2 person to cover a certain distance is 36 minutes, then the time taken by the first person to cover the same distance is ___________ 1) 36 minutes 2) 48 minutes 3) 27 minutes 4) none 9. If the speed of a vehicle changes in the ratio a : b, then the ratio of times taken is 1) a : b 2) 1 ÷ b a 3) b : a 4) 1 ÷ a b 10. A car driver makes his journey by the speed of 75km/hr and returns to initial place with 50 km/hr. Then his average speed of journey is ___________ 1) 30 km/hr 2) 40 km/hr 3) 50 km/hr 4) 60 km/hr 11. A vehicle travels 715 km at a uniform speed. If the speed of the car is 10 kmph more, it takes 2 hours less to cover the same distance. The original speed was _______________ 1) 45 kmph 2) 65 kmph 3) 55 kmph 4) 75 kmph 12. Two persons P and Q run at 8 kmph and 12 kmph on a circular track of length 6 km in the same direction starting at same time from same place. After how many hours will they meet each other any where on the track? 1) 1.5 hours 2) 2 hours 3) 2.5 hours 4) 3.5 hours 13. A car driver driving at a speed of 68kmph locates a truck 40 meters ahead of him. After 10 seconds, the truck is 60 meters behind. The speed of truck is ____________ 1) 30 km/hr 2) 32 km/hr 3) 23 km/hr 4) 3 km/hr 14. Rajan is traveling on his cycle and has calculated to reach a point at 2 p.m. if he travels at 10 kmph. He would reach there by 12 noon if he travels at 15 kmph. At what speed must he travel to reach the same place at 1.p.m? 1) 12 kmph 2) 14 kmph 3) 15 kmph 4) 13 kmph 15. Two persons start running simultaneously around a circular track of length 300m from the same point at speeds 15 and 25km/hr. When will they meet first time on the track, when move in opposite direction? 1) 21 sec 2) 22 sec 3) 27 sec 4) 24 sec 16. A robber steals a Maruthi car at 2.30 pm and drives at 60 kmph. The theft is discovered at 3 p.m. and the owner sits in Police jeep running at 75 kmph. When will he catch the thief? 1) 5.30 pm 2) 5.15 pm 3) 5 pm 4) 5.45 pm 17. Two planes move along a circle of circumference 1.2 km with constant speeds. When they move in different directions they meet every 15 sec and then they move in the same direction one plane over takes the other every 60 sec. The speed of slower plane is 1) 0.04 km/s 2) 0.03 km/s 3) 0.05 km/s 4) 0.02 km/s 18. A 150 m long train crosses a man walking at a speed of 6 kmph in his opposite direction in 6 sec. The train (in kmph) is: 1) 66 2) 84 3) 96 4) 106 19. A train of length 150 m takes 10 sec to pass over another train 100 m long coming from the opposite direction. If the speed of the train is 30 kmph. Then the speed of the second train in kmph is _________ 1) 54 2) 60 3) 72 4) 36 20. If a train 110m long passes a signal pole in 3 sec. Then the time taken by it to cross a railway platform 165m long is : 1) 3secs 2) 4secs 3) 7.5secs 4) 5secs 21. An Engine of 10 m length travels at 60 kmph. How long does it take to cross another train 170 m long, running at 54 kmph in the same direction? 1) 16 sec 2) 16.8 sec 3) 108 sec 4) none 22. Two trains starting at the same time from two stations 200 km apart and going in opposite directions cross each other at a distance of 110 km from one of the stations. What is the ratio of their speeds? 1) 9:11 2) 11:9 3) 10:9 4) 9:10 23. A train M leaves Mumbai at 5am. And reaches Delhi at 9am. Another train leaves Delhi at 7am. And reaches Mumbai at 11.00am. At what time do the two trains across each other? 1) 8 a.m. 2) 9 a.m. 3) 7 a.m. 4) 6 a.m. 24. Train P leaves Hyderabad at 6.00am. And reaches Vijayawada at 10.00am. Train Q leaves Vijayawada at 7.00am. And reaches Hyderabad at 1.00pm. At what time do the trains meet? 1) 8.48 a.m. 2) 8.12 a.m. 3) 8.42 a.m. 4) 9.00 a.m. 25. A train running at 52kmph takes 36 seconds to pass a platform. Next it takes 24 seconds to pass a man walking at 10 kmph in the same direction. Find the length of the train and that of the platform? 1) 800 m; 440 m 2) 280 m; 440 m 3) 280 m; 240 m 4) 420 m; 300 m 26. Two trains running in the same direction at 40 kmph and 22 kmph completely pass one another in 60 seconds. If the length of the first train is 125 meters, then the length of second train is? 1) 125 m 2) 128 m 3) 175 m 4) 900 m 27. Two trains 220 meters and 380 meters in length respectively are running in opposite direction. One at the rate of 35 kmph and other at 25 kmph. In what time they will cross each other? 1) 36 seconds 2) 30 seconds 3) 60 seconds 4) None 28. A man misses a train by 40 minutes if he travels at 30 kmph. If he travels at 40 kmph, then also he misses the train by 10minutes. What is the minimum speed required to catch the train on time? 1) 44 kmph 2) 45 kmph 3) 48 kmph 4) 49 kmph 29. A boat traveled from A to B and back to A from B in 5 hours. If the speed of boat in still water and the speed of stream be 7.5 kmph and 1.5 kmph, then what is the distance between A and B? 1) 80 km 2) 45 km 3) 18 km 4) 19 km 30. A man can row downstream at 18 kmph and upstream at 10 kmph. Find the speed of the man in still water and the speed of stream (in kmph) 1) 13; 3 2) 15; 3 3) 12; 6 4) 14; 4 31. A man can row at 9 kmph in still water. He takes 4 ½ hours to row from P to Q and back. What is the distance between P and Q if the speed of the stream is 1 kmph? 1) 32 km 2) 28 km 3) 20km 4) 24 km 32. A man can row 30 km downstream in 3 hours 45 minutes, and 11 km upstream in 2 hours 12 minutes. What is the speed of the man in still water and speed of stream (in kmph)? 1) 6; 2 2) 6.8; 1.8 3) 6.5; 1.5 4) 7; 3 33. A man rows 22 km upstream in 4 hours and 45 km downstream in 6 hours. In 10 hours how much more distance can he row downstream than the distance he can row upstream? 1) 24 km 2) 22 km 3) 20 km 4) 18 km 34. A person can row 10 km in 1 hour in still water. If the speed of the water current is 2 kmph and it takes two hours for him to go to a certain place and back. Find the distance he traveled in upstream? 1) 9 ½ km 2) 9.6 km 3) 48 km 4) 5 km 35. A person can row 5 3 of a km in upstream in 10 minutes and return in 6 minutes. Find the speed of man in still water? 1) 4.4 kmph 2) 4.5 kmph 3) 4.8 kmph 4) 4.9 kmph 36. A boat can travel 10 kmph in still water. It traveled 91 km downstream and then returned, taking altogether 20 hours. Find speed of the stream? 1) 4 kmph 2) 5 kmph 3) 8 kmph 4) 3 kmph 37. The time taken for a boat to cover certain distance in upstream is equal to the time taken by the boat to cover three times the distance in downstream. If the speed of current is 5 kmph, what is the speed of boat in still water? 1) 14 kmph 2) 15 kmph 3) 10 kmph 4) 19 kmph 38. The time taken by a person to row upstream is twice the time taken by him to row the same distance downstream. If the speed of the boat in still water is 42 kmph, find the speed of current? 1) 14 kmph 2) 32 kmph 3) 12 kmph 4) 8 kmph 39. A man rows his boat to a certain place covering a distance of 72 km and back again in 15 hours. He finds that he takes same time to row 3 km in downstream as much he takes for 2 km in upstream. Find the speed of the stream? 1) 4 kmph 2) 3 kmph 3) 1 kmph 4) 2 kmph 40. A man can row 6 km/hr in still water. If the speed of stream is 2km/hr, it takes him 3 hours to row to a place and back. How far is the place? 1) 16 km 2) 10 km 3) 12 km 4) 8 km Time and Work If a person can complete a work in „n‟ days then he can do 1/n part of the work in one day. The amount of work done be a person in 1 day is called his efficiency. Example: A can do a work in 10 days. Then the efficiency of A is given by A = 1 / 10. Note: Number of days required to do a work = work to be done / work per day. Example 1: If A can do a work in 10 days, B can do it in 20 days and C in 30 days in how many days will the three together do it? Soln: The efficiencies are A = 1/10, B = 1/20 and C = 1/30 So work done per day by the three = 1/10 + 1/20 + 1/30 = 11/60 => No of days = 60/11 = 5.45 days. Example 2: If A and B can do a work in 10 days , B and C can do it in 20 days and C and A can do it in 40 days in what time all the three can do it? Soln: A+B = 1/10 B+C = 1/20 C+A = 1/40 Adding all the three we get 2(A+B+C) = 7/40 => A+B+C = 7/80 => No of days = 80/7 days. Note: If all the people do not work for all the time then the principle below can be used: mA + nB + oC = 1. (1 is the total work) Here, m=no of days A worked n=no of days B worked o=no of days C worked A,B,C = efficiencies Example 3: If A can do a work in 12 days, B can do it in 18 days and C in 24 days. All the three started the work. A left after two days and C left three days before the completion of the work. How many days are required to complete the work? Soln: Let the total no of days be x. A worked only for 2 days, B worked for x days and C worked for x-3 days. So, mA + nB + oC = 1  2(1/12) + x(1/18) + (x-3)(1/24) = 1  12 + 4x + 3(x-3) = 72  x = 69 / 7 days. Note: The ratio of dividing wages = ratio of efficiencies = ratio of parts of work done Example 4: A can do a work in 10 days and B can do it in 30 days and C in 60 days. If the total wages for the work is Rs. 1800 what is the share of A? Soln: Ratio of wages = 1/10 : 1/30 : 1/60 = 6 : 2 : 1 (Multiplying each term by LCM 60) So total 9 equal parts in Rs. 1800 => each part = Rs. 200 => share of A = 6 parts = Rs. 1200. Note: When pipes are used filling the tank they are treated similar to the men working but some outlet pipes emptying the tank are present whose work will be considered negative. Example 5: A pipe can fill a tank in 5 hrs but because of a leak a the bottom it takes 1 hr extra. In what time can the leak alone empty the tank? Soln: Let the filling pipe be A. A = 1 / 5. But with the leak L, A – L = 1 / 6 ( A-L because leak is outlet) So, 1/L = 1 / 5 – 1/ 6 = 1/30 => Leak can empty the tank in 30 hrs. Example 6: A pipe A can fill the tank in 10 hrs, B can fill it in 20 hrs and C can empty in 40 hrs. All are opened at the same time. After how many hours shall the pipe B be closed such that the tank can be filled in 10 hrs? Soln: Let the pipe B be closed after x hrs. Then A worked for 10 hrs, B worked for x hrs and C worked for 10 hrs. mA + nB – oC = 1 (since C is outlet) 10(1/10) + x(1/20) – 10(1/40) = 1 x = 5 hrs. Exercise: 1. A alone can complete the work in 12 days while A and B together can complete the same work in 8 days. The number of days that B will take to complete the work alone is ___________ 1) 10 2) 24 3) 20 4) 9 2. A can do a work in 6 days and B in 9 days. How many days will both take together to complete the work. 1) 7.5 2) 5.4 3) 3.6 4) 3 3. A can do a piece of work in 4 hours, B and C can do it in 3hrs, A and C can do it in 2hrs. How long will B alone take to do it? 1) 10hrs 2) 12hrs 3) 8hrs 4) 24hrs 4. 10 men and 15 women finish a work in 6 days. One man alone finishes that work in 100 days. In how many days will a woman finish the work? 1) 125 2) 150 3) 90 4) 225 5. A completes a work in 12 days; B completes the some work in 15 days. A started working alone and after 3 days B joined him. How many days will they now take together to complete the remaining work? 1) 5 2) 8 3) 6 4) 4 6. 10 men can complete a piece of work in 15 days & 15 women can complete the same work in 12 days. If all the 10 men & 15 women work together, in how many days will the work get completed? 1) 6 2) 3 2 7 3) 3 2 6 4) None of these 7. A can do a certain work in the same time in which B & C together can do it. If A and B together could do it in 10 days and C alone in 50 days then B alone could do the work in 1) 15 days 2) 20 days 3) 25 days 4) 30 days 8. A& B under took to do a piece of work for Rs.4,500. A alone could do it in 8 days and B alone in 12 days. With the assistance of C they finished the work in 4 days. Then C‟s share of the money is ____________ 1) Rs.2,250 2) Rs.1,500 3) Rs.750 4) Rs.375 9. A can finish a work in 24 days, B in 9 days and C in 12 days. B & C start the work but are forced to leave after 3 days. The remaining work is done by A in _____________ 1) 5 days 2) 6 days 3) 10 days 4) 2 1 10 days 10. If 3 men (or) 4 women can plough a field in43 days, how long will 7 men and 5 women take to plough it. 1) 10 days 2) 11 days 3) 9 days 4) 12 days 11. A can do th 4 3 of a work in 12 days. In how many days can he finish th 8 1 of work? 1) 1 day 2) 2 days 3) 4 days 4) 8 days 12. If 72 men can build a wall 280m. long in 21 days, how many men will take 18 days to build a similar type of wall of length 100m.? 1) 30 2) 10 3) 18 4) 28 13. A takes twice as much time as B or thrice as much time as C to finish a piece of work. Working together, they can finish the work in 2 days. B can do the work alone in 1) 12 days 2) 4 days 3) 8 days 4) 6 days 14. A does 5 4 of a piece of work in 20 days; he then calls in B and they finish the remaining work in 3 days. How long will B alone take to do the whole work? 1) 2 1 37 days 2) 37 days 3) 40 days 4) 23 days 15. A does half as much work as B in 1/6 of the time. If together they take 10 days to complete a work, how many days shall B take to do it alone? 1) 15 days 2) 30 days 3) 40 days 4) 50 days 16. A man, a woman and a boy can together complete a piece of work in 3 days. If a man alone can do it in 6 days and a boy alone can do it in 18 days, how long will a woman alone take to complete the work. 1) 9 days 2) 21 days 3) 24 days 4) 27 days 17. If the wages of 6 men for 15 days be Rs.700, then the wages of 9 men for 12 days will be ___________ 1) Rs.700 2) Rs.840 3) Rs.1050 4) Rs.900 18. A man is paid Rs.20 for each day he works, and forfeits Rs.3 for each day he is idle. At the end of 60 days he gets Rs.280. Then he was idle for _____________ 1) 20 days 2) 25 days 3) 30 days 4) 40 days 19. A team of 10 men can complete a particular job in 12 days. A team of 10 women can complete the same job in 6 days. How many days are needed to complete the job if the two teams work together? 1) 4 2) 6 3) 9 4) 18 20. A contractor undertook to finish a certain work in 124 days and employed 120 men on it. After 64 days, he found that he had already done rd 3 2 of the work. How many men he can discharge now so that the work may finish in time 1) 24 2) 56 3) 64 4) 80 21. A work could be completed in 100 days. However, due to the absence of 10 workers, it was completed in 110 days. The original number of workers was ___________ 1) 100 2) 110 3) 55 4) 50 22. A contractor under takes to make a road in 40 days and employs 25 men. After 24 days, he finds that only one-third of the road is made. How many extra men should he employ so that he is able to complete the work 4 days earlier? 1) 100 2) 60 3) 75 4) none of these 23. 30 men complete one third of a work in 30 days. How many more men should be employed to finish the rest of the work in 40 more days? 1) 15 2) 45 3) 20 4) 25 24. A and B under took to do a piece of work for Rs.900. A alone could do it in 60 days and B in 30 days. If A & B work together and complete the work, then the share of B _______ 1) Rs.600 2) Rs.400 3) Rs.300 4) Rs.200 25. 5 men or 6 women or 10 boys can do a work in 15 days. How long will it take to complete the work by a group of 5 men, 6 women and 10 boys? 1) 5 days 2) 6 days 3) 10 days 4) 45 days 26. A can do a piece of work in 30 days. B in 15 days and C in 10 days. They started the work all together but B put 2 1 time daily and C put 3 1 time daily to help A in doing the work. The work will last in ______________ 1) 30 days 2) 10 days 3) 20 days 4) 25 days 27. A can do a work in 15 days & B the same work in 12 days. B started the work and was joined by A, 5 days before the end of work. The work lasted for _____ days. 1) 8 2) 12 3) 13 4) 24 28. A and B can do a piece of work in 40 days while C & A can do it in 60 days. If B is twice as good as C, then C alone will do the work in ___________ days. 1) 120 2) 100 3) 80 4) 24 29. A hostel has provision for 800 men for 24 days at the rate of 2 kg per man per day. For how many men is the provision sufficient, for 20 days at the rate of 1.5 kg per man per day? 1) 1280 2) 1000 3) 1820 4) 1240 30. 12 men can do a work in 15 days working 8 hours a day. In how many days can 9 men do the same work, working 10 hours a day? 1) 10 2) 16 3) 18 4) 24 31. Two taps A and B can separately fill a tank in 20 and 30 hours respectively. If both the pipes are opened simultaneously, how much time will be taken to fill the tank? 1) 10 hrs 2) 11 hrs 3) 18 hrs 4) 12 hrs 32. A tap can fill a tank in 12 minutes and another tap in 15 minutes, but a third tap can empty it in 6 minutes. The three taps are kept open together. Find when the cistern is emptied or filled? 1) 60 min. to fill 2) 30 min. to fill 3) 60 min to empty 4) 30 min to empty 33. Two taps A & B can fill a cistern in 12 and 16 minutes respectively. Both fill taps are opened together, but 4 minutes before cistern is full, one tap A is closed. How much time will the cistern take to fill? 1) 9 1 /7 min. 2) 3 1 /7 min. 3) 11 1 /7 min. 4) None. 34. A ship 55 km from the shore springs a leak which admits 2 tonnes of water in 6 minutes. 80 tonnes would suffer to sink her, but the pumps can throw out 12 tonnes an hour. Find the average rate of sailing that she may just reach the shore as she begins to sink. 1) 5.5 kmph 2) 2.5 kmph 3) 1.8 kmph 4) 4 kmph 35. A tap can fill a swimming pool in h hours. What part of the pool is filled in y hours? 1) yh 2) y h 3) h y 4) h – y 36. Three pipes A, Band C can fill a tank in 30 min, 40 min and 60 min respectively. A and B work in alternative minutes, A beginning the work whereas C works continuously. In how many minutes will the tank be filled? 1) 16.4 2) 21.8 3) 18.2 4) 19.6 37. A tank has a leak, which would empty it in 8 hrs. A tap is turned on which admits 6 litres of water a minute into the tank and it is now emptied in 12 hrs. How many litres does the tank hold? 1) 8640 2) 8460 3) 8064 4) 8406 38. A cistern is normally filled with water in 10 hours but takes 5 hours longer to fill because of a leak in its bottom. If the cistern is full, then the leak will empty the cistern in 1) 20 hours 2) 40 hours 3) 50 hours 4) 30 hours 39. Two pipes A and B can separately fill a cistern in 60 and 75 minutes respectively. There is a third pipe at the bottom of the cistern to empty it. If all the three pipes are simultaneously opened, then the cistern is full in 50 minutes. In how much time can third pipe alone empty the cistern? 1) 110 minutes 2) 100 minutes 3) 120 minutes 4) 90 minutes 40. A tap can fill a tank in 6 hours. After half the tank is filled, three more similar taps are opened. What is the total time taken to fill the tank completely? 1) 4 hours 2) 4 hours 15 minutes 3) 3 hours 15 minutes 4) 3 hours 45 minutes Mensuration Types of Plane Figures 1. Triangle 2. Quadrilateral 3. Polygon 4. Circle 5. Sector of a circle 6. Rectangular Paths 7. Circular paths I. Triangle (a). Any triangle a, b and c are three sides of the triangle; h is the altitude and AC is the base. Perimeter (P) : P = a + b + c = 2s Area (A) : A = × 2 1 base × altitude = 2 1 × any side × length of ±r dropped on that side = ) c s ( ) b s ( ) a s ( s ÷ ÷ ÷ (b). Equilateral a is the length of each side Perimeter (P) : P = 3a Area (A) : A = 4 3 a 2 (c). Right-angled b, c are the lengths of the two legs Perimeter (P) : P = a + b + c = 2s Area (A) : A = × 2 1 product of two legs (d). Isosceles B A C a a a B A C a b c 90 o B A C a D a b/2 b/2 B A C a b c h a is the length of two equal sides b is the base BD is the perpendicular dropped on base such that it divides the base equally AD = CD = 2 b Perimeter (P) : P = 2a+b Area (A) : A = 2 2 b a 4 4 b ÷ (e). Right-angled Isosceles Perimeter (P) : P = 2 × a × ( 2 +1) Area (A) : A = × 2 1 (a) 2 II. Quadrilateral (a). Any Quadrilateral AC is the diagonal = d, DE and BF are two perpendicular drawn on the diagonal (AC) P1, and P2 are the lengths of the two perpendiculars Perimeter (P) : P = sum of the four sides. Area (A) : A = × 2 1 d×(p1+p2) = × 2 1 any diagonal × (sum of ±rs drawn on that diagonal) (b). Rectangle l = length b = breadth d = diagonal Perimeter (P) : P = 2(l + b) = 2(l+ 2 2 l d ÷ ) = 2(b+Error! Objects cannot be created from editing field codes.) = 2 A 2 d 2 + Area (A): A = l ×b = l × 2 2 l d ÷ = b×Error! Objects cannot be created from editing field codes., when p and A are known and l and b are unknown. d A B C D E F P 1 P 2 d A B C D b b l l O Hypotenuse - h a a The two values of x will give l and b. (c). Square a = length of side d = diagonal Perimeter (P) : P = 4a = 2d 2 Area (A) : A = a 2 = 16 p = 2 d 2 2 (d). Rhombus a = each side d1 = one diagonal d2 = another diagonal h = height Perimeter (P) : P = 4a = 2 2 2 2 1 d d + Area (A) : A = × 2 1 d1 × d2 = 2 1 2 1 2 d a 2 d ( ¸ ( ¸ ÷ × = 2 2 2 2 2 d a 2 d ( ¸ ( ¸ ÷ × = a × h (e). Trapezium a and b are two parallel sides, h is the height Area (A) : A = 2 1 (a + b) × h = 2 1 ×(sum of parallel sides) × (perpendicular distance between parallel sides) (f). Parallelogram b is the base h is the perpendicular distance between the base and its opposite side Area (A) : A = b × h = base × (perpendicular distance between the base and its opposite sides) = 2 × area of Δ ABD (or Δ BCD) III. Polygon Polygon is a n-sided closed figure bounded only by line segments. In a polygon if the internal angle at each vertex is less than 180 o then the polygon is a convex polygon, else a concave polygon. D A A B A C B A d C B A O B A a O B A a O B A a O B A a O B A 90 o a OB A 90 o a OB A A B C B D C B a A b a A h b a A A B C B D C B b a A h b a A A B A C B A D C B A a D C B A a D C B A a D C B A a D C B A d 2 O a D C B A 90 o OaD CB A 90 o OaD CB A d 1 h Convex Polygon: i. Area of a regular polygon = 2 1 ×perimeter × r ± distance from the center of the polygon to any side. ii. Number of diagonals in a polygon = 2 ) 3 n ( n ÷ iii. Sum of all interior angles of a polygon = (2n-4) × 90 o iv. Each interior angle of n-sided regular polygon = × ( ¸ ( ¸ ÷ n 2 n 180 o v. Sum of all exterior angles of n-sided regular polygon = 360 o vi. Each exterior angle of n-sided regular polygon = n 360 IV. Circle O is the center of the circle OA = OC = OB = OD = radius of circle = r AC = BD = diameter of circle = d = 2r Circumference (or Perimeter) C = 2π r = π d Area of circle A = π r 2 = π 4 d 2 If C = circumference, A = area then A = 2 r C A and π 4 C 2 = V. Sector of a circle Area of sector AOB = 2 o r π 360 θ × Length of the Arc AB = r π 2 360 θ o × VI. Rectangular Paths θ A B O W w M N K A B A C B A D C B A O K N K M N K L M N K D N K A D N K B A D N K C B A D N K L C B A D N K Rectangle Path way Case - I K N K M N K L M N K D N K A D N K B A D N K C B A D N L C B A D N K W Case - II Case - I Pathway is outside the rectangle The length of rectangle AB = l, Breadth BC = b and , Width of path way = W, then Area of Pathway = 2W (l+b+2w) (shaded portion) Case – II Path way is inside the rectangle Area of Pathway = 2W(l+b-2W) (shaded portion) VII. Circular Pathway OAC is a circle of radius = r, there is pathway, outside the circle of width = W Area of circular pathway = π ×W (2r+W) When, the pathway is inside the circle, Area of circular pathway = π ×W (2r - W) Examples: 1. If three sides of a triangle are 5, 6 and 7 cm respectively, find the area of triangle. Sol: Area of A = s(s a)(s b)(s c) ÷ ÷ ÷ W r R W A O C A W r W C A W W O Now, s = a b c 5 6 7 2 2 + + + + = = 9 Area = 9 (9 5)(9 6)(9 7) 9 4 3 2 × ÷ ÷ ÷ = × × × = 216 6 6 = cm 2 . 2. ABC is an equilateral triangle of side 24 cm. Find the in radius of the triangle. Sol: In a equilateral triangle, the altitude, median and perpendicular are equal. AD = 3 /2 x 24 = 12 3 GD (in radius) = 1/3 x 12 3 = 4 3 cm 3. The base and other side of an isosceles triangle is 10 and 13 cm respectively. Find its area. Sol: Area of Isosceles A = 2 2 b 4a b 4 ÷ Given, base b = 10 Other side a = 13 Area (A) = 2 2 10 10 4 (13) 10 676 100 4 4 × ÷ = ÷ = 10 4 × 24 = 60 cm 2 . 4. In a right-angled triangle, the length of two legs are 12 and 5 cm. Find the length of hypotenuse and its area. Sol: In a right angled triangle, (Hypotenuse) 2 = (one leg) 2 + (other leg) 2 = 12 2 + 5 2 Hypotenuse = 2 2 12 5 + = 169 = 13 cm. In a right angled triangle, Area = 1 2 1 1 (leg) (leg) 12 5 2 2 × × = × × = 30 cm 2 . 5. If the perimeter and diagonal of a rectangle and 14 and 15 cm respectively. Find its area. Sol: In a rectangle, 2 (Perimeter) 4 = (diagonal)2 + 2 x Area ; 2 (14) 4 = (5) 2 + 2 x Area ¬ 2 x Area = 196 4 - 25 Area = 49 25 2 ÷ = 12 cm 2 . 6. Find the length of the diagonal and the perimeter of a square plot if its area is 900 square metres. Sol: In a square, A = 2 2 d p 2 16 = (Diagonal) 2 = 2 x Area = 900 Diagonal (d) = 2 900 30 2 × = × = 42.42 metres (Perimeter) 2 = 16 x Area = 16 x 900 Perimeter (P) = 16 900 × = 120 metres. 7. A field in the shape of a rhombus has the distances between pairs of opposite vertices as 14 m and 48 m. What is the cost (in rupees) of fencing the field at Rs.20 per metre? Sol: The diagonals are 14 m and 48 m Sides of rhombus = 2 2 14 48 625 2 2 | | | | + = | | \ . \ . = 25 Perimeter of rhombus = 4 x 25 = 100 m. Cost of fencing the field = 100 x 20 = Rs.2000 8. In a trapezium, the length of parallel sides are 20 and 25 metres respectively and the perpendicular distance between the parallel sides is 12 metres. Find the area of trapezium. Sol: One parallel side a = 20 metres. Second parallel side b = 25 metres. Height (perpendicular distance between a and b) = 12 metres. Area = 1 1 (a b) h (20 25) 12 2 2 + × = + × = 270 m 2 . 9. The distance between a pair of opposite vertices of a quadrilateral is 32 units. The lengths of the perpendiculars drawn on to this diagonal from the other two vertices are 4 1/3 units and 6 2/3 units respectively. Find the area (in sq units) of the quadrilateral? Sol: Area of quadrilateral = 1/2 x 32 x 13 20 3 3 | | + | \ . = 178 sq units. A B D C 10. In the above parallelogram ABCD, A Z = x + 30 o and D Z = x – 40 o , what is the measure of DCB Z ? Sol: In a parallelogram, sum of adjacent angles is equal to 180 o x + 30 + x – 40 = 180 ¬ x = 95 o DAB Z = x + 30 = 95 + 30 = 125 o DCB Z = DAB Z = 125 o (opposite angles of a parallelogram are equal) 11. In a circle of radius 49 cm, an arc subtends an angle of 36 o at the centre. Find the length of the arc and the area of the sector. Sol: Length of the arc = 2 r 2 22 49 36 360 7 360 θ H × × × = × = 30.8 cm Area of the sector = 2 r 22 49 49 36 360 7 360 θ H × × × = × = 754.6 cm 2 12. A rectangular plot of dimensions 13 m x 17 m is surrounded by a garden of width 5 m. What is the area (in sq m) the garden? Sol: Let ABCD be the rectangular plot of given dimension. The shaded part is the surrounding garden. Now, the plot ABCD together with the garden forms another rectangular form PQRS. Dimensions of PQRS, as can be seen from the diagram, are: Length PQ = width of garden + AB + width of garden = 5 + 17 + 5 = 27 m Similarly, breadth = PS = 5 + 13 + 5 = 23 m Area of garden = Area of PQRS – Area of ABCD = (27 x 23) – (17 x 13) = 621 – 221 = 440 sq m. 13. There is a rectangular field of length 100 m and breadth 40 m. A carpet of 2 m width is to be spread from the centre of each side to the opposite side. What is the area of the carpet? Sol: Area of the carpet ABCD = 40 m x 2 m = 80 m 2 Area of the carpet EFGH = 100 m x 2 m = 200 m 2 But the common area of two carpets = 2 x 2 = 4m 2 So, area of the carpet = 200 + 80 – 4 = 276 m 2 14. There is an equilateral triangle of which each side is 3 m. With all the three vertices as centres, circles with radius 1.5 cm are described (i) Calculate the area common to all the circles and the triangle. (ii) Find the area of the remaining portion of the triangle. Sol: (i) Area of each sector = 2 1 r 6 × H × So area common to the all the circles and triangle = 3 2 2 1 1 r r 6 2 × × H × = H = 1 22 1.5 1.5 2 7 × × × = 3.53 m 2 (ii) Area of the shaded portion = Area of the triangle – Area common to the triangle and the circles But area of the triangle = 2 2 3 3 9 3 a (3) 4 4 4 = = m 2 So area of the shaded portion = 9 3 4 m 2 – 3.53 m 2 = 3.89 m 2 – 3.53 m 2 = 0.36 m 2 Exercise: 1. The base and other side of an isosceles triangle is 10 cm and 13 cm respectively. Find its area. 1. 23 cm 2 2. 60 cm 2 3. 65 cm 2 4. 23 cm 2 2. If the area of triangle is 150 m 2 and base : height is 3 : 4, find its height and base respectively. 1. 75 m, 100 m 2. 100 m, 75 m 3. 75 m, 75 m 4. None 3. Find the area of an equilateral triangle of side of 12 cm. 1. 72 sq cm 2. 36 3 sq cm 3. 12 3 sq cm 4. 18 3 sq cm 4. The height of a triangle is 8/9 th of its base and its area is 576 sq cm. Find its height. 1. 36 cm 2. 52 cm 3. 72 cm 4. 32 cm 5. Find the area of a triangle whose sides are 66 cm, 88 cm and 1.1 m. 1. 2640 sq cm 2. 2904 sq cm 3. 2940 sq cm 4. 1452 sq cm 6. Area of an equilateral triangle is 16 3 sq cm, Find its perimeter. 1. 12 cm 2. 48 cm 3. 24 cm 4. 16 cm 7. What is the height of an equilateral triangle if its side is 8 3 cm? 1. 6 cm 2. 8 cm 3. 24 cm 4. 12 cm 8. In a quadrilateral, the length of its diagonals is 12 cm and the offsets drawn on this diagonal measure 13 cm and 7 cm respectively. Find its area. 1. 546 m 2 2. 273 m 2 3. 60 m 2 4. 120 m 2 9. In a parallelogram, the lengths of adjacent sides are 11 m and 13 m respectively. If the length of one diagonal is 16 m, find the length of other diagonal. 1. 18 m 2. 96 m 3. 18 m 4. 40 m 10. The two adjacent sides of a parallelogram are 12 m and 14 m respectively, and if the diagonal connecting the ends is 22 m respectively, find the area of the parallelogram. 1. 151.87 m 2 2. 115.78 m 2 3. 151.78 m 2 4. 115.87 m 2 11. The base and the height of a parallelogram are 25 cm and 20 cm respectively. Find its area. 1. 500 sq cm 2. 250 sq cm 3. 45 sq cm 4. 125 sq cm 12. If the perimeter and diagonal of a rectangle and 14 cm and 5 cm respectively. Find its area. 1. 6 cm 2 2. 19 cm 2 3. 12 cm 2 4. 9 cm 2 13. The area and the perimeter of a rectangle are 84 m 2 and 38 m respectively. Find its length and breadth. 1. 12 m, 7 m 2. 14 m, 6 m 3. 42 m, 19 m 4. None 14. A rectangular grass field is 112 m x 78 m. It has a gravel path 2.5 m wide all round it on the inside. Find the area of gravel path. 1. 8736 sq m 2. 925 sq m 3. 4368 sq m 4. 952 sq m 15. A rectangular lawn 70 m x 30 m has two roads each 5 m wide, running in the middle of it, one parallel to the length and the other parallel to the breadth. Find the cost of gravelling the road at the rate of Rs.4 per sq m. 1. Rs.1000 2. Rs.2700 3. Rs.1700 4. Rs.2100 16. The length of a rectangle is increased by 20% and the breadth is decreased by 30%. Find the percentage change in its area. 1. 10% increase 2. 16% decrease 3. 8% decrease 4. 16% increase 17. The length and the breadth of a rectangle are in the ratio of 15 : 8 and its perimeter is 230 cm. Find its area. 1. 3000 sq cm 2. 2300 sq cm 3. 1500 sq cm 4. 6000 sq cm 18. There is a path of 1 m width around the outside of a rectangular field of 98 m x 48 m. Find the area of the path. 1. 148 sq m 2. 296 sq m 3. 598 sq m 4. 2352 sq m 19. The breadth of a rectangle is 4/5 th of its length and its area is 720 sq cm. Find its length. 1. 15 cm 2. 30 cm 3. 60 cm 4. 576 cm 20. The sides of a rectangle are in the ratio 4 : 3 and its area is 768 sq m. Find its perimeter? 1. 56 m 2. 112 m 3. 96 m 4. None 21. The perimeter of a rectangle is 216m. If its sides are in the ratio 5 : 4 the area is _______ 1. 1140 sq m 2. 2880 sq m 3. 960 sq m 4. 1260 sq m 22. The sides of rectangular garden are 75 m x 48 m. What is the perimeter of a square with same area? 1. 60 m 2. 120 m 3. 240 m 4. None 23. Find the length of the diagonal of a square plot if its area is 900 sq m. 1. 10 2 m 2. 15 2 m 3. 30 2 m 4. 9 2 m 24. Find the perimeter of a square plot if its area is 1600 sq m. 1. 80 m 2. 160 m 3. 320 m 4. 40 m 25. Find the ratio of area and the perimeter of a square of side 8 cm. 1. 1 : 2 2. 4 : 1 3. 3 : 1 4. 2 : 1 26. Find the diagonal of a square whose perimeter is 128 2 sq m. 1. 64 m 2. 32 m 3. 32 2 m 4. 64 2 m 27. The perimeter of a square is 88 cm. Find its area. 1. 484 sq cm 2. 174 sq cm 3. 242 sq cm 4. None 28. There is a square shaped grass lane of 14 m side. Four cows are tethered with the ropes of 3.5 m length each at one corner. Find the area of the grass lane over which the cows are unable to graze the grass. 1. 157.5 sq m 2. 38.5 sq m 3. 175.5 sq m 4. 157.7 sq m 29. The area of two squares is in the ratio of 16 : 49. Find the ratio of their diagonals. 1. 7 : 4 2. 49 : 16 3. 4 : 7 4. None 30. If an error of 10% excess in made in calculating the side of square the % error in its area is ___________ 1. 20 2. 21 3. 22 4. None 31. The area of a square garden is 576 sq m. What is the cost of fencing, it at the rate of Rs.1.25 per m? 1. Rs.24 2. Rs.50 3. Rs.90 4. None 32. The area of a square garden is 625 sq m. What is the area of a path of width 2.5 m around it, if the path is outside the garden? 1. 900 sq m 2. 275 sq m 3. 30 sq m 4. None 33. The diagonal of a square is 24 m. Its area is __________ 1. 144 sq m 2. 576 sq m 3. 288 sq m 4. None 34. In a rhombus, the lengths of the two diagonals are 40 m and 30 m respectively. Find its area and perimeter. 1. 600 sq m, 100 m 2. 100 sq m, 600 m 3. 1200 sq m, 600 m 4. 600 sq m, 200 m 35. In a rhombus the side and one of its diagonals are 25 m and 40 m respectively. Find its perimeter. 1. 50 m 2. 100 m 3. 200 m 4. 10 m 36. The side and one of the diagonals of a rhombus are 25 cm and 14 cm respectively. Find its area. 1. 350 sq cm 2. 390 sq cm 3. 168 sq cm 4. 336 sq cm 37. The diagonals of a rhombus are in the ratio of 8 : 3 and area is 432 sq cm., Find its diagonals. 1. 18 : 48 2. 3 : 8 3. 48 : 18 4. None 38. If the side and the height of a rhombus are 12 m and 30 m respectively. Find the cost of painting both the surfaces of an aluminum sheet of same shape and size at the rate of Rs.5 per sq m. 1. Rs.1200 2. Rs.3600 3. Rs.3000 4. Rs.4200 39. The cross-section of a canal is a trapezium in shape. If the canal is 7 m wide at the top and 9 m at the bottom and the area of cross-section is 128 sq m, find the height of the canal. 1. 32 m 2. 8 m 3. 4 m 4. 16 m 40. The parallel sides of a trapezium are 18 cm and 22 cm and the distance between them is 10 cm. Find its area. 1. 100 sq cm 2. 250 sq cm 3. 200 sq cm 4. 150 sq cm 41. Find the area of a triangle having sides 3 m, 4 m and 5 m. 1. 60 sq m 2. 10 sq m 3. 12 sq m 4. 6 sq m 42. Find the area of a triangle whose base is 4.6m and height is 67 cm. 1. 154.10 sq m 2. 15410 sq m 3. 15.410 sq m 4. None 43. Find the area of an equilateral triangle each of whose sides measures 6 cm. 1. 36 sq cm 2. 3 3 sq cm 3. 9 3 sq cm 4. 12 sq cm 44. Length of the side of an equilateral triangle is 3 4 cm. Find its height. 1. 2 cm 2. 4 cm 3. 6 cm 4. None 45. Height of an equilateral triangle is 4 3 cm. Find its area. 1. 4 3 sq cm 2. 2 3 sq cm 3. 16 3 sq cm 4. 8 3 sq cm 46. An isosceles right-angled triangle has two equal sides of length 6 m each. Find its area 1. 8 sq m 2. 36 sq m 3. 18 sq m 4. None 47. The perimeter of an isosceles triangle is 80 cm. If the length of the equal sides is given by 0.15 m, find the length of the base. 1. 40 m 2. 50 m 3. 12 m 4. 90.5 m 48. The perimeter of an isosceles triangle is 42 cm. If the base is 16 cm, find the length of equal sides. 1. 13 cm 2. 8 cm 3. 21 cm 4. 29 cm 49. The two adjacent sides of a parallelogram are 5 m and 6 m respectively, and if the diagonal connecting the ends is 9 m, find the area of the parallelogram (approximately). 1. 29 sq m 2. 28 sq m 3. 58 sq m 4. 50 sq m 50. Find the area of a quadrilateral of whose diagonal is 38 cm long and the lengths of perpendiculars from the other two vertices are 31 cm and 19 cm, respectively. 1. 950 sq cm 2. 475 sq cm 3. 138 sq cm 4. 276 sq cm 51. Find the area of a parallelogram whose two adjacent sides are 130 m and 140 m and one of the diagonals is 150 m long. 1. 8400 sq cm 2. 16,800 sq cm 3. 2100 sq cm 4. None 52. Find the diagonal of a rectangle whose sides are 8 cm and 6 cm. 1. 14 cm 2. 5 cm 3. 20 cm 4. 10 cm 53. Find the perimeter of a rectangle of length 12 m and breadth 6 m. 1. 18 m 2. 72 m 3. 36 m 4. 144 m 54. Calculate the area of a rectangular field whose length is 12.5 cm and breadth is 8 cm. 1. 10 sq cm 2. 100 sq cm 3. 200 sq cm 4. 1 sq cm 55. Calculate the area of a rectangular field whose one side is 16 cm and the diagonal is 20 cm. 1. 192 sq cm 2. 96 sq cm 3. 294 sq cm 4. 72 sq cm 56. A rectangular carpet has an area of 120 sq m and perimeter of 46 m. Find the length of its diagonal. 1. 34 m 2. 51 m 3. 93 m 4. 17 m 57. The perimeter of a rectangle is 82 cm and its area is 400 sq m. Find the length of the rectangle. 1. 8 m 2. 16 m 3. 32 m 4. 64 m 58. If the area of a square field be 6050 sq m, find the length of its diagonal. 1. 220 m 2. 110 m 3. 55 m 4. None 59. Find the area of a square with perimeter 48 m. 1. 288 sq m 2. 72 sq m 3. 144 sq m 4. 96 sq m 60. Find the diagonal of a square field whose side is of 6 m length. 1. 12 2 m 2. 6 2 m 3. 2 m 4. 3 2 m 61. Perimeter of a square field is 16 2 cm. Find the length of its diagonal. 1. 16 cm 2. 4 cm 3. 8 cm 4. 64 cm 62. The area of a rhombus is 156 sq m. If one of its diagonals is 13 m, find the length of the other diagonal. 1. 12 m 2. 6 m 3. 48 m 4. 24 m 63. Find the area of a rhombus whose one side is 13 cm and one diagonal is 24 cm. 1. 60 sq cm 2. 120 sq cm 3. 240 sq cm 4. 74 sq cm 64. If the perimeter of a rhombus is 73 cm and one of its diagonals is 27.5 cm, find the other diagonal and the area of the rhombus. 1. 24 cm, 330 sq cm 2. 20 cm, 115 sq cm 3. 30 cm, 660.8 sq cm 4. 40 cm, 100.5 sq cm 65. In a rhombus, the lengths of two diagonals are 18 m and 24 m. Find its perimeter. 1. 15 m 2. 30 m 3. 60 m 4. 120 m 66. The diagonally of Rhombus are 12 cm and 5 cm respectively. Find the side of the Rhombus. 1. 5 cm 2. 6.5 cm 3. 6 cm 4. 8.5 cm 67. What is the radius of a circular plot whose circumference is 176 m? 1. 14 m 2. 56 m 3. 88 m 4. 28 m 68. A circular plot covers an area of 154 sq m. How much wire is required for fencing the plot? 1. 44 m 2. 22 m 3. 88 m 4. 77 m 69. Find the area of sector of a circle whose radius is 10 cm and the angle at the center is 36 o . 1. 30 7 3 sq cm 2. 31 3 7 sq cm 3. 30 3 7 sq cm 4. 31 7 3 sq cm 70. Find the area of sector of a circle whose radius is 12 cm and the length of the arc is 20 cm. 1. 60 sq cm 2. 240 sq cm 3. 120 sq cm 4. 64 sq cm Cuboid : A right prism with a rectangular base is called a Cuboid. The sides of the base are length (l) and breadth (b). The height is h. Lateral Surface Area = 2h(l + b) Total Surface Area = 2h(l + b) + 2lb = 2(lb + bh + hl) Longest diagonal = 2 2 2 h b l + + Volume = lbh Cube: If the length, breadth and height of a cuboid are all equal, it is called a cube. Then, if edge of the cube = a Longest diagonal = 3 a Lateral Surface Area = 6a 2 Total surface Area = 6a 2 Volume = a 3 Cylinder : A cylinder can be considered to be a right prism except that instead of identical polygons a cylinder has identical circles for its top and h l b a a a r h base and it has a single lateral surface also called curved surface, instead of several rectangular surfaces. The basic measurements are the radius of the base (or top) r and the height h. Curved Surface (Lateral Surface Area) = 2π rh Total surface Area = 2π rh+2π r 2 = 2π r(h + r) Volume = π r 2 h Hollow Cylinder: The cross section of a hollow cylinder is a ring. Volume of the material of a hollow cylinder = π h(R 2 -r 2 ) Here R is outer radius and r is inner radius of the hollow cylinder. Cone: A cone can be formed from the sector of a circle by rolling it and joining together its two straight edges. If r is the radius of the cone, and R is the radius of the sector of angle θ , then 1. r = R 360 θ × 2. Relation between r, l and h. (the radius, the slant height and height) is l 2 = h 2 +r 2 3. Curved Surface area of Cone = prl 4. Total Surface Area = π rl + π r 2 = π r(l + r) 5. Volume = 3 1 π r 2 h Sphere: All points on the surface of a sphere are at the same distance from the center of the sphere. This distance is called the radius, r. Surface Area of Sphere = 4π r 2 Volume of a Sphere = 3 4 π r 3 The sphere has only one surface and hence only one surface area. Hemisphere: The radius is r. r R h h r r r Curved Surface Area = 2π r 2 Total Surface Area = 2π r 2 +π r 2 = 3π r 2 Volume = 3 2 r π 3 4 2 1 3 = × π r 3 Examples: 1. A cuboid is 20 m x 10 m x 8 m. Find the length of diagonal, surface area and volume. Sol: In a cuboid , Diagonal d = 2 2 2 l b h + + = 2 2 2 20 10 8 + + = 23.75 Surface are S = 2 (20 x 10 + 10 x 8 + 8 x 20) = 880 m 2 Volume = l x b x h = 20 x 10 x 8 = 1600 m 3 . 2. A cube has edge 12 m. Find its length of diagonal, surface area and volume. Sol: In a cube Diagonal d = Edge x 3 = 12 x 3 = 20.78 m Surface area S = 6 x (Edge) 2 = 6 x (12) 2 = 864 m 2 Volume V = Edge 3 = (12) 3 = 1728 m 3 . 3. The base of a right prism is a regular pentagon of side 18 cm. If the height of the prism is 2/3 rd of the side of the base, how much is the lateral surface area (in sq cm) of the prism? Sol: Perimeter of the base of the prism = number of sides x length of each side = 5 x 18 = 90 cm. Lateral surface area of a right prism = (Base perimeter) x (height) = (90) 2 18 3 | | × | \ . = 1080 sq cm 4. If the radius of a sphere is increased by 50%, find the increase percent in volume and the increase percent in the surface area. Sol: Let original radius = R. Then new radius = 150 3R R 100 2 = . Original volume = 3 4 R 3 H , New volume 3 3 4 3R 9 R 3 2 | | H = H | \ . . Increase % in volume = 3 3 19 3 R 100 6 4 R | | H × × | H \ . % = 237.5% Original surface area = 4H R 2 . New surface area = 2 2 3R 4 9 R 2 | | H = H | \ . . Increase % in surface area = 2 2 5 R 100 4 R | | H | × | H \ . % = 125%. 5. A cylinder with base radius of 8 cm and height of 2 cm is melted to form a cone of height 6 cm. Find the radius of the cone? Sol: Let the radius of the cone be r cm. Then, 2 2 1 8 8 2 3 r 6 8 8 2 r 3 6 × × × | | × H × × =H × × × · = | \ . = 64 · r = 8 cm. 6. A brick measures 10 cm x 5 cm x 3 cm. How many bricks will be required for a wall of 100 metre long 6 metre high and 1.5 metre thick? Sol: Volume of the wall = 100 m x 6 m x 1.5 m = 900 m 3 Volume of one brick = 3 1 1 3 3 m m m m 10 20 100 20000 × × = No. of bricks required = 3 900m 3 = 60,00,000 3 20000 m 3 7. What is the maximum length of a pencil which can be inscribed in a box of length 24 units, breadth 3 units and height 4 units? Sol: Maximum length in a cuboid is its diagonal Length of main diagonal is 2 2 2 length breadth height + + = ( ) ( ) ( ) 2 2 2 24 3 2 576 9 4 589 + + = + + = units 8. The height and base-radius of a right circular cone are 10 cm and 24 cm respectively. What is the area of the curved surface area (in sq cm) if the cone? Sol: Curved surface area of a cone = H rl, R and l being radius and slant height. It is given that height h = 10 cm and radius = 24 cm. L2 = h2 + r2 = 102 +242 l = 26 (10 and 24 are in the ratio of 5 : 12; hence l will be the 2 x 13 = 26 Hence, curved surface area = H rl = H x 24 x 26 624H sq cm. Exercise: 1. The surface area of cube is 96 sq cm. Find its volume. 1. 48 cm 3 2. 64 cm 3 3. 16 cm 3 4. 32 cm 3 2. The volume of a cube is 125 cm 3 . Find its surface area. 1. 25 cm 2 2. 375 cm 2 3. 150 cm 2 4. 250 cm 2 3. The diagonal of a cube is 3 cm. Find its surface area. 1. 12 cm 2 2. 102 cm 2 3. 18 cm 2 4. 36 cm 2 4. A cube of 6 cm side melted and smaller cubes of 2 cm side are manufactured. Find the number of smaller cubes so formed. 1. 12 2. 27 3. 24 4. 8 5. Two cubes have their volumes in the ratio 8 : 27. The ratio of their surface areas is ___________ 1. 2 : 3 2. 9 : 4 3. 2 : 9 4. 4 : 9 6. A cube of side 6 cm is cut into a number of cubes, each of side 3 cm. Find the number of cubes. 1. 8 2. 9 3. 24 4. 5 7. The percentage increase in the surface area of a cube when each side is doubled is ______________ 1. 100% 2. 200% 3. 300% 4. 400% 8. How many bullets can be made out of a cube of lead whose edge measures 22 cm each bullet being 2 cm in diameter? 1. 5324 2. 2662 3. 1347 4. 2541 9. The maximum length of a pencil which can be accommodated in a cubical box of 10 cm side. 1. 10 3 cm 2. 5 3 cm 3. 20 3 cm 4. 100 3 cm 10. The length, breadth & height of a cuboid are in the ratio of 4 : 3 : 2 and its volume is 3000 m 3 . Find its surface area. 1. 1300 m 2 2. 1500 m 2 3. 1333 m 2 4. 27000 m 2 11. Two cubes each with 6 cm edge are joined end to end. The surface area of the resulting cuboid is ___________ 1. 360 cm 2 2. 36 cm 2 3. 216 cm 2 4. 360 m 2 12. Find the area of the four walls of a room of 6 m x 4 m x 3 m. 1. 120 m 3 2. 84 m 3 3. 42 m 3 4. 60 m 3 13. The dimensions of a room are 200 m x 15 m x 10 m. What is the cost of painting its four walls at the rate of Rs.15 per 100 sq m? 1. Rs.70 2. Rs.105 3. Rs.225 4. None 14. The dimensions of a room are 16 m x 10 m. There are 2 doors 5 m x 4 m and 4 windows 5 m x 2.5 m. What is the cost of painting the wall and the top at the cost of Rs.1.50 per 10 sq m? 1. Rs.96 3 Rs.112.5 3. Rs.126 4. None 15. A well with 14 m inside diameter is dug 10 m deep. Earth taken out of it has been evenly spread all around it to a width of 21 m to form an embankment. The height of the embankment is ____ 1. 2 1 m 2. 3 2 m 3. 4 3 m 4. 5 3 m 16. The radius and height of a cylinder are 6 cm & 14 cm respectively. Find the ratio of its curved surface area and volume. 1. 1584 : 528 2. 36 : 196 3. 528 : 1584 4. None 17. The radius and height of a cylinder are in the ratio of 2 : 1 and its volume is 616 cubic cm. Find its curved surface area. 1. 1848 cm 2 2. 627 cm 2 3. 612 cm 2 4. 672 cm 2 18. The radii of two cylinders are in the ratio 2 : 3 and the heights are in the ratio of 3 : 4. Find the ratio of their volumes. 1. 4 : 3 2. 3 : 1 3. 1 : 3 4. 6 : 12 19. A cylinder of radius 2 cm is melted and 11 cubes of 2 cm side are manufactured. Find the height of the cylinder melted. 1. 7 cm 2. 15 cm 3. 44 cm 4. 11 cm 20. Two circular cylinders of equal volumes have their heights in the ratio 2 : 1. The ratio of their radii is _________ 1. 2 : 1 2. 1 : 2 3. 1 : 2 4. 2 : 1 21. If the radius of the base of a right circular cylinder is halved, keeping the height same, what is the ratio of the volume of the reduced cylinder to that of original one? 1. 1 : 4 2. 1 : 8 3. 1 : 2 4. 8 : 1 22. In what ratio are the volumes of a cylinder, a cone and a sphere, if each has the same diameter and the same height? 1. 1 : 3 : 2 2. 2 : 3 : 1 3. 3 : 1 : 2 4. 3 : 2 : 1 23. Two cylindrical jars have their diameters in the ratio of 3 : 1 and their heights in the ratio of 1 : 3. The volumes are in the ratio of __________ 1. 1 : 2 2. 3 : 1 3. 6 : 1 4. 1 : 2 24. The radius of sphere is 21 cm. Find its surface area and volume. 1. 5544 cm 3 ; 38808 cm 2 2. 5454 cm 2 ; 38808 cm 3 3. 5544 cm 2 ; 38088 cm 3 4. 5544 cm 2 ; 38808 cm 3 25. Volumes of two spheres are in the ratio of 729 : 343. Find the ratio of their surface areas. 1. 49 : 81 2. 343 : 729 3. 7 : 9 4. 81 : 49 26. A sphere and a cube have equal surface areas. Find the ratio of the volume of the sphere to that of the cube. 1. 2a : r 2. 2r : a 3. r : 2a 4. a : 21 27. The radius of a sphere is increased by 50%. The increase in the surface area of the sphere is _______ 1. 100% 2. 125% 3. 150% 4. None 28. If the radius of a sphere is doubled, then its surface area is increased by _______ 1. 50% 2. 100% 4. 300% 4. 200% 29. If the surface areas of two spheres are in the ratio of 4 : 25, then the ratio of their volumes is ________ 1. 4 : 25 2. 25 : 4 3. 8 : 125 4. 125 : 8 30. The radius of a cylinder is the same as that of a sphere. Their volumes are equal. The height of the cylinder is how many times its radius? 1. 3 4 2. 3 2 3. 1 4. 2 Comprehensive Test – II (Chapters 5 – 7) 1. Travelling at 3/5 th of his actual speed a man is late by 20 min. What is the actual time he takes? a. 25 min b. 30 min c. 40 min d. 35 min 2. A person covered 1/4 th of the distance at 16kmph and the remaining at 24 kmph. His average speed is a. 22.66 b. 21.33 c. 22.33 d. 21.66 3. A person takes 20 min to cover a distance by decreasing his speed by 20%. What time he takes at 50% speed? a. 24 min b. 30 min c. 32 min d. 36 min 4. Travelling from his house art 30 kmph a person reaches his office 5 min late. If he increases speed by 10 kmph, he is early by 15min. The distance to the office is a. 36 km b. 32km c. 30 km d. 40 km 5. A train A started from X at 72 kmph and after 30s another train B started from same station and meets A after 15s. The speed of B is a. 50 kmph b. 135 kmph c. 144 kmph d. None 6. A train 180m long crossed 120m long platform in 20s and another train at same speed crossed a pole in 10s. In what time can these trains cross each other in opposite directions? a. 11s b. 13s c. 12s d. 14s 7. Two trains each of 100m long pass each other in same direction in 60s and in opposite directions in 10s. The speed of the slower train is a. 30 kmph b. 42 kmph c. 48 kmph d. 60 kmph 8. A boat travels 12 km downstream in 48min. If the speed of the streram is 2 kmph then the speed of the boat is a. 13 kmph b. 15 kmph c. 17 kmph d. None 9. A man rows 40 km upstream in 8 hrs and 36 km downstream in 6 hrs. The speed in still water is a. 0.5 b. 5.5 c. 6 d. 5 10. In a stream running at 2kmph, a man goes 10 km upstream and comes back in 55min. Find his speed in still water. a. 20 b. 22 c. 24 d. 28 11. A can do a work in 10 days and B can do it in 20 days. With the help of C they do it in 5 days. In how many days can C alone do it? a. 20 b. 10 c. 35 d. 15 12. 12 men complete a work in 18 days. 6 days after they start 4 men join them. How many more days are required to do it? a. 10 b. 15 c. 12 d. 9 13. A and B can do a work in 10 and 12 days. They start the work and B leaves after two days. If daily wages are Rs. 20 for each how much does A get? a. 160 b. 180 c. 200 d. None 14. A and V together can do a work in 7 days. If A does twice as much work as V, how long does A alone take to do it? a. 6.33 days b. 10.5 days c. 11 days d. None 15. 24 men working 8hrs a day can do a work in 10 dyas. In how many days 32 men working 10 hrs a day do it? a. 10 b. 6 c. 5 d. 8 16. Pipe A can fill a tank in 16min and pipe B can empty it in 24 min. If both are opened after how many min should B be closed to fill the tank in 30min? a. 20 b. 21 c. 23 d. 22 17. Two pipes can fill a tank in 18min and 27min. A third pipe can empty it in 6 min. All three are opened with tank 2/3 full. In how many min will it be empty? a. 11 b. 9 c. 13 d. 7 18. A, B and C can fill a tank in 12, 24, 48 min. They are opened together but B is closed 3 min before and C closed 2 min before filling the tank. In how many min was the tank full? a. 6 b. 8 c. 7 d. 9 19. P, Q and R can fill a ank n 20, 30 and 60 hrs. If they are opened in rotation, one hour each starting with P in how many hrs will the tank be full? a. 28.33 b. 30 c. 32 d. 34 20. Two pipes A and B can fill a tank in 10min and 15 min and C can empty it in 5 min. A and B are opened for 4 min and then C is also opened. In how many min tank will be empty? a. 16 b. 18 c. 20 d. 25 21. What is the ratio of areas of in-circle to that of circumcircle of a square? a. 1`:5 b. 1:2 c. 2:1 d. None 22. The front wheels of a wagon are 3pi feet in circumference and the rear wheels are 4pi feet. When the front ones make 12 more revolutions than the rear ones, how many feet will the wagon move? a. 48pi b. 56pi c. 64pi d. None 23. Three circles of radius 4.2 cm are placed in such a way that each touches the other two. The are enclosed between them is a. 28 b. 29 c. 30 d. None 24. A person uses a sheet measuring 30cmX40 cm. If margin of 3 cm is left on each side of the sheet the percentage of the paper used for typing is a. 50 b. 68 c. 80 d. None 25. The length of a rectangle is increased by 20% and its breadth is decreased by 8%. Then what is the % change in area? a. 10 b. 20 c. 30 d. 40 26. The radius of a cylinder is increased by 20% and height is decreased by 33.33%, then what is the % change in volume? a. 4 b. 8 c. 33 d. 20 27. The area of a square is increased by 69%. The % increase in its side is a. 13 b. 15 c. 30 d. 40 28. The base radius of a cone and cylinder are in the ratio of 2:3 and their heights are in the ratio of 3:2. The ratio of their volumes is a. 1:1 b. 2:3 c. 3:2 d. None 29. What is the maximum volume of a cube that can be cut from a spherical wood of diameter 6cm? a. 216 b. 27 c. 64 d. None 30. If a sphere of radius 7cm was melted and moulded into a cylinder of same radius, find the height of the cylinder. a. 2.1 cm b. 1.4 cm c. 9.33 cm d. none Interest Read this please: Raju borrowed Rs.1000 from Ramesh. After some days Raju paid back Rs.1200 to Ramesh. Means Raju paid Rs.200 excess than the amount he borrowed from Ramesh. - This excess amount is called interest. - The total amount of money borrowed by Raju from Ramesh is called the Principal or Sum. - The money paid back to Ramesh, which is the combination of both Principal and interest is called the Amount. - So, Amount = Principal + Interest Rate of interest: The interest is usually charged according to a specified term, which is expressed as some per cent of the principal and is called the rate of interest for the fixed period of time. - If the fixed period is a year, the rate of interest is charged annually. - If the fixed period is six months, the rate of interest is charged semi- annually. - If the fixed period is three months, the rate of interest is charged quarterly. - If the fixed period is a month, the rate of interest is charged monthly. Example: If the rate of interest is 10% per annum, then the interest payable on Rs.100 for one year is Rs.10. Simple Interest: When the interest is payable on the principal only, it is called the simple interest. It is the interest calculated on the principal for the entire period it is borrowed. It is denoted by S.I. Example: S.I. on Rs.100 at 10% per annum will be Rs.10 each year. At the end of one year, the total amount will be Rs.100+10 = Rs.110. At the end of second year, the total amount will be Rs.100+10+10 = Rs.120 and so on. Formulae: 1. If P stands for Principal, R the rate per cent per annum, T the number of years, A the amount and S.I. the simple interest then S.I. = 100 R T P × × 2. T R . I . S 100 P × × = 3. % T P . I . S 100 R × × = 4. R × P . I . S × 100 = T years 5. Amount, ( ¸ ( ¸ + = 100 RT 1 P A 6. If a certain sum in T years at R% per annum amounts to Rs.A, then the sum will be ) T R ( 100 A 100 P × + × = . 7. The annual payment that will discharge a debt of Rs.A due in T years at R% per annum = 2 ) 1 T ( RT T 100 A 100 ÷ + × . 8. If a certain sum is invested in n types of investments in such a manner that equal amount is obtained on each investment where interest rates are R1,R2,…….,Rn respectively and time periods and time periods are T1,T2,…., Tn respectively, then the ratio in which the amounts are invested is n n 2 2 1 1 T R 100 1 .... .......... .......... : T R 100 1 : T R 100 1 + + + . 9. If a certain sum of money becomes n times itself in T years at S.I., then the rate of interest per annum is, % T ) 1 n ( 100 R ÷ = . 10. If a certain sum of money becomes n times itself at R% per annum S.I. in T years, then 100(n 1) T R ÷ = years. 11. If a certain sum of money becomes n times itself in T years at a simple interest, then the time ' T in which it will become m times itself is given by = T ' m 1 T n 1 ÷ ( × ( ÷ ¸ ¸ years. 12. If the rate of interest (R) changes from R1 to R2 and P, T are constant, then Change in S.I. = ) R R ( 100 PT 2 1 ÷ × . 13. If Principal (P) changes from P1 to P2 and R, T are constant, then Change in S.I. = ) P P ( 100 RT 2 1 ÷ × . 14. If Rate (R) Changes from R1 to R2 and time (T) changes from T1 to T2 but principal (P) is constant, then Change in S.I. = ) T R T R ( 100 P 2 2 1 1 ÷ × . 15. If a debt of Rs.X is paid in n number of installments and if the value of each installment is a, then the borrowed (debt) amount is given by 2 ) 1 n ( n b 100 Ra na X ÷ × × + = . Where, R is the rate of interest per annum b is the no. of installments per year Note: b = 1, when each installment is paid yearly. b = 2, when each installment is paid half-yearly. b = 4, when each installment is paid quarterly. b = 12, when each installment is paid monthly. 16. If a certain sum of money P lent out at S.I. amounts to A1 in T1 years and to A2 in T2 years, then, 1 2 1 2 2 1 T ~ T T A T A = P ~ and % 100 × T A T A A ~ A = R 1 2 2 1 2 1 ~ 17. If a certain sum of money P lent out for a certain time T amounts to A1at R1% per annum and to A2 at R2% per annum, then 2 1 2 1 1 2 R R R A R A = P ~ ~ and . years 100 × R A R A A A = T 2 1 1 2 2 1 ~ ~ 18. If an amount P1 lent at S.I. rate of interest R1% p.a. and another amount P2 at S.I. rate of R2% p.a., then the rate of interest for the whole sum is ( ¸ ( ¸ + + = 2 1 2 2 1 1 P P R P R P R . 19. If a certain sum of money is lent out in n parts in such a manner that equal sum of money is obtained as S.I. on each part where interest rates are R1,R2,……,Rn respectively and time periods are T1,T2,…..,Tn respectively, then the ratio in which the sum will be divided in n parts is given by . T R 1 .... .......... .......... : T R 1 : T R 1 n n 2 2 1 1 20. If there is a change in principal (P), rate of interest (R) and time (T), then the value of S.I also changes and is given by 2 2 2 1 1 1 2 2 1 1 2 2 2 1 1 1 2 1 T R P T R P P A P A T R P T R P I . S I . S × × × × = ÷ ÷ ¬ × × × × = 21. Out of a certain sum P, x 1 part is invested at R1%, y 1 part is invested at R2% and the remainder ( ¸ ( ¸ ÷ ÷ y 1 x 1 1 say, z 1 part at R3%. If the annual income from all these investments is Rs.A, the original sum is given by ( ( ( ( ¸ ( ¸ + + × = z R y R x R 100 A P 3 2 1 . Examples: 1. Find the S.I. on Rs.3500 for 3 years at 5% per annum. Sol: Here, P = Rs.3500, T = 3 years and R = 5% S.I. = 525. . Rs 100 5 3 3500 = × × 2. Find the Principal, if S.I. = 624 for 2 years at 3% per annum. Sol: 0400. 1 . Rs 3 2 624 100 T R . I . S 100 P = × × = × × = 3. At what rate per annum will a sum of Rs.4000 amount to Rs. Rs.6000 in 5 years? Sol: S.I. = 6000 – 4000 = 2000 %. 10 5 4000 2000 100 T P . I . S 100 R = × × = × × = 4. In what time will Rs.1500 earn an interest of Rs.150 at 2% per annum? Sol: . years 5 2 1500 150 100 R P . I . S 100 T = × × = × × = 5. Sunny borrowed Rs.2000 from his friend Praveen at 10% per annum for 5 years. Find the interest and money returned by Sunny to Praveen. Sol: S.I. = 2000 5 10 1000 100 × × = A = P + S.I. = 2000 + 1000 = Rs.3000 6. What sum will amount to Rs.420 at 2% per annum in 2 1 2 years? Sol: 400 . Rs 105 420 100 ) 2 5 2 ( 100 420 100 ) 2 1 2 2 ( 100 420 100 ) T R ( 100 A 100 P = × = × + × = × + × = × + × = 7. Find the annual installment that will discharge a debt of Rs.16200 in 5 years at 4% per annum. Sol: Annual installment = 2 ) 1 T ( RT T 100 A 100 ÷ + × = . 3000 . Rs 540 16200 100 2 80 500 16200 100 2 ) 1 5 ( 5 4 ) 5 ( 100 16200 100 = × = + × = ÷ × × + × 8. A sum of Rs.3454 is divided among three such parts that amount obtained on these three parts of money after 3, 4 and 5 years, respectively at rate of 5% per annum remains equal. Find such three parts of the sum. Sol: The three parts will be in the ratio n n 2 2 1 1 T R 100 1 .... .......... .......... : T R 100 1 : T R 100 1 + + + = 125 1 : 120 1 : 115 1 ) 5 5 ( 100 1 : ) 4 5 ( 100 1 : ) 3 5 ( 100 1 = × + × + × + = 552 : 575 : 600 125 69000 1 : 120 69000 1 : 115 69000 1 = × × × [Since the L.C.M. of 115, 120 and 125 is 69000.] Ratio = 552 : 575 : 600 Sum of proportional = 600 + 575 + 552 = 1727 1 st part = 1200 . Rs 3454 1727 600 = × 2 nd part = 1150 . Rs 3454 1727 575 = × 3 rd part = . 1104 . Rs 3454 1727 552 = × 9. A certain sum of money quadruples itself in 6 years S.I. Find the rate percent per annum. Sol: %. 50 = 6 ) 1 4 ( 100 = % T ) 1 n ( 100 = R 10. In what time a sum of money will double itself at a rate of S.I. of 6% per annum? Sol: years 3 2 16 6 4 16 100 6 ) 1 2 ( years 100 R 1 n T = = × ÷ = ( ¸ ( ¸ × ÷ = 11. A sum of money put on S.I. doubles itself in 10 years. In how many years would it quadruple itself? Sol: Required Time, ' T = 4 1 10 2 1 ÷ ( × ( ÷ ¸ ¸ = 30 years. 12. If simple interest on Rs.500 increases by Rs.20, when the rate % increases by 8% per annum, find the time. Sol: Change in S.I. = ) R R ( 100 PT 2 1 ÷ × . years 2 1 T T 40 20 8 100 T 500 20 = ¬ = ¬ × = ¬ 13. If the S.I. on Rs.3500 be more than the interest on Rs.2000 by Rs.60 in 4 years, then find the rate per cent per annum. Change in S.I. = ) P P ( 100 RT 2 1 ÷ × %. 1 R 1500 100 R 4 60 ) 2000 3500 ( 100 R 4 60 = ¬ × = ¬ ÷ × = ¬ 14. If the S.I. on a certain sum at 3% per annum for 5 years is Rs.90 more than the interest on the same sum for 2 years at 6% per annum. Find the sum. Sol: Change in S.I. = ) T R T R ( 100 P 2 2 1 1 ÷ × . 3000 . Rs P 3 100 P 90 ) 6 2 5 3 ( 100 P 90 = ¬ × = ¬ × ÷ × × = ¬ 15. A sum of Rs.4 is lent to be paid back in 3 equal monthly installments of Re.1 each. Find the rate percent. Sol: Here, X = Rs.4, a = Re.1, n = 3, b = 12, R = ? 2 ) 1 n ( n b 100 Ra na X formula, Required ÷ × × + = %. 400 R 1600 R 1200 400 R 1200 4 3 1200 R 3 4 2 ) 1 3 ( 3 12 100 1 R ) 1 ( 3 4 = ¬ = + ¬ + = ¬ × + = ¬ ÷ × × × + = ¬ 16. Anitha deposits Rs.8000 in S.B.I at 2% per annum and Rs.6000 at 5% per annum in ICICI bank. Find the rate of interest for the whole sum. Sol: Required rate, ( ¸ ( ¸ + + = 2 1 2 2 1 1 P P R P R P R %. 14 5 1 14000 19000 6000 8000 5 6000 2 8000 = = + × + × = 17. If a sum of Rs.3800 is divided into two such parts that the S.I. on the first part for 2 1 1 years at the rate of 2% per annum, equals the S.I. on the second part for 4 years at the rate of 4% per annum, then find two such divisions of the sum. Sol: Required Ratio = 2 2 1 1 T R 1 : T R 1 1 st part: 2 nd part = 3 : 16 16 1 : 3 1 4 4 1 : 2 1 1 2 1 = = × × Sum of proportionals = 16 + 3 = 19 So, 1 st part = 3200 . Rs 3800 19 16 = × 2 nd part = 600 . Rs 3800 19 3 = × . 18. If Rs.50 amounts to Rs.85 in 2 years, what Rs. 340 amount to in 15 years at the same rate? Sol: By using, 2 2 2 1 1 1 2 2 1 1 T R P T R P P A P A × × × × = ÷ ÷ we get 2 2 2 2 2 85 50 85 R 2 A 340 340 R 15 35 170 35 1 A 340 340 15 A 340 2 15 A 340 30 35 1050 A 1050 340 1390 ÷ × × = ÷ × × ¬ = ¬ = ÷ × ÷ × ¬ ÷ = × = ¬ = + = 19. From a certain sum Krishna invested, th 4 1 at 2%, th 5 1 at 4% and the rest at 6%. If the annual income of Krishna is Rs.1840 from all these investments, then find the original sum. Sol: Required formula is, ( ( ( ( ¸ ( ¸ + + × = z R y R x R 100 A P 3 2 1 5 1 y 1 , 4 1 x 1 = = and 20 11 20 4 5 20 5 1 4 1 1 y 1 x 1 1 z 1 = ÷ ÷ = ÷ ÷ = ÷ ÷ = Original sum = 11 20 6 5 4 4 2 100 1840 + + × . 000 , 40 . Rs 20 92 100 1840 20 66 16 10 100 1840 20 66 5 4 4 2 100 1840 = × × = + + × = + + × = Exercise: 1. Find the S.I. on Rs.16,000 for 3 years 3 months at 4 ½ % per annum? 1. Rs.5200 2. Rs.1800 3. Rs.2340 4. None 2. Find the S.I. on Rs.12,000 for 8 years 4 months at 3% p. a.? 1. Rs.2000 2. Rs.15000 3. Rs.3000 4. None 3. On what Sum of money will the S.I. for 7 years 6 months at 5% p.a. be Rs.450? 1. Rs.11,000 2. Rs.1200 3. Rs.13000 4. Rs.12,000 4. The S.I. on the certain Sum of money for 2 years at 8% p.a. is Rs.2560. What is the Sum? 1. Rs.16000 2. Rs.15000 3. Rs.13000 4. None 5. In what time will the S.I. on Rs.4000 at 7.5% be Rs.1050? 1. 2 ½ years 2. 5 ½ years 3. 3 ½ years 4. None 6. At what rate% per annum will the S.I. on Rs.2500 be Rs.750 for 3 years? 1. 15% 2. 10% 3. 20% 4. None 7. What Sum will amount to Rs.3300 in 2 years 6 months at 15% p.a. S.I.? 1. Rs.2000 2. Rs.2400 3. Rs.2800 4. Rs.2500 8. What Sum will amount to Rs.8160 in 4 ½ years at 8% p.a. S.I.? 1. Rs.6600 2. Rs.5000 3. Rs.6000 4. 7000 9. In how many years will a Sum of money becomes double at 5% p.a. S.I.? 1. 18 years 2. 20 years 3. 15 years 4. None 10. At what rate% p.a. a Sum of money becomes four times of itself in 15 years? 1. 8% 2. 10% 3. 15% 4. 20% “The aim of education is the knowledge not of fact, but of values.” 11. At what rate% p.a. a Sum of money becomes three times in 12 years 6 months? 1. 15% 2. 14% 3. 16% 4. None 12. A Sum of money becomes triple of itself in 8 years at S.I. In twelve years, it will become how many times at the same rate? 1. 6 times 2. 4 times 3. 5 times 4. None 13. A Sum of money becomes double itself in 4 years. In twelve years, it will become how many times at the same rate? 1. 6 times 2. 4 times 3. 3 times 4. None 14. A man deposited Rs.9000 in a bank at 6% p.a. for 4 years. For how many years, must another man deposit an amount of Rs.5400 at 5% p.a. in another bank so that both of them get the same interest? 1. 6 years 2. 4 years 3. 3 years 4. None 15. A Sum of Rs.450 amounts to Rs.495 in two years. In what time will the Sum of Rs.820 amounts to Rs.943 at the same rate? 1. 3 years 2. 2 years 3. 6 years 4. None 16. The S.I. on a Sum of money will be Rs.600 after 10 years. If the S.I. (or Principal) is tripled after 5 years find the total S.I. at the end of 10 years? 1. Rs.3000 2. Rs.1200 3. Rs.1000 4. None 17. A certain Sum of money amounts to Rs.1680 in 3 years and to Rs.1920 in 7 years. What is the Sum? 1. Rs.3000 2. Rs.1200 3. Rs.1000 4. None 18. A Sum of money amounts to Rs.3000 in 2 years and Rs.4250 in 7 years. What is rate% p.a.? 1. 9% 2. 10% 3. 3% 4. 7% 19. A Sum of money amounts to Rs.312 at 4% p.a. interest, Rs.324 at 8% interest p.a. Find the Principal and time period? 1. Rs.300, 1 year 2. Rs.200, 1 year 3. Rs.100, 1 year 4. None 20. A Sum was put at S.I. at a certain rate for 3 years. Had it been at 1% higher rate, it would have fetched Rs.36 more. What is the Sum? 1. Rs.1000 2. Rs.1800 3. Rs.1200 4. Rs.1600 21. A man deposited certain amount in a bank at 4% p.a. for 7 years. However, he would get Rs.380 less as interest, if he deposits the same amount at 3% p.a. for 3 years. What is the Sum? 1. Rs.2400 2. Rs.2600 3. Rs.2000 4. Rs.1500 22. A lent Rs.600 to B for 2 years and Rs.150 to C for 4 years and received Rs.90 as a S.I. in all. Find the rate% p.a. 1. 4% 2. 6% 3. 5% 4. None 23. The S.I. on a certain Sum of money is 2/5 of the Principal. If the time period is 4 years, what is the rate % p.a.? 1. 8% 2. 6% 3. 10% 4. None 24. The S.I. on a Sum of money is 4/9 of the Principal and its rate% p.a. is equal to the number of years. What is the time period? 1. 8 years 6 months 2. 6years 2 months 3. 6 years 8 months 4. None 25. A part of certain Sum of money is invested at 8% p.a. S.I. and the rest at 6% p.a. If the interests earned in each case for the same period are equal, the ratio of the Sum invested is _____. 1. 3 : 5 2. 3 : 4 3. 5 : 3 4. 1 : 5 26. Rs.15000 is invested partly at 5% and rest 8% p.a. The whole annual interest received was Rs.930. What is the amount lent at 8% per annum? 1. Rs.9000 2. Rs.8000 3. Rs.6000 4. None 27. Rs.26,650 is lent into two parts so that the interest on first part for 3 years at 5% may be equal to the interest for 8 years at 3% p.a. What is the second Sum? 1. Rs.10,000 2. Rs.10,750 3. Rs.10,250 4. None 28. What annual payment will discharge a debt of Rs.2210 due at 7% p.a. in 4 years? 1. Rs.480 2. Rs.400 3. Rs.500 4. None 29. A money lender finds that due to fail in the rate of interest from 8% to 7 ¾%, his yearly income diminishes by Rs.61.50. His capital at ______. 1. Rs.24,600 2. Rs.24,000 3. Rs.3,000 4. Rs.35,000 30. A man invested 1/3 of his capital at 7%, ¼ at 8% and the remaining at 10%. If his annual income is Rs.561, find his capital. 1. Rs.6000 2. Rs.6600 3. Rs.7000 4. None 31. Find the S.I. on Rs.200 for 7 months at 5 paise per rupee per month. 1. Rs.60 2. Rs.70 3. Rs.80 4. None 32. If the interest on Rs.1200 be more than the interest on Rs.1000 by Rs.50 in 3 years. Find the rate%. 1. 8% 2. 8 1/3% 3. 9% 4. None 33. Rs.1200 amount to Rs.1632 in 4 years at a certain rate of S.I. If the rate of interest increased by 1%, it amounts to how much S.I.? 1. Rs.400 2. Rs.500 3. Rs.350 4. Rs.480 34. If the S.I. on Rs.2000 increased by Rs.40, then the rate% is increased by 2% p.a., find the time? 1. 12 years 2. 3 years 3. 2 years 4. 1 year 35. If Rs.85 amounts to Rs.95 in 3 years, what Rs.102 will amount in 5 years at the same rate%? 1. Rs.122 2. Rs.150 3. Rs.200 4. Rs.300 36. A father left a will of Rs.68,000 to be divided between his two sons aged 10 years and 12 years such that they may get equal amount when each attain 18 years. If the money reckoned at 10% p.a., find how much each gets at the time of the will in thousands? 1. 30, 38 2. 34, 34 3. 32, 36 4. None 37. A Sum of money doubles itself in 7 years. In how many years it becomes four- fold? 1. 11 years 2. 12 years 3. 21 years 4. 42 years 38. If x is the S.I. on y, and y is the S.I. on z, rate% and time period being the same in both cases, what is the relation between x, y and z? 1. z y x 2 = 2. z x y 2 = 3. y x z 2 = 4. xyz = 1 39. What annual payment will discharge a debt of Rs.2160 due in 2 years at 16% p.a. S.I.? 1. Rs.1000 2. Rs.1600 3. Rs.250 4. Rs.360 40. Ram lent Rs.750 to Raghu for 5 years and to Rs.800 to Raju for 4 ½ years and got Rs.1470 S.I. from both the cases. Find the rate%. 1. 25% 2. 22% 3. 20% 4. 15% Compound Interest: In this method, the interest for each period is added to the principal before; interest is calculated for the next period. So, the principal grows as the interest is added to it. It is denoted by C.I. Formulae: 1. If a principal P is given on C.I. at the rate of interest R% p.a., then the Amount A after t years is . 100 R 1 P A t ( ¸ ( ¸ + = 2. C.I. = A – P = ( ( ¸ ( ¸ ÷ | | . | \ | + = ÷ ( ¸ ( ¸ + 1 100 R 1 P P 100 R 1 P t t 3. Rate of interest (R) = . a . p % 1 P A 100 t 1 ( ( ( ¸ ( ¸ ÷ | | . | \ | × Note: S.I. and C.I. for 1 year at a given rate of interest per annum are always equal. 4. If the interest is compounded half-yearly, then a) Amount, . 2 100 R 1 P A t 2 ( ¸ ( ¸ × + = b) C.I. = ( ( ¸ ( ¸ ÷ | | . | \ | × + 1 2 100 R 1 P t 2 . c) Rate (R) = . a . p % 1 P A 100 2 2 t 1 ( ( ( ¸ ( ¸ ÷ | | . | \ | × × × 5. If the interest is compounded quarterly, then a) Amount, . 4 100 R 1 P A t 4 ( ¸ ( ¸ × + = b) C.I. = ( ( ¸ ( ¸ ÷ | | . | \ | × + 1 4 100 R 1 P t 4 . c) Rate (R) = . a . p % 1 P A 100 4 4 t 1 ( ( ( ¸ ( ¸ ÷ | | . | \ | × × × 6. If the interest is compounded n times a year, then a) Amount, . n 100 R 1 P A t n× ( ¸ ( ¸ × + = b) C.I. = ( ( ¸ ( ¸ ÷ | | . | \ | × + × 1 n 100 R 1 P t n . c) Rate (R) = . a . p % 1 P A 100 n n t 1 ( ( ( ¸ ( ¸ ÷ | | . | \ | × × × 7. If the rate of interest is different for different years, say R1%, R2%, R3% for first, second and third years respectively, then Amount, . 100 R 1 100 R 1 100 R 1 P A 3 2 1 | | . | \ | + | | . | \ | + | | . | \ | + = 8. If the time is in the form of fraction, say z y x years, then Amount, . 100 R z y 1 100 R 1 P A x | | | | . | \ | + × | | . | \ | + = 9. The difference between the C.I. and the S.I. on a certain sum of money f or 2 years at R% p.a., is a) C.I. – S.I. = 2 100 R P | | . | \ | if P and R are given b) C.I. – S.I. = 100 2 . I . S R × × if S.I. and R are given 10. The difference between the C.I. and the S.I. on a certain sum of money for 3 years at R% p.a., is a) C.I. – S.I. = ( ( ¸ ( ¸ | | . | \ | + | | . | \ | 2 3 100 R 3 100 R P if P and R are given b) C.I. – S.I. = ( ( ¸ ( ¸ | | . | \ | + | | . | \ | 100 R 3 100 R 3 . I . S 2 if S.I. and R are given 11. If a certain sum becomes n times in t years at C.I., a) Then the same sum becomes n t in mt years. b) Rate of C.I., %. 1 ) n ( 100 R t 1 ( ( ¸ ( ¸ ÷ = 12. If a certain sum of money at C.I. amounts to Rs.x in A years and to Rs.y in B years, then the rate of interest p.a. is %. 100 1 x y R A B 1 × ( ( ( ¸ ( ¸ ÷ | | . | \ | = ÷ 13. If a loan of Rs.P at R% C.I. p.a., is to be repaid in n equal yearly installments, then the value of each installment = n 2 R 100 100 ........ R 100 100 R 100 100 P . Rs | | . | \ | + + + | | . | \ | + + | | . | \ | + . Examples 1. Ravi invested Rs.25000 at C.I. rate 4% p.a., for a period of 3 years. What amount will he receive at the end of 2 years? Sol: P = Rs.25000, R = 4%, t = 3 years, A =? . 60 . 121 , 28 . Rs 25 26 25 26 25 26 25000 100 4 1 25000 100 R 1 P A 3 t = × × × = ( ¸ ( ¸ + = ( ¸ ( ¸ + = 2. Find the C.I. on Rs.2000 for 2 years at 5% p.a. Sol: P = Rs.2000, R = 5%, t = 2 years, C.I. =? C.I. = ( ( ¸ ( ¸ ÷ | | . | \ | + 1 100 R 1 P t = ( ( ¸ ( ¸ ÷ | | . | \ | = ( ( ¸ ( ¸ ÷ | | . | \ | + 1 20 21 2000 1 100 5 1 2000 2 2 . 205 . Rs ) 1025 . 0 ( 2000 ) 1 025 . 1 ( 2000 = = ÷ = 3. Ram invested Rs.5548 for 3 years at C.I. and received an amount of Rs.6750 on maturity. What is rate percent? Sol: P = Rs.5548, A = Rs.6750, t= 3 years, R =? Rate of interest (R) = . a . p % 1 P A 100 t 1 ( ( ( ¸ ( ¸ ÷ | | . | \ | × % 1 2774 3375 100 % 1 5548 6750 100 3 1 3 1 ( ( ( ¸ ( ¸ ÷ | | . | \ | = ( ( ( ¸ ( ¸ ÷ | | . | \ | × = . a . p %. 7 1 7 7 50 14 100 % 1 14 15 100 % 1 14 15 100 3 1 3 = = = ( ¸ ( ¸ ÷ = ( ( ( ( ¸ ( ¸ ÷ | | . | \ | | | . | \ | × = 4. Find the amount of Rs.16000 in 2 1 1 years at 10% p.a., C.I. payable half- yearly. Sol: P = Rs.16000, R = 10%, t = 2 1 1 = 2 3 years, A =? Amount, t 2 2 100 R 1 P A ( ¸ ( ¸ × + = . 522 , 18 . Rs 9261 2 8000 ) 21 ( 16000 20 21 16000 2 100 10 1 16000 3 3 2 3 2 = × = × = | | . | \ | = ( ¸ ( ¸ × + = × 5. Find the C.I. on Rs.8192 at 50% p.a., compounded quarterly for 1 year. Sol: P = Rs.8192, R = 50%, t = 1 year, C.I. =? C.I. = ( ( ¸ ( ¸ ÷ | | . | \ | × + 1 4 100 R 1 P t 4 4930 . Rs 4096 2465 8192 4096 4096 6561 8192 1 8 9 8192 1 4 100 50 1 8192 4 1 4 = × = | | . | \ | ÷ = ( ( ¸ ( ¸ ÷ | | . | \ | = ( ( ¸ ( ¸ ÷ | | . | \ | × + = × 6. Find the C.I. on Rs.2000 at 12% p.a. for 2 months compounded monthly. Sol: P = Rs.2000, R = 12%, t = 2 months = years 6 1 12 2 = , C.I. =? C.I. = ( ( ¸ ( ¸ ÷ | | . | \ | × + × 1 12 100 R 1 P t 12 | | 40.2. . Rs 0201 . 0 2000 1 0201 . 1 2000 1 100 101 2000 1 12 100 12 1 2000 2 6 1 12 = × = ÷ = ( ( ¸ ( ¸ ÷ | | . | \ | = ( ( ( ¸ ( ¸ ÷ | | . | \ | × + = × 7. Lakshmi invests Rs.50000 in a mutual fund which gives interest at 2% p.a., during first year, 5% during the second year and 8% during the third year. How much does she get at the end of the third year? Sol: P = Rs.50000, R1 = 2%, R2 = 5%, R3 = 8% Amount at the third year, | | . | \ | + | | . | \ | + | | . | \ | + = 100 R 1 100 R 1 100 R 1 P A 3 2 1 | | . | \ | + | | . | \ | + | | . | \ | + = 100 8 1 100 5 1 100 2 1 50000 57834. . Rs 25000 28917 50000 25 27 20 21 50 51 50000 = × = | | . | \ | | | . | \ | | | . | \ | = 8. What will be the C.I. on Rs.93750 for 2 1 2 years at 4% p.a.? Sol: P = Rs.93750, t= 2 1 2 years, R = 4%. Required C.I. = ( ( ( ( ¸ ( ¸ ÷ | | | | . | \ | + × | | . | \ | + 1 100 R z y 1 100 R 1 P x 9678 . Rs 31250 3226 93750 1 50 51 25 26 25 26 93750 1 100 4 2 1 1 100 4 1 93750 2 = × = ( ¸ ( ¸ ÷ × × × = ( ( ( ( ¸ ( ¸ ÷ | | | | . | \ | × + × | . | \ | + × = 9. Find the difference between C.I. and S.I. on a sum of Rs.6250 put for 2 years at 4% p.a. Sol: P = Rs.6250, t = 2 years, R = 4% For 2 years, C.I. – S.I. = 2 100 R P | | . | \ | if P and R are given 10 . Rs 25 1 25 1 6250 100 4 6250 2 = × × = | | . | \ | × = 10. The difference between C.I. and S.I. on a certain sum of money for 3 years, at 4% p.a. is Rs.76. Find the sum. Sol: C.I. – S.I. = Rs.76, R = 3% For 3 years, C.I. – S.I. = ( ( ¸ ( ¸ | | . | \ | + | | . | \ | 2 3 100 R 3 100 R P if P and R are given 76 = ( ( ¸ ( ¸ | | . | \ | + | | . | \ | 2 3 100 4 3 100 4 P 76 = ( ( ¸ ( ¸ | | . | \ | + | | . | \ | 2 3 25 1 3 25 1 P 76 = ( ( ¸ ( ¸ | | . | \ | + | | . | \ | 2 3 25 1 3 25 1 P 76 = ( ¸ ( ¸ × × × + 25 25 25 ) 25 3 ( 1 P 76 = ( ¸ ( ¸ 15625 76 P 15625 . Rs P = . 11. Certain sum of money placed at C.I. doubles itself in 3 years. In how many years will it amount to eight times itself? Sol: Here, n = 2, t = 3 years and m = 3 Then the same sum becomes m n in mt years = 3 x 3 = 9 years. 12. At what percent C.I. does a sum of money become eight-fold in 3 years. Sol: Required Rate percent is, %. 100 1 ) 8 ( 100 1 ) n ( 100 R 3 1 t 1 = ( ( ¸ ( ¸ ÷ = ( ( ¸ ( ¸ ÷ = 13. A certain sum of money at C.I. amounts to Rs.800 in two years and to Rs.1152 in four years. Find the rate of interest per annum. Sol: x = Rs.800, y = Rs.1152, A = 2 and B = 4 Required rate of interest, % 100 1 x y R A B 1 × ( ( ( ¸ ( ¸ ÷ | | . | \ | = ÷ % 100 1 400 576 % 100 1 800 1152 2 1 2 4 1 × ( ( ( ¸ ( ¸ ÷ | | . | \ | = × ( ( ( ¸ ( ¸ ÷ | | . | \ | = ÷ = %. 20 100 20 20 24 % 100 1 20 24 2 1 2 = × ( ¸ ( ¸ ÷ = × ( ( ( ( ¸ ( ¸ ÷ ¦ ) ¦ ` ¹ ¦ ¹ ¦ ´ ¦ | | . | \ | 14. If a sum of Rs.18120 is to be paid back in two equal installments at % 3 1 1 per annum, what is the amount of each installment? Sol: P = Rs.18120, R = % 3 4 = % 3 1 1 Each installment = 2 R 100 100 R 100 100 P . Rs | | . | \ | + + | | . | \ | + = 2 2 3 304 100 3 304 100 18120 3 4 100 100 3 4 100 100 18120 | | | | . | \ | + | | | | . | \ | = | | | | . | \ | + + | | | | . | \ | + = ( ¸ ( ¸ + = | | . | \ | + | | . | \ | 304 300 1 304 300 18120 304 300 304 300 18120 2 = 604 300 304 304 18120 304 604 304 300 18120 × × × = × = 9241.60 . Rs 10 304 304 = × . Exercise: 1. Find the C.I. on Rs.3000 for 3 years at 10% p.a. 1. Rs.1000 2. Rs.1200 3. Rs.993 4. Rs.300 2. On what sum of money will be the C.I. be Rs.168 in 2 years at 10% p.a.? 1. Rs.800 2. Rs.1000 3. Rs.1200 4. Rs.900 3. At what rate% p.a. will Rs.8000 amount to Rs.9261 in 3 years at C.I.? 1. 6% 2. 7% 3. 5% 4. 10% 4. At what rate% C.I. does a sum of money become 2 ¼ times itself in 2 years? 1. 50% 2. 75% 3. 60% 4. 40% 5. In what time will Rs.2000 amount to Rs.2420 at 10% p.a. C.I.? 1. 3 years 2. 2 years 3. 5 years 4. 9 years 6. Find the C.I. on Rs.24,000 at 10% p.a. for 1 year 6 months, the interest being compounded half-yearly. 1. Rs.12000 2. Rs.15000 3. Rs.14000 4. None 7. In what time will Rs.64000 invested at 5% p.a. fetch an interest of Rs.4291 the interest being compounded half-yearly? 1. 3/2 years 2. 4/7 years 3. 3 years 4. 2 years 8. The difference between the C.I. and S.I. on a certain sum of money for 2 years at 5% p.a. is Rs.30. Find the sum. 1. Rs.12000 2. Rs.15000 3. Rs.20000 4. None 9. The difference between the S.I. and C.I. on Rs.1250 for 2 years is 8. Find the rate% p.a. 1. 8% 2. 6% 3. 9% 4. None 10. A and B borrowed equal sum for 3 years at 10% S.I. and C.I. respectively. At the time of the repayment B has to pay Rs.15.50 more than A. Find the sum borrowed by each. 1. Rs.500 2. Rs.600 3. Rs.800 4. None 11. The C.I. on a certain sum for 2 years is Rs.40.80 and the S.I. is Rs.40. Find the rate% p.a. and the sum. 1. 5%, Rs.500 2. 4%, Rs.500 3. 6%, Rs.600 4. None 12. The S.I. on a sum at 4% p.a. for 2 years is Rs.80. Find the C.I. on the same sum for same period. 1. Rs.90 2. Rs.96.60 3. Rs.84.60 4. Rs.81.60 13. At a C.I. a sum becomes double itself in 3 years. In how many years will become 8 times? 1. 9 years 2. 10 years 3. 7 years 4. None 14. At a C.I. a sum becomes thrice itself in 8 years. In 16 years, it will become how many times? 1. 9 times 2. 10 times 3. 18 times 4. 27 times 15. The annual increase in the population of a town is 5%. What will be the population 3 years hence, if it is 80,000 now? 1. 92,610 2. 12,000 3. 75,000 4. None 16. Two cars A and B are of worth Rs.72,900 and Rs.1,33,100 respectively. After how many years will the value of both be same, if the car A appreciates at 10% p.a. and the car B depreciates at 10% p.a.? 1. 4 years 2. 5 years 3. 3 years 4. None 17. A sum of money is borrowed and paid back in two equal installments of Rs.729 allowing 8% C.I. What was the sum borrowed? 1. Rs.1300 2. Rs.15000 3. Rs.16000 4. Rs.18000 18. Find the difference between C.I and S.I on Rs.6400/- for 2 years at 12½% per annum? 1. Rs.90 2. Rs.101 3. Rs.100 4. Rs.1000 19. What annual payment will discharge a debt of Rs.50440 due in 3 years at 5% p.a. correspond annually? 1. Rs.18,000 2. Rs.18,522 3. Rs.16,500 4. None 20. A tree increases annually by 1/8 th of its height. By how much will it increase after 2 ½ years of it stands today 8 m high? 1. 10.25 cm 2. 10.75 cm 3. 9.25 cm 4. 9.75 cm 21. A sum of money put at C.I. amounts to Rs.2809 in 2 years and to Rs.2977.54 in 3 years. Find the sum. 1. Rs.2500 2. Rs.3000 3. Rs.4000 4. Rs.5000 22. A man opened a restaurant with an initial investment of Rs.3200. In that first year, he incurred a loss of 5%. However during the second year, he earned a profit of 10% which is third year rise to 12 ½ %. Calculate his net profit for the entire period for 3 years? 1. Rs.5000 2. Rs.700 3. Rs.5620 4. None 23. At what rate% C.I. does a sum of money become nine-fold in 2 years? 1. 200% 2. 300% 3. 500% 4. 600% 24. Arjun invested Rs.8000 for 3 years at 5% C.I. in a bank. If the interest is compounded once in a year, what sum will get after 3 years? 1. Rs.9261 2. Rs.8265 3. Rs.9365 4. Rs.9465 25. Find the C.I. on Rs.2000 at 5% p.a. compounded yearly, for 2 years is 1. Rs.315 2. Rs.425 3. Rs.205 4. Rs.215 26. If the interest is compounded yearly the find at what rate% p.a. will Rs.1000 amount to Rs.1331 in 3 years? 1. 10% 2. 12% 3. 13% 4. 14% 27. What is the present worth Rs.9261 due 3 years hence 5% p.a. compounded yearly? 1. Rs.7000 2. Rs.8000 3. Rs.9000 4. Rs.10,000 28. The C.I. on Rs.10,000 at 20% p.a. at the end of 1 year 6 months if the interest is calculated half-yearly will be 1. Rs.5320 2. Rs.3310 3. Rs.4340 4. Rs.2340 29. A sum put out at 4% C.I. interest payable half-yearly amounts to Rs.6632.55 in 1 ½ years. The sum is 1. Rs.6530 2. Rs.6250 3. Rs.6470 4. None 30. The C.I. on Rs.12,000 for 9 months at 20% p.a. interest being compounded quarterly is 1. Rs.1891.50 2. Rs.1901.50 3. Rs.1791.50 4. None 31. The difference of C.I. on Rs.800 for 1 year at 20% p.a. when compounded half- yearly and quarterly is ______ 1. Rs.4.40 2. Rs.5.40 3. Rs.6.40 4. None 32. The difference between the S.I. and the C.I. on Rs.600 for 1 year at 10% p.a., reckoned half-yearly is 1. Re.1 2. Rs.1.5 3. Rs.2 4. None 33. Rs.800 at 5% p.a. C.I. amount to Rs.882 in _____. 1. 6 years 2. 2 years 3. 4 years 4. None 34. What will be the C.I. on a sum of Rs.1875 after 2 years if the rate of interest for the first year is 4% and that for the second year is 8%? 1. Rs.231 2. Rs.341 3. Rs.241 4. None 35. What will be the amount if a sum of Rs.5000 is placed at C.I. for 3 years while rate of interest for first, second and third years is 2, 3 and 4% respectively? 1. Rs.5643.12 2. Rs.5463.12 3. Rs.6413.12 4. None 36. What sum will amount to Rs.15916.59 in 3 years at C.I., the interest for 1 st , 2 nd and 3 rd year being 3, 2 and 1% respectively? 1. Rs.18000 2. Rs.12000 3. Rs.15000 4. None 37. The C.I. on Rs.800 in 2 ½ years at 5% p.a. is 1. Rs.105.05 2. Rs.104.05 3. Rs.106.05 4. None 38. On what sum will the C.I. for 2 ½ years at 10% amount to Rs.6352.50? 1. Rs.7000 2. Rs.8000 3. Rs.5000 4. None 39. The C.I. on a sum of money for 3 years at 5% is Rs.1324.05. What is the S.I.? 1. Rs.1460 2. Rs.1365 3. Rs.1260 4. None 40. On what sum of money will the compound interest be Rs.102 in 2 years at 4% per annum? 1. Rs.1250 2. Rs.1365 3. Rs.1200 4. None Clocks In a clock the most important hands are the minutes hand and the hours hand. Whatever may be the shape of the dial they move in a circular track. The total angle of 360 degrees in a watch is divided into 1 sectors, one for each hour. So one hour sector = 360 / 12 = 30 degrees. For every one hour (60 min), The minutes hand moves through 360 deg. The hours hand moves through 30 deg. So for every minute, The minutes hand moves through 6 deg The hours hand moves through 0.5 deg. They move in same direction. So their relative displacement for every minute is 5.5 deg. This 5.5 deg movement constitutes the movements of both the hands. So for every minute both the hands give a displacement of 5.5 deg. Note: 1. Between every two hours i.e., between 1 and 2, 2 and 3 and so on the hands of the clock coincide with each other for one time except between 11, 12 and 12, 1. In a day they coincide for 22 times. 2. Between every two hours they are perpendicular to each other two times except between 2, 3 and 3, 4 and 8, 9 and 9, 10. In a day they will be perpendicular for 44 times. 3. Between every two hours they will be opposite to each other one time except between 5, 6 and 6, 7. In a day they will be opposite for 22 times. Examples: 1. At what time between 5 and 6 will the hands of the clock coincide? Soln: At 5 the angle between the hands is 150 deg. To coincide, they collectively have to travel this distance. Every minute they travel 5.5 deg. So no. of minutes required to coincide = 150 / 5.5 = 300 / 11 = 27 3/11 min. 2. At what time between 6 and 7 will the hands be perpendicular? Soln: At 6 the angle between the hands is 180 deg. To form 90 deg they have to cover 90 deg (out of 180 if 90 is covered 90 will remain) So no. of minutes required = 90 / 5.5 = 180 / 11 = 16 4/11 min. But they will be perpendicular for two times. The second one will happen after the minutes hand crosses the hours hand and then for 90 deg. So it has to travel 180+90 = 270 deg. So time = 270 / 5.5 = 540 / 11 = 49 1/11 min. 3. What is the angle between the hands of the clock at 3.45? Soln: At 3, the angle between the hands = A = 90 deg. In 45 min the hands will move angle of B = 45 X 5.5 deg (since 5.5 deg for 1 min) B = 247.5 deg. Required angle = A ~ B = 157.5 deg. 4. What is the angle between the hands at 4.40? Soln: At 4 the angle between the hands, A = 120 deg. In 40 min, B = 40 X 5.5 = 220 deg. The required angle = A ~ B = 100 deg. 5. A clock loses 5 min for every hour and another gains 5 min for every hour. If they are set correct at 10 am on Monday then when will they be 12 hrs apart? Soln: For every hour watch A loses 5 min and watch B gains 5 min. So for every hour they will differ by 10 min. For 12 hrs (720 min) difference between them the time required = 720 / 10 = 72 hrs So they will be 12 hrs apart after 3 days i.e., at 10 am on Thursday. Exercise: 1. What is the angle between the hands of the clock at 2.45? 1) o 2 1 180 2) o 2 1 182 3) o 2 1 172 4) o 2 1 181 2. At o 9 clock find the angle between the hands of the clock. 1) o 2 1 270 2) o 2 1 250 3) o 2 1 150 4) o 2 1 220 3. At what time between 6 O‟ clock and 7 O‟ clock the hands of the clock will coincide? 1) 11 8 30 min 2) 11 8 32 min 3) 11 8 20 min 4) 11 8 25 min 4. At what time between 6 O‟ clock and 4 O‟ clock the hands of the clock will be at right angles? 1) 11 8 30 min 2) 11 8 10 min 3) 11 8 32 min 4) 11 8 34 min 5. At what time between 1 O‟ clock and 2 O‟ clock the hands of the clock will be in opposite direction? 1) 11 8 30 min 2) 11 8 20 min 3) 11 8 10 min 4) 11 4 32 min 6. At what time between 5 O‟ clock and 6 O‟ clock the hands of the clock will be at o 180 ? 1) 60 min 2) 50 min 3) 40 min 4) 30 min 7. A clock which gains 6 minutes every three hours is set at 1.00 P.M. on a certain day. Find the time shown by the watch on next day at 13:50 hours. 1) 15 hrs 21 min 40 sec 2) 15 hrs 11 min 40 sec 3) 15 hrs 41 min 40 sec 4) 15 hrs 31 min 40 sec 8. A clock which loses 5 minutes in every hour is set at 10.30 A.M. on a certain day. Next day at 18.00 hours what is the time shown by this watch? 1) 15 hrs 12 min 30 sec 2) 15 hrs 22 min 30 sec 3) 15 hrs 31 min 40 sec 4) 15 hrs 41 min 30 sec 9. A clock, which loses 40 seconds every four minutes, is set at 18.00 hours on a certain day. What is the time shown by this watch if the current time is 4.00 P.M.? 1) 12:10 P.M. 2) 11:10 P.M. 3) 10:10 P.M. 4) 9:10 P.M. 10. A clock, which gains 6 minutes in every three hours, is set at 6 P.M. on a certain day. If on next day, the time shown by this watch is 11 P.M. what is the correct time? 1) 8 hrs 2 min (PM) 2) 8 hrs 4 min (PM) 3) 8 hrs 8 min (PM) 4) 8 hrs 6 min (PM) 11. A clock, which loses 5 minutes in every two hours, is set at 9.00 A.M. on a certain day. Next day if the time shown by this watch is 11 P.M. what is the correct time? 1) 23 15 10 min 2) 23 15 11 min 3) 23 15 9 min 4) 23 15 12 min 12. How many times in a day the hands of a clock are straight? 1) 20 2) 22 3) 19 4) 18 13. How many times do the hands of a clock point towards each other in a day? 1) 18 2) 19 3) 22 4) 20 14. A clock which gains 5 minutes in every two hours is set at 12.00 P.M. on a certain day. Find the time shown by the watch on the next day 11 A.M. 1) 12 hrs 47 min 30 sec 2) 12 hrs 45 min 30 sec 3) 12 hrs 20 min 30 sec 4) 12 hrs 15 min 30 sec 15. A clock which loses 10 seconds in every minute is set at 2.00 P.M. on a certain day. Find the time shown by the watch on the next day 8 P.M. 1) 1 P.M. 2) 2 P.M. 3) 3 P.M. 4) 4 P.M. 16. A clock which loses 50 seconds every two minutes is set at 6.00 P.M. on a certain day. What is the time shown by this watch if the current time is 3.00 P.M.? 1) 4 P.M. 2) 9 P.M. 3) 5 P.M. 4) 6 P.M. 17. A clock which gains 5 minutes in every two hours is set at 12 noon on a certain day. If on the next day, the time shown by this watch is 1 P.M. then find the correct time. 1) 10 P.M. 2) 12 P.M. 3) 11 P.M. 4) 8 P.M. 18. A clock, which loses 3 minutes in every hour, is set at 10.00 A.M. on a certain day. Next day if the time shown by this watch is 2.30 P.M. What is the correct time? 1) 29 1 19 min 2) 29 3 19 min 3) 29 4 19 min 4) 29 2 19 min 19. How many times do the hands of a clock coincide in a day? 1) 22 2) 23 3) 24 4) 48 20. How many times are the hands of a clock at right angles in a day? 1) 22 2) 48 3) 34 4) 46 21. If a clock takes 22 seconds to strike 12, how much time will it take to strike 6? 1) 6 sec 2) 10 sec 3) 8 sec 4) None 22. At what angle the hands of a clock are inclined when the time is 15 minutes past five? 1) o 2 1 67 2) o 68 3) o 70 4) None 23. At what time between 3 and 4 O‟ clock are the hands of a clock together? 1) 18 min past 3 2) 4 6 12 min past 8 3) 11 4 16 min past 3 4) None 24. At what time between 8 and 9 O‟ clock are the hands of a clock be in the straight line but not together? 1) 11 5 10 min past 3 2) 11 10 10 min past 8 3) 11 10 8 min past 8 4) None 25. The minute hand of a clock overtakes the hour hand at intervals of 65 minutes of correct time. How much in a day does the clock gain or lose? 1) 143 10 10 min 2) 11 10 10 min 3) 43 10 10 min 4) None 26. A watch gains uniformly, is 5 min slow at 8 O‟ clock in the morning on a Monday, and is 5 min.48 seconds fast at 8 P.M. on following Monday. When was it correct? 1) 3 days 11 hours 20 min 2) 8 min 3) 6 days 10 hours 4) None 27. A clock is set right at 8 A.M. The clock gains 10 minutes in 24 hours. What will be the true time when the clock indicates 1 P.M. on the following day? 1) 28 hours 2) 28 hours 48 min 3) 30 hours 4) None 28. At what time between 7 A.M. and 7.30 A.M. will the two hands of a clock be at right angle to each other? 1) 11 9 21 min past 7 2) 11 5 5 min past 7 3) 11 10 21 min past 7 4) None 29. At what time between 9 O‟ clock and 10 O‟ clock will the two hands of a clock be in a straight line but in opposite directions? 1) 11 4 16 min past 9 2) 11 5 5 min past 9 3) 10 11 10 min past 9 4) None 30. A watch which gains uniformly is 6 minutes slow at 4 P.M. on a Sunday and 3 2 10 minutes fast on the following Sunday at 8 A.M. During this period when (Day and Time) was the watch correct? 1) 1.30 A.M. , Tuesday 2) 1.36 P.M., Thursday 3) 1.36 A.M. , Wednesday 4) None Calendars - Here you mainly deal in finding the day of the week on a particular given date. - The process of finding this depends on the number of odd days. - Odd days are quite different from the odd numbers. Odd Days: The days more than the complete number of weeks in a given period are called odd days. Ordinary Year: An year that has 365 days is called Ordinary Year. Leap Year: The year which is exactly divisible by 4 (except century) is called a leap year. E.g. 1968, 1972, 1984, 1988 and so on are the examples of Leap Years. 1986, 1990, 1994, 1998, and so on are the examples of non leap years. Note: The Centuries divisible by 400 are leap years. Important Points: An ordinary year has 365 days = 52 weeks and 1 odd day. A leap year has 366 days = 52 weeks and 2 odd days. Century = 76 Ordinary years + 24 Leap years. Century contain 5 odd days. 200 years contain 3 odd days. 300 years contain 1 odd day. 400 years contain 0 odd days. Last day of a century cannot be Tuesday, Thursday or Saturday. First day of a century must be Monday, Tuesday, Thursday or Saturday. Explanation: 100 years = 76 ordinary years + 24 leap years = 76 odd days + 24 x 2 odd days = 124 odd days = 17 weeks + 5 days 100 years contain 5 odd days. No. of odd days in first century = 5 Last day of first century is Friday. No. of odd days in two centuries = 3 Wednesday is the last day. No. of odd days in three centuries = 1 Monday is the last day. No. of odd days in four centuries = 0 Sunday is the last day. Since the order is continually kept in successive cycles, the last day of a century cannot be Tuesday, Thursday or Saturday. So, the last day of a century should be Sunday, Monday, Wednesday or Friday. Therefore, the first day of a century must be Monday, Tuesday, Thursday or Saturday. 39. The no. of odd days in 400 years is _______. 1. 1 2. 0 3. 3 4. 4 40. Smt. Indira Gandhi died on 31 st October, 1984. The day of the week is _____. 1. Monday 2. Tuesday 3. Wednesday 4. Friday 41. What will be the day of the week on April 29, 2005? 1. Friday 2. Tuesday 3. Saturday 4. Sunday 42. The first day of the year 1998 was Wednesday. If the birthday of Raju falls on 25 th June, then on which day of 1998 was his birthday? 1. Friday 2. Tuesday 3. Wednesday 4. Sunday 43. If you are born on 13 th April, 1992 which is a Saturday, then which day of the week is your birthday in 1993? 1. Sunday 2. Monday 3. Tuesday 4. Wednesday 44. Find the day of the week on 15 th July, 1776? 1. Sunday 2. Monday 3. Tuesday 4. Wednesday 45. How many odd days are there in 352 days? 1. 1 2. 2 3. 3 4. 4 46. If 9 th March, 1988 is Tuesday, on what day of the week will 9 th March, 1989 falls? 1. Sunday 2. Monday 3. Tuesday 4. Wednesday 47. What will be the day of the week on April 29, 2005? 1. Saturday 2. Monday 3. Tuesday 4. Friday 48. On which day of the week does 5 th June, 2001 fall? 1. Thursday 2. Monday 3. Tuesday 4. Wednesday 49. If Ram was born on 29 th June, 1988 which is Monday, on what day was your birthday in 1989? 1. Friday 2. Monday 3. Tuesday 4. Wednesday 50. Find the day of the week of April 16 th , 1976, if April 16 th 1974 was Tuesday? 1. Friday 2. Monday 3. Tuesday 4. Saturday 51. Find the day of the week on 15 th January, 1979? 1. Sunday 2. Monday 3. Friday 4. Wednesday 52. If 23 rd May, 2003 is a Friday, what day of the week will be 23 rd December? 1. Tuesday 2. Monday 3. Tuesday 4. Friday 53. January 3 rd , 1992 was a Friday. What day of the week was January 3 rd , 1993? 1. Sunday 2. Thursday 3. Friday 4. Saturday 54. On which day of the week does 28 th May, 2003 fall? 1. Monday 2. Tuesday 3. Wednesday 4. Thursday 55. If your birthday is on 28 th May, 1991, then what was the day it was? 1. Tuesday 2. Wednesday 3. Friday 4. Sunday 56. What day of the week is 1 st March, 1990? 1. Sunday 2. Thursday 3. Tuesday 4. Friday 57. Which year will have the same calendar that of 2007? 1. 2008 2. 2013 3. 2010 4. 2018 58. Which year will have same calendar that of 2001? 1. 2002 2. 2005 3. 2006 4. 2007 59. You entered the college first time on 4 th June, 2001. What was the day? 1. Monday 2. Tuesday 3. Wednesday 4. Thursday 60. The no. of odd days in an ordinary year is _______. 1. 1 2. 2 3. 3 4. 4 61. If 3 rd April, 2003 was Thursday then which day of the week is 28 th December of the same year? 1. Sunday 2. Monday 3. Tuesday 4. Wednesday 62. Which among the following is a leap year? 1. 2600 2. 2700 3. 2800 4. 3000 63. What day of the week was 25 th April, 1901? 1. Monday 2. Tuesday 3. Wednesday 4. Thursday 64. Raju‟s brother was born on 7 th November, 1984. The day of the week was _____. 1. Monday 2. Tuesday 3. Wednesday 4. Thursday 65. What was the day of the week on 23 rd July, 1970? 1. Monday 2. Tuesday 3. Wednesday 4. Thursday 66. If today is Monday, then what day of the week will be 427 th day from today? 1. Sunday 2. Monday 3. Tuesday 4. Wednesday 67. Which day of the week was January 29 th , 1601? 1. Monday 2. Tuesday 3. Wednesday 4. Thursday 68. If Sundays are holidays, and in a particular year 2 nd April is Sunday. Is 30 th September in that year a holiday? 1. Yes 2. No 3. Insufficient Data 4. None 69. On what dates of September 1972 did Wednesday 1. 6, 13, 20, 27 2. 4, 11, 18, 25 3. 5, 12, 19, 26 4. 3, 10, 17, 24 70. If 15 th February, 1995 was a Wednesday then 15 th February, 1994 was on which day? 1. Monday 2. Tuesday 3. Wednesday 4. Thursday 71. Today is Saturday. After 100 days it will be _______. 1. Monday 2. Tuesday 3. Wednesday 4. Thursday 72. On which day this year (2008) you celebrated the Independence Day? 1. Monday 2. Friday 3. Wednesday 4. Thursday 73. 4 th April, 2002 was Thursday. The day of the week on 4 th April, 2003 was ______. 1. Monday 2. Friday 3. Wednesday 4. Thursday 74. 31 st March, 2003 was Monday. The day of the week on 31 st March, 2004 was _____. 1. Monday 2. Friday 3. Wednesday 4. Thursday 75. 15 th August, 1947 was Friday. Find the day of the week on 15 th August, 1960. 1. Monday 2. Tuesday 3. Wednesday 4. Thursday 76. 17 th May, 1989 was Wednesday. The day of the week on 9 th November, 1989 was _______. 1. Monday 2. Tuesday 3. Wednesday 4. Thursday 77. 27 th October, 1992 was Tuesday. The day of the week on 29 th March, 1993 was ________. 1. Monday 2. Tuesday 3. Wednesday 4. Thursday 40. The day of your birthday was __________ PROBABILITY Experiment An operation which results in some well-defined outcomes is called an experiment. Random Experiment An experiment whose outcome cannot be predicted with certainty is called a random experiment. In other words, if an experiment is performed many times under similar conditions and the outcome of each time is not the same, then this experiment is called a random experiment. Example: a) Tossing of a fair coin b) Throwing of an unbiased die c) Drawing of a card from a well shuffled pack of 52 playing cards Sample Space The set of all possible outcomes of a random experiments is called the sample space for that experiment. It is usually denoted by S. Example: f) When a die is thrown, any one of the numbers 1, 2, 3, 4, 5, 6 can come up. Therefore. Sample space S = {1, 2, 3, 4, 5, 6} g) When a coin is tossed either a head or tail will come up, then the sample space w.r.t. the tossing of the coin is S = {H, T} h) When two coins are tossed, then the sample space is Sample point / event point Each element of the sample spaces is called a sample point or an event point. Example: When a die is thrown, the sample space is S = {1, 2, 3, 4, 5, 6} where 1, 2, 3, 4, 5 and 6 are the sample points. Discrete Sample Space A sample space S is called a discrete sample if S is a finite set. Event A subset of the sample space is called an event. Problem of Events  Sample space S plays the same role as universal set for all problems related to the particular experiment.  | is also the subset of S and is an impossible Event.  S is also a subset of S which is called a sure event or a certain event. Types of Events A. Simple Event/Elementary Event An event is called a simple Event if it is a singleton subset of the sample space S. Example: a) When a coin is tossed, then the sample space is S = {H, T} Then A = {H} occurrence of head and B = {T} occurrence of tail are called Simple events. b) When two coins are tossed, then the sample space is S = {(H,H); (H,T); (T,H); (T,T)} Then A = {(H,T)} is the occurrence of head on 1 st and tail on 2 nd is called a Simple event. B. Mixed Event or Compound Event or Composite Event A subset of the sample space S which contains more than one element is called a mixed event or when two or more events occur together, their joint occurrence is called a Compound Event. Example: When a dice is thrown, then the sample space is S = {1, 2, 3, 4, 5, 6} Then let A = {2, 4 6} is the event of occurrence of even and B = {1, 2, 4} is the event of occurrence of exponent of 2 are Mixed events Compound events are of two type: a) Independent Events, and b) Dependent Events C. Equally likely events Outcomes are said to be equally likely when we have no reason to believe that one is more likely to occur than the other Example: When an unbiased die is thrown all the six faces 1, 2, 3, 4, 5, 6 are equally likely to come up. D. Exhaustive Events A set of events is said to be exhaustive if one of them must necessarily happen every time the experiments is performed. Example: When a die is thrown events 1, 2, 3, 4, 5, 6 form an exhaustive set of events. Important We can say that the total number of elementary events of a random experiment is called the exhaustive number of cases. E. Mutually Exclusive Events Two or more events are said to be mutually exclusive if one of them occurs, others cannot occur. Thus if two or more events are said to be mutually exclusive, if not two of them can occur together. Hence, A1, A2, A3,…, An are mutually exclusive if and only if Ai·Aj = | ¬ i = j Example: a) When a coin is tossed the event of occurrence of a head and the event of occurrence of a tail are mutually exclusive events because we cannot have both head and tail at the same time. b) When a die is thrown, the sample space is S = {1, 2, 3, 4, 5, 6} Let A is an event of occurrence of number greater than 4 i.e., {5, 6} B is an event of occurrence of an odd number {1, 3, 5} C is an event of occurrence of an even number {2, 4, 6} Here, events B and C are Mutually Exclusive but the event A and B or A and C are not Mutually Exclusive. F. Independent Events or Mutually Independent events Two or more event are said to be independent if occurrence or non-occurrence of any of them does not affect the probability of occurrence of or non-occurrence of their events. Thus, two or more events are said to be independent if occurrence or non-occurrence of any of them does not influence the occurrence or non-occurrence of the other events. Example: Let bag contains 3 Red and 2 Black balls. Two balls are drawn one by one with replacement. Let A is the event of occurrence of a red ball in first draw. B is the event of occurrence of a black ball in second draw. then probability of occurrence of B has not been affected if A occurs before B. As the ball has been replaced in the bag and once again we have to select one ball out of 5(3R + 2B) given balls for event B. G. Dependent Events Two or more events are said to be dependent, if occurrence or non-occurrence of any one of them affects the probability of occurrence or non-occurrence of others. Example: Let a bag contains 3 Red and 2 Black balls. Two balls are drawn one by one without replacement. Let A is the event of occurrence of a red ball in first draw B is the event of occurrence of a black ball in second draw. In this case, the probability of occurrence of event B will be affected. Because after the occurrence of event A i.e. drawing red ball out of 5(3R + 2B), the ball is not replaced in bag. Now, for the event B, we will have to draw 1 black ball from the remaining 4(2R + 2B) balls which gets affected due to the occurrence of event A. H. Complementary Events Let S be the sample space for a random experiment and let E be the event. Also, Complement of event E is denoted by E‟ or E, where E‟ means non occurrence of event E. Thus E‟ occurs if and only if E does not occur. n(E) + n(E‟) = n(S) Occurrence of an Event For a random experiment, let E be an event Let E = {a, b, c}. If the outcome of the experiment is either a or b or c then we say the event has occurred. Sample Space : The outcomes of any type Event : The outcomes of particular type Probability of Occurrence of an event Let S be the same space, then the probability of occurrence of an event E is denoted by p(E) and is defined as P(E) = n(E)/n(S) = number of elements in E/number of elements in S P(E) = number of favourable/particular cases total number of cases Example: a) When a coin is tossed, then the sample space is S = {H, T} Let E is the event of occurrence of a head ¬ E = {H} b) When a die is tossed, sample space S = {1, 2, 3, 4, 5, 6} Let A is an event of occurrence of an odd number And B is an event of occurrence of a number greater than 4 ¬ A = {1, 3, 5} and B = {5, 6} P(A) = Probability of occurrence of an odd number = n(A)/n(S) = 3/6 = ½ and P(B) = Probability of occurrence of a number greater than 4 = n(B)/n(S) = 2/6 = 1/3 EXERCISE Questions 1 – 7 A coin is flipped three. Find the probability of getting 1. A head exactly once. 1. 1/8 2. 1/ 4 3. 3/8 4. 1/ 2 2. tails exactly twice. 1. 1 /4 2. 3/8 3. 1/8 4. None of these 3. heads all three times. 1. 1/8 2. ¼ 3. 3/8 4. 1/ 2 4. a tail at least once. 1. 1 /4 2. 7/8 3. 1/8 4. 3/8 5. a head at least two times. S 1. 3/8 2. 1 /4 3. 1/8 4. 1 /2 6. a head in the first throw, a tail in the second, and a head in the third. 1. 1 /8 2. 1/ 4 3. 3/8 4. 1 /2 7. a head in the third toss, if in the first two tosses the coin landed tails. 1. 1/ 2 2. 1/ 8 3. 7/8 4. 1 /4 Questions 8 – 11 From a pack of 52 cards, a card is chosen at random. Find the probability of it being 8. a knave. 1. 1/13 2. 1 /4 3. 1 /2 4. 1/52 9. a card of hearts. 1. 1 /2 2. 1 /4 3. 1 /2 4. 1/52 10. a 7 of clubs. 1. 1/26 2. 5/52 3. 1/13 4. 1/52 11. a king of diamonds or hearts. 1. 1/13 2. 3/26 3. 1/26 4. 1 /4 Questions 12 – 16 A bag contains 5 red, 6 blue and 9 black balls. Find the probability that a ball drawn at random 12. is either red or blue or black. 1. 0 2. 19/20 3. 21/20 4. 20/20 13. is blue. 1. 1 /4 2. 7/10 3. 3/10 4. 9/20 14. is red or blue. 1. 11/20 2. 1 /4 3. 3 /4 4. 7/10 15. is blue or black. 1. 11/20 2. 1 /4 3. 3 /4 4. 7/10 16. is not blue. 1. 1 /4 2. 7/10 3. 3/10 4. 9/20 17. Two cards are drawn successively with replacement from a well shuffled deck of 52 cards, the probability that both of these will be aces is: 1. 1/169 2. 1/201 3. 1/2652 4. 4/663 18. Find the probability that there are 53 Mondays in Leap year. 1. 1/7 2. 2/7 3. 3/7 4. 4/7 19. if P (A)=0.3 P(B)=0.4 and P(AB)=0.6, then find P(A·B). 1. 0.3 2. 0.4 3. 0.1 4. 0.5 20. In throwing a fair dice, what is the probability of getting the number „3‟? 1. 1/3 2. 1/6 3. 1/9 4. 1/12 21. What is the number of throwing a number greater than 4 with an ordinary dice whose faces are numbers from 1 to 6. 1. 1 /3 2. 1/6 3. 1/9 4. 1/12 22. Three coins are tossed. What is the probability of getting (i) 2 Tails and 1 Head 1. 1 /4 2. 3/8 3. 2/3 4. 1/ 8 (ii) 1 Tail and 2 Heads 1. 3 /8 2. 1 3. 2 /3 4. 3 /4 23. Three coins are tossed. What is the probability of getting (i) neither 3 Heads nor 3 Tails 1. 1 /2 2. 1 /3 3. 2/3 4. 3 /4 (ii) three heads 1. 1 /8 2. 1 /4 3. 1 /2 4. 2/ 3 24. What is the probability of throwing a number greater than 2 with a fair dice 1. 2 /3 2. 2/5 3. 1 4. 3/5 25. A can hit the target 3 times in 6 shots, B 2 times in 6 shots and C 4 times in 6 shots. They fire a volley. What is the probability that at least 2 shots hit? 1. 1 /2 2. 1/3 3. 2 /3 4. 1/ 4 26. If 4 whole numbers are taken at random and multiplied together, what is the chance that the last digit in the product is 1, 3, 7 or 9 ? 1. 15/653 2. 12/542 3. 16/625 4. 13/625 27. A life insurance company insured 25,000 young boys, 14,000young girls and 16,000young adults. The probability of death within 10 years of a young boy, young girl and a young adult arte 0.02, 0.03 and 0.15 respectively. One of the insured persons dices. What is the probability that the dead person is a young boy? 1. 36/165 2. 25/166 3. 26/165 4. 30/165 28. A team of 4 is to be constituted out of 5 girls and 6 boys. Find the probability that the team may have 3 girls. 1. 4 /11 2. 3/11 3. 5/11 4. 2/11 29. 12 persons are seated around a round table. What is the probability that two particular persons sit together? 1. 2/11 2. 1/6 3. 3/11 4. 3/15 30. Six boys and six girls sit in a row randomly. Find the probability that all the six girls sit together. S 1. 3/22 2. 1/132 3. 1/1584 4. 1/66 31. A bag contains 5 red, 4 green and 3 black balls. If three balls are drawn out of it at random, find the probability of drawing exactly 2 red balls. 1. 7/22 2. 10/33 3. 7/12 4. 7/11 32. A bag contains 100 tickets numbered 1, 2, 3,…., 100. If a ticket is drawn out of it at random, what is the probability that the ticket drawn has the digit 2 appearing on it. 1. 19/100 2. 21/100 3. 32/100 4. 23/100 33. A fair coin is tossed repeatedly. If tail appears on first four tosses, then the probability of head appearing on fifth toss equals: 1. 1 /2 2. 1/32 3. 31/32 4. 1/5 34. Three mangoes and three apples are kept in a box. If two fruits are selected at random from the box, the probability that the selection will contain one mango and one apple, is: 1. 3/5 2. 5/6 3. 1/36 4. None of these ANALYTICAL Blood Relations Examples 1. If Neena says, “Anita‟s father Raman is the only son of my father-in- law Mahipal”, then how is Bindu, who is the sister of Anita, related to Mahipal? (a) Daughter (b) Wife (c) Daughter-in-law (d) None of these Solution. None of these. Only son of Neena‟s father-in-low Mahipal Neena‟s husband. So raman is Neena‟s husband and Anita and Bindu are his daughters. Thus, Bindu is the grand daughter of Mahipal. Example 2. Pointing to a photograph, a woman says, “This man‟s son‟s sister is my mother-in-law.” How is the woman‟s husband related to the an in the photograph? (a) Son (b) Son-in-law (c) Grandson (d) Nephew Solution. Grand son. Man‟s son‟s sister-man‟s daughter. So, the man‟s daughter is the mother of the woman‟s husband. Thus, the woman‟s husband is the grandson of the man in the photograph. Example 3. Pointing towards a person in a photograph, Raman said, “She is the only daughter of the mother of my brother‟s sister”. How is that person related to Raman? (a) Uncle (b) Father (c) Mother (d) Sister Solution. Sister. The mother of Roman‟s brother‟s sister is the mother of Raman and only daughter of Raman‟s mother means Raman‟s sister. Therefore the person in the photograph is related as sister to Raman. Example 4. A is father of C and D is son of B. e is brother of A. If C is sister of D, how is B related to E? (a) Husband (b) Brother-in-law (c) Sister-in-law (d) Daughter Solution. Daughter. A is father of C and C is sister of D. So A is father of D. But D is son of B. So, B is the mother of D and wife of A. Also, E is the brother of A So, B is the sister-in-law of E. Example 5. If P + Q means P is the husband of Q: P ÷ Q means P is the sister of Q and P × Q means P is the son of Q. Which of the following shows A is the daughter of B? Solution. A ÷ D × B. A is the daughter of B means A is the sister of the son (say D) of B i.e., A ÷ D × B. The standard definitions of relations are given below A/An ¹ is related to a PERSON as ¹ Grandfather The father of his/her mother or father Grandmother The mother of his/her mother or father Grandson The son of his/her daughter/son Granddaughter The daughter of his/her daughters/son Uncle The brother of his/her mother or father Aunt The sister of his/her mother or father Nephew The son of his/her brother or sister Cousin The son or daughter of his/her aunt of uncle Niece The daughter of his/her brother or sister Spouse as her husband or his wife Father-in-law the father of his/her spouse Mother-in-law the mother of his/her spouse Sister-in-law the sister of his/her spouse Brother-in-law the brother of his/her spouse Son-in-law the spouse of his/her daughter Daughter-in-law the spouse of his/her son Exercise: 1. When Amit saw Manoj, he recalled and said “He is the son of the father of the mother of my daughter”. What is Manoj to Amit? 1. Brother-in-law 2. Brother 3. Cousin 4. Uncle 2. Introducing a girl, Vinod said, “Her mother is the only daughter of my mother- in-law”. How is Vinod related to the girl? 1. Uncle 2. Husband 3. Brother 4. Father 3. Pointing to an old man Karim said, “His son is my son‟s uncle”. How is the old man related to Karim? 1. Brother 2. Uncle 3. father 4. Grand father 4. Seetha told to Malini, “The girl I met yesterday in the market was the youngest daughter of the brother-in-law of my friend‟s mother”. How is the girl related to Seetha‟s friend? 1. Cousin 2. Daughter 3. Niece 4. Aunt 5. Rohit told to Amit, “Yesterday I met the only brother of the daughter of my grand father”. Whom did Rohit met? 1. Son 2. Father 3. Brother 4. Uncle 6. Showing the lady at the door, Kailash said, “She is the daughter of my grand father‟s only son”. How is Kailash related to that lady? 1. Brother 2. Cousin 3. Father 4. Uncle 7. Pointing a man in a photograph, Anuradha said, “His mother‟s only daughter is my mother”. How is Anuradha related to that man? 1. Niece 2. Nephew 3. Sister 4. Wife 8. Pointing a person a man said to a woman, “His mother is only daughter of your father”. How was the woman related to that person? 1. Aunt 2. Mother 3. Wife 4. Daughter 9. Showing the man in the park, Sulthana said, “He is the brother of my uncle‟s daughter”. What is the man to sulthana? 1. Son 2. Brother-in-law 3. Cousin 4. Uncle 10. C is A‟s father‟s Nephew. D is A‟s cousin but not the sibling of C. How is D related to C? 1. Cousin 2. Sister 3. Mother 4. Aunt 11. K is brother of N and X. Y is mother of N, and Z is father of K. Which of the following statement is not true? 1. K is the son of Z 2. Y is the wife of Z 3. N is the brother of X 4. K is the father of X. 12. A woman walking with a boy meets another woman and on being asked about her relationship with the boy, she says, “My maternal uncle and his maternal uncle‟s maternal uncle are brothers”. How is the boy related to the woman? 1. Father 2. Son 3. Brother 4. Father in law 13. Pointing to a person, a man said to a woman, “His mother is the only daughter of your father”. How was the woman related to the person? 1. Sister 2. Mother 3. Wife 4. Daughter 14. Pointing to his son‟s portrait, a man said to a woman, “His mother is the only daughter of your mother”. How was the woman related to the man? 1. Sister 2. Mother 3. Wife 4. Daughter 15. Pointing to a girl in the photograph Umesh said, “Her mother‟s brother is the only son of my mother‟s father”. How is the girl‟s mother related to Umesh? 1. Mother 2. Sister 3. Aunt 4. Can‟t be determined 16. Introducing Kamala, Mahesh said, “Her father is the only son of my father”. How is Mahesh related to Kamala? 1. Brother 2. Father 3. Uncle 4. Son 17. A man said to a woman, “Your only brother‟s sister is my mother”. How is the woman related to the man‟s maternal grand mother? 1. Mother 2. Sister 3. Daughter 4. Mother in law 18. A man said to a woman, “Your only brother‟s son is my wife‟s brother”. How is the woman related to the man‟s wife? 1. Mother 2. Aunt 3. Sister 4. Can‟t be explained 19. Pointing the man in the photograph, Reeta said, “He is the brother of my uncle‟s daughter”. How is the man in the photograph is related to Reeta? 1. Son 2. Brother in law 3. Nephew 4. Cousin 20. Introducing a girl in the photograph, Sunil said, “Her mother is the only daughter of my mother in law”. How is Sunil related to the girl in the photograph? 1. Uncle 2. Brother 3. Husband 4. Father 21. Pointing to a lady, a man said, “The son of her only brother is the brother of my wife”. How is the lady related to the man? 1. Maternal Aunt 2. Mother in law 3. Mother‟s sister 4. Grand Mother 22. Pointing to a photograph, a person tells his friend, “She is the grand daughter of the elder brother of my father”. How is the girl in the photograph related to this man? 1. Aunt 2. Maternal aunt 3. Sister 4. None 23. Pointing to a man in a photograph a woman said, “His brother‟s father is only son of my grand father”. How is the woman related to the man in the photograph? 1. Mother 2. Aunt 3. Daughter 4. Sister 24. A is related to B and C, D is C‟s mother. Also D is B‟s sister and A is B‟s sister. How is C related to A? 1. Niece 2. Cousin 3. Sister 4. Aunt 25. Sandhya is mother in law of Vrunda, who is sister in law of Dhanraj. Ravi is the father of Ramana, the only brother of Dhanraj. How is Sandhya related to Dhanraj? 1. Mother in law 2. Aunt 3. Mother 4. Wife 26. A, the son of B was married to C, whose sister D was married to E, the brother of A. How is D related to B? 1. Sister 2. Daughter in law 3. Sister in law 4. Cousin 27. Introducing Swapna, Madhavi said, “She is the only daughter of my father‟s only daughter”. How is Madhavi related to Swapna? 1. Niece 2. Aunt 3. Cousin 4. None 28. Rohit said to Mohit, “The boy playing basket ball is younger brother of the two brothers of the daughter of my father‟s wife”. How is the boy playing basket ball related to Rohit? 1. Cousin 2. Nephew 3. Brother in law 4. Brother 29. Introducing a man to her husband, a woman said “His brother‟s father is the only son of my grand-father”. How is the woman related to this man? 1. Mother 2. Sister in law 3. Sister 4. Aunt 30. A and B are brother. C and D are sisters. A‟s son is D‟s Brother. How is B related to C? 1. Uncle 2. Brother 3. Father 4. Brother in law Directions (Questions 31-35): Read the following information carefully and answer the questions below: A family consists of six members P, Q, R, S, T and U. There are two married couples. Q is a doctor and the father of T. U is the grandfather of R and is a contractor. S is grandmother of T and is a housewife. There is one doctor, one contractor, one nurse, one housewife and two students in the family. 31. Who is the husband of P? 1. R 2. U 3. Q 4. S 32. Who is the sister of T? 1. R 2. U 3. T 4. Information insufficient 33. What is the profession of P? 1. Doctor 2. Nurse 3. Doctor of nurse 4. Housewife 34. Which of the following are two married couple? 1. US, QT 22. US, QP 3. TS, RU 4. US, RP 35. Which of the following is definitely a group of male members? 1. QU 2. QUT 3. QUP 4 UT Direction (Questions 36-40): X+Y means X is the father of Y, X-Y means X is the wife of Y, X×Y means X is the brother of Y, X ÷ Y means X is the daughter of Y. 36. A x B-C means _______________ 1. A is brother in law of C 2. A is the son of C 3. A is the husband of C 4. None of these 37. In A-B+C, which of the statement is true? 1. A is the mother of C 2. C is the daughter of A 3. A is the sister of C 4. None 38. In A÷ B+C+D, which of the following is true? 1. A is the daughter of C 2. C is the aunt of A 3. A is the aunt of C 4. None 39. In A x B+C, which of the following is true? 1. A is the uncle of C 2. A is the father of C 3. A is brother in law of C 4. A is grand father of C 40. In A x B÷ C, which of the following statement is true? 1. A is the uncle of C 2. A is the father of C 3. A is the son of C 4. A is the brother of C 41. Pointing to man, a woman said, “His mother is the daughter of my mother‟s only daughter”. How is the man related to that woman? 1. Son 2. Father 3. Brother 4. Grandson 42. Pointing towards Woman, Madhu said, “I am the only son of her father‟s one of the son‟s”. How the woman is related to Madhu? 1. Nephew 2. Cousin 3. Uncle 4. Aunt 43. Pointing to a man in the photograph, a woman said, “He is the only son of my mother‟s father”. How is the woman related to the man in the photograph? 1. Niece 2. Sister 3. Mother 4. Daughter 44. Pointing to a gentleman, Daniel said, “His only brother is the father of my daughter‟s father”. How is the gentleman related to Daniel? 1. Father 2. Grandfather 3. Uncle 4. Brother 45. Pointing towards Neeraj, Asha said, “I am the only daughter of his mother‟s son”. How is Neeraj related to Asha? 1. Uncle 2. Cousin 3. Niece 4. None 46. Pointing to a person a man said to a woman, “His mother is the only daughter of your father”. How was the woman related to the person? 1. Aunt 2. Mother 3. Wife 4. Daughter 47. Pointing towards a photograph of a girl, Ramu said, “she has no sisters or daughters but her mother is the only daughter of my mother”. How is the girl in the photograph related to Ramu‟s mother? 1. Sister in law 2. Grand Daughter 3. Daughter in law 4. Can‟t be determined 48. Pointing towards a person in a photograph, Raman said, “She is the only daughter of the mother of my brother‟s sister”. How is the person in photograph related to Raman? 1. Daughter 2. Sister 3. Wife 4. Cousin 49. Pointing to a man in a photograph, a woman said, “His brother‟s father is the only son of my grandfather”. How is the woman related to the man in the photograph? 1. Sister 2. Mother 3. Grandmother 4. Aunt 50. If Monika says, “Rahul‟s father is the only son of my father”, how is Monika related to Rahul? 1. Daughter 2. Sister 3. Aunt 4. Can‟t be determined 51. If Vijay says, “Vinay‟s mother is the only daughter of my mother”, how is Vijay related to Vinay? 1. Brother 2. Grandfather 3. Father 4. Maternal Uncle 52. Pointing towards a person in a photograph, Amrutha said, “He is the only son of the father of my sister‟s brother”. How is that person related to Amrutha? 1. Maternal uncle 2. Mother 3. Father 4. Brother 53. Introducing a man, a woman said, “His wife is the only daughter of my mother.” How is the woman related with the man? 1. Sister in law 2. Wife 3. Mother in law 4. Aunt 54. Pointing to Neha, Mahesh said, “Her mother‟s only daughter is my daughter”. How is Mahesh related to Neha? 1. Brother 2. Uncle 3. Son 4. Father 55. Pointing to a boy in the photograph Manasa said, “His sister is the only daughter of my father”. How is the boy related to Manasa‟s father? 1. Father 2. Brother 3. Son 4. Cousin 56. Pointing to a lady in the photograph, Vinay said, “She is the daughter of my grandfather‟s only son”. How is Vinay related to that lady? 1. Brother 2. Cousin 3. Father 4. Uncle 57. Introducing a man a woman said, “He is the only son of my mother‟s mother”. How is woman related to the man? 1. Mother 2. Aunt 3. Niece 4. Sister 58. Introducing a man, a woman said, “His wife is the only daughter of my father”. How that man was related to the woman? 1. Maternal uncle 2. Father in law 3. Brother 4. Husband 59. Pointing to a man in photograph a woman said, “His brother‟s father is the only son of my grandfather”. How is the woman related to the man in the photograph? 1. Mother 2. Aunt 3. Sister 4. Daughter 60. Pointing to a person, a man said to a woman, “His mother is the only daughter of your father”. How was the woman related to the person? 1. Sister 2. Mother 3. Wife 4. Daughter 61. Introducing a girl, Vishal said, “Her mother is the only daughter of my mother in law”. How is Vishal related to the girl? 1. Uncle 2. Husband 3. Brother 4. Father 62. Pointing to a lady, a man said “The son of her only brother is the brother of my wife”. How is the lady related to the man? 1. Mother‟s sister 2. Grand mother 3. Mother in law 4. Sister of father in law 63. Pointing to an old man, Karunakar said, “His son is my son‟s uncle”. How is the old man related to Karunakar? 1. Brother 2. Uncle 3. Father 4. Grandfather Directions (Questions 64-68): Read the following information carefully and answer the questions that follow. In a family, there are six members A, B, C, D, E and F. A and B are a married couple, A being the male member. D is the only son of C, who is the brother of A, E is the sister of D. B is the daughter in law of F, whose husband had died. 64. How is F related to A? 1. Mother 2. Sister in law 3. Sister 4. Mother in law 65. How is E is related to C? 1. Sister 2. Daughter 3. Cousin 4. Aunt 66. Who is C to B? 1. Brother 2. Brother in law 3. Son in law 4. Nephew 67. How many male members are there in the family? 1. Two 2. Three 3. Four 4. Five 68. How is F related to C? 1. Mother in law 2. Sister in law 3. Mother 4. Aunt Directions (Questions 69-73): Read the following information carefully and answer the questions given below. A family consists of six members P, Q, R, X, Y, Z. Q is the son of R but R is not the mother of Q. P and R are a married couple. Y is the brother of R, X is the daughter of P, Z is the brother of P. 69. Who is the brother in law of R? 1. P 2. Z 3. Y 4. X 70. Who is the father of Q? 1. P 2. Z 3. R 4. Can‟t be determined 71. How many children does P have? 1. Four 2. Two 3. Three 4. One 72. How many female members are there in the family? 1. One 2. Two 3. Three 4. Four 73. How is Q related to X? 1. Uncle 2. Brother 3. Father 4. Husband Directions (Questions 74-77): In a family there are 6 members A, B, C, D, E and F. A is Husband of B. D is only son of C, who is the brother of A. E is the sister of D. B is daughter-in-law of F, whose husband has died. 74. How is F related to A? 1. Mother 2. Sister-in-law 3. Sister 4. Mother-in-law 75. How is E related to C? 1. Sister 2. Son-in-law 3. Brother-in-law 4. None 76. Who is C to B? 1. Brother 2. Brother in law 3. Nephew 4. Son in law 77. How many male members are there in the family? 1. 2 2. 3 3. 4 4. 5 Directions (Question 78-80): There are 6 persons P1, P2, P3, P4, P5 and P6. P3 is the sister of P6. P2 is brother of P5‟s Husband. P4 is the father of P1 and grand father of P6. There are 2 fathers, 1 mother and 3 brothers in the family. 78. How many male members are there? 1. 4 2. 3 3. 2 4. 1 79. Who is the mother in given options? 1. P5 2. P3 3. P1 4. P2 80. Who is P5‟s husband? 1. P3 2. P6 3. P1 4. P4 Directions Examples Example 1. Ravi traveled 4 km straight towards south. He turned left and traveled 6 km straight, then turned right and traveled 4 km straight. How far is he from the starting point? (e) 8 km (f) 10 km (g) 18 km (h) 12 km Solution. 10 km. B is the finishing point and A is starting point. The distance of A from B is Example 2. A is to the South-East of C, B is to the East of C and North-East of A. If D is to the North of A and North-West of B. In which direction of C is D located? (a) North-West (b) South-West (c) North-East (d) South-East Solution. North-East D is located to the North-East of C. Example 3. A rat runs 20‟ towards East and turns to right, runs 10‟ and turns to right, runs 9‟ and again turns to left, runs 5‟ and then runs to left, runs 12‟ and finally turns to left and runs 6‟. Now, which direction is the rat facing? (e) East (f) West (g) North (h) South Solution. North. The movements of the rat from A to G are as shown in the fig. It is clear, rat is walking in one direction FG, i.e., North. Example 4. From his house, Lokesh went 15 km to the North. Then he turned west and covered 10 km, then he turned South and covered 5 km. Finally, turning to East, he covered 10 km. In which direction is he from his house? (a) East (b) South (c) North (d) West Solution. North. Starting point is A and ending point is E. E is to the north of his house at A. Exercise 1. After starting from office Ravendra turns left twice and then turns right. Now he turns towards South. In which direction Ravendra had started walking? (a) East (b) West (c) North (d) South 2. Facing towards south Varun walked 50 mts. He then turned to his right and walked 30 mts. He again turned right and walked 50 mts. How for was he from his original position and towards which direction? (a) 20m, East (b) 30m, South (c) 30m, West (d) 20m, North 3. Lalit walks 8 km east, turns South-West and walks another 8km. He again takes a turn towards North-West and walks another 8m. In which direction from his starting point is he standing now? In which direction from his starting point is he standing now? (a) North-East (b) North (c) East (d) West 4. Six persons are playing a game sitting in a circle facing the centre. Vijay was to the left of Sudhir. Amar was between Rakesh and Sarv, Neerav was second to the left of Amar. Which of the following is the position of Amar from Neerav? (a) Second from right (b) Second to the left (c) Third from the left (d) Third from right 5. Ankit started walking towards North. After walking 30 metres, he turned towards left and walked 40 metres. He then turned left and walked 50 metres. How far is he from his original position? (a) 50 metres (b) 40 metres (c) 30 metres (d) None of these 6. Rahim started from point X and walked straight 5 km West, then turned left and walked straight 2 km and again turned left and walked straight 7 km. In which direction is he from the point X? (a) North-East (b) South-West (c) South-East (d) North-West 7. B is to the South-west of A,C is to the East of B and South-East of A and D is to the North of C in line with B & A. In which direction of A is D located? (a) North (b) East (c) South-East (d) North-East 8. A walks 10 metres towards East and then 10 metres to his right, then every time turning to his left, he walks 5.15 and 15 metres respectively. How far is he now from his starting point? (a) 5 metres (b) 10 metres (c) 15 metres (d) 20 metres 9. A man walks 1 km towards. East and then he turns so South and walks 5km. Again he turns to East and walks 2 km, after this he turns to North and walks 9 km. Now how far is he from his starting point? (a) 7 km (b) 5 km (c) 4 km (d) 3 km 10. I am facing South. I turn right and walk 20 m, then I turn right again and walk 10 m. Then I turn left and walk 10 m and then turning right walk 20 m. Then I turn right again and walk 60 metres. In which direction am I from the starting point? (a) North (b) East (c) North-West (d) North-East 11. A man is facing North-West. He turns 90 0 in the clock wise direction, then 135 0 in the anticlockwise direction which direction is he facing now? (a) North (b) East (c) North-West (d) North-East 12. One day, Ravi left home and cycled 10 km Southwards, turned right and cycled 5 km and turned right and cycled 10 km and turned left and cycled 10 km. How many kilometers will he have to cycle to reach his home straight? (a) 10 km (b) 20 km (c) 15 km (d) 25 km 13. A Child is looking for his father. He went 90 metres in the east before turning to his right. He went 20 metres before turning to his right again to look for his father at his uncle‟s place 30 metres from this point. His father was not there. From there, he went 100 metres to his north before meeting his father in a street. How far did the son meet his father from starting point? (a) 180 metres (b) 100 metres (c) 140 metres (d) 120 metres 14. Varun walks 20 m North, then he turns right and walks 30 m, then he turns right and walks 35 m, then he turns left and walks 15 m. Then he again turns left and walks 15 m. In which direction and how many metres away is he from his original position? (a) 15 metres West (b) 30 metres East (c) 45 metres East (d) 30 metres West 15. I am facing East. I turn 100 0 in the clockwise direction and then 145 0 in the anticlockwise direction which direction and I facing now? (a) South-West (b) North (c) North-East (d) East 16. A man is facing North-West. He turns 90 0 in the clockwise direction, then 180 0 in the anticlockwise direction and then another 90 0 in the same direction. Which direction is he facing now? (a) South-East (b) West (c) South-West (d) South Directions (Questions 17-20) : P, Q, R and S are standing on the four corners of a square field. Study the following questions which are based on the figure. 17. P, Q, R and S from the position shown in the above fig., walk across the field along the diagonals to reach the opposite end from where Q and R walk anticlockwise and P and S walk clockwise along the sides. Each one covers ½ side. Now indicate which one of the following statements is true? (a) P is to the North-West of Q (b) Q is to the North-East of P (c) P is to the South-West of S (d) R is to the North-West of Q 18. From the position in question 17, P,Q and S walk clockwise and R walks anticlockwise along the sides and cover one side each assuming that they walk with the same speed, indicate which one of the following statements is true. (a) P will meet Q on the North-Eastern corner. (b) S will meet P on the North-Western corner. (c) Q will meet R on the South-Eastern corner. (d) S will meet R on the South-Western corner. 19. From the position in question 18, P and R walk across field to reach the opposite side from where they turn of their right and cover 1 ½ sides each. Now indicate which one of the following statements is not true? (a) R and Q are not opposite to each other. (b) R and S are not opposite to each other. (c) P and Q are not opposite to each other. (d) Q and S are opposite to each other. 20. From the position in question 18, P and R walk across field to reach the opposite side from where they turn of their right and cover 1 ½ sides each. Now indicate which one of the following statements is not true? (a) P will reach the North-Western corner after Q (b) P and R will cross each other at the centre. (c) S and P will cross each other on the Southern side. (d) R and Q will not cross each other on Northern side. 21. A is 40 m. South-West of B. C is 40 m South-East of B. Then C is in which direction of A? (a) South (b) North-East (c) West (d) East 22. Ravi wants to go to the university. He starts from his home which is in the East and comes to a crossing. The road to the left ends in a theatre, straight ahead is the hospital. In which direction is the university? (a) West (b) East (c) North (d) South 23. P, Q, R and S are playing a game of carom. P,R and S,Q are partners. S is to the right of R who is facing West. Then, Q is facing (a) East (b) West (c) North (d) South Directions (Qs24-27): Read the following information carefully and answer the question given below it: (i) Six flats on a floor in two rows facing North and South are allotted to P, Q, R, S, T and U (ii) Q gets a North facing flat and is not next to S. (iii) S and U get diagonally opposite flats. (iv) R, next to U, gets a South facing flat and T gets a North facing flat. 24. Which of the following combinations get South facing flats? a) Q T S b) U R P c) U P T d) None of these 25. Whose flat is between Q and S? (a) P (b) R (c) U (d) T 26. If the flats of T and P are interchanged, whose flat will be next to that of U? (a) T (b) R (c) Q (d) P 27. The flats of which of the other pairs SU, is diagonally opposite to each other? (a) TS (b) PT (c) QR (d) QP 28. One evening before sunset, two friends Sumit and Mohit were talking to each other face to face. If Mohit‟s shadow was exactly to his right side, which directions was Sumit facing? (a) North (b) West (c) South (d) None of these 29. One morning after sunrise, Daya and Bhavna were talking to each other face to face at Tilak square. If Bhavna‟s shadow was exactly to the right of Daya, which direction Bhavna was facing? (a) North (b) East (c) South (d) None of these 30. After walking 6 km, I turned right and covered a distance of 2 km, then turned left and covered a distance of 10 km. In the end, I was moving towards the North. From which direction did I start my journey? (a) West (b) East (c) South (d) North Directions (31-32): Stady the information given below carefully and answer the questions that follow on playing ground, Dinesh, Kunal, Nitin, Atul and Prashant are standing as described below facing the North (i) Kunal is 40 mts to the right of Atul (j) Dinesh is 60 mts to the south of Kunal (k) Nitin is 25 mts to the west of Atul (l) Prashant is 90 mts tot eh North of Dinesh 31. Who is to the North-East of the person who is to the left of Kunal? (a) Atul (b) Dinesh (c) Nitin (d) None of these 32. If a boy walks from Nitin, meets Atul followed by Kumal. Dinesh and then Prashant, how many metres has he walked is he has traveled the straight distance all through? (a) 215 m (b) 155 m (c) 185 m (d) 245m 33. Vikas starts walking straight towards east. After walking 75 meters, he turns to the left and walks 25 meters straight. Again, he turns to left walks a distance of 40 meters straight, again he turns to left and walks a distance of 25 meters. How far is he from the starting point? 1. 40 m 2. 30 m 3. 35 m 4. 50 m 34. A is standing at P. He walks 10 meters towards the south; then he walks 20 meters towards the west; then he walks 10 meters towards the south; then he walks 20 meters towards the North and reaches Q. What is the straight distance between P and Q in meters? 1. 15 m 2. 8 m 3. 9 m 4. None 35. Facing towards north, Goel walks 20 meters, he turns left and walks 40 meters, he again turns left and walks 20 meters, then he turns right and walks 20 meters. How far is he now from his original position? 1. 30 m 2. 40 m 3. 45 m 4. 60 m 36. Facing towards north, Rajesh walked 30 meters. He then turns left and walks 50 meters. He again turns left and walks 30 meters. How far is he from his original position and towards which direction? 1. 50 m, west 2. 60 m, west 3. 50 m, east 4. 60 m, east 37. In the Olympic Games, the flags of 6 nations were flown on the masts in the following way. The flag of America was found to the left of Indian Tricolor and to the right of the flag of France. The flag of Australia was on the right of the Indian flag but was to the left of the flag of Japan, which was to the left of the flag of China. Find the two flags which are in the center. 1. America and India 2. Japan and Australia 3. America and Australia 4. India and Australia 38. One day Jack left home and cycled 10 km southwards, turned right and cycled 5 km and turned right and cycled 10 km and turned left and cycled 10 km. How many kms will he have to travel to reach his home straight? 1. 10 km 2. 15 km 3. 20 km 4. 25 km 39. Anil travels from a point to east 10 km and turned right and traveled 8 km and turned right traveled 6 km and turned right traveled 5 km. How far is he from the starting point? 1. 4 km 2. 6 km 3. 5 km 4. 22 km 40. A person walks facing north 10 m and then he turns left and walks 5 m. He again turns left and walks 10 m. How far is he from his original position and towards which direction? 1. 20 m, south 2. 15 m, west 3. 10 m, south 4. 5 m, west 41. One morning after sunrise, Mahender and Manoj were standing in a chowk in Delhi with their backs towards each other. Mahender‟s shadow fell exactly towards his left hand side. Which direction was Manoj facing? 1. East 2. West 3. South 4. North 42. Mr. S. Bharat goes 30 meters North, then turns right and walks 40 meters, then again turns right and walks 20 meters, then again turns right and walks 40 meters. How many meters is he from his original position? 1. 10 2. 15 3. 20 4. 18 43. Saurav travels 5 km to the north. Then turn to his right and travel 12 km. How many kms away is he from the starting point? 1. 2 2. 13 3. 10 4. 12 44. Suman is 40 meters south-west of Ashok. Prakash is 40 meters south-east of Ashok. Prakash is in which direction of Suman? 1. South 2. West 3. East 4. North-east 45. Niraj who is facing south turns to his left and walks 8 meters. Then he faces North and walks 25 meters, and then turning to his left he walks a few meters so that he is 25 meters away from the original position. What is the total distance in meters covered by him in west? 1. 25 2. 8 3. 41 4. Can‟t be determined 46. A man goes five kilometers towards east, then he takes a turn to south-west and goes five kilometers. He again takes a turn towards north- east and goes five kilometers with respect to the point from where he started. Where is he now? 1. at the starting point 2. in the west 3. in the east 4. in the north-east 47. Starting from a point, Raju walked 12 meters towards north, he turned right and walked 10 meters, he again turned right and walked 12 meters, then he turned left and walked 5 meters. How far is he now and in which direction from the starting point? 1. 27 m, east 2. 5 m, east 3. 10 m, west 4. 15 m, east 48. Mr. X travels towards north 3½ km. Then he turns left and travels towards west for 1½ km, then turns left and travels for 3½ km. How far is he from the starting point? 1. 7 km 2. 4½ km 3. 2½ km 4. 1½ km 49. I went 15 m to the North, then I turned west and covered 5 m, and then I turned east and covered 10 m. In which direction am I from the house? 1. North-East 2. South-West 3. North-East 4. South-East 50. Yugal started walking towards south. After walking 15 meters he turned to the left and walked 15 meters. He again turned to his left and walked 15 meters. How far is he from his original position and in which direction? 1. 15 m, north 2. 15 m, south 3. 15 m, east 4. 15 m, west 51. A is east of B and west of C. H is south-west of C. B is south- east of X. Which is the farthest west? 1. A 2. B 3. C 4. X 52. If Shiny starts from point A and walks 5 miles, then turns left and walks 4 miles towards north, turns left again and walks 3 miles, in which direction is she going at the end? 1. West 2. North 3. South 4. East 53. While going northwards a police-Inspector turns right and walks 5 km straight. Then, he turns right and walks 8 km. In the end he turns left to reach his office. In which direction is his office from starting point? 1. North 2. South 3. East 4. West 54. A walks 10 m in front and 10 m to the right. The everytime turning to his left, he walks 5, 5, 15 meters respectively. How far is he now from his starting point? 1. 10 m 2. 20 m 3. 5 m 4. 15 m 55. A man walks 10 km towards north. From there he walks 6 km towards south. Then he walks 3 km towards east. How far and in which direction is he with reference to his starting point? 1. 5 km towards west 2. 7 km towards east 3. 5 km towards north-east 4. 7 km towards west 56. Lalith walks 7 km east, turns south-west and walks another 8 km. He again takes a turn towards north-east and walks another 8 km. In which direction from his starting point is he standing now? 1. North-east 2. South-east 3. West 4. East 57. One day John left home and cycled 10 km southwards, turned right and cycled 5 km and turned right and cycled 10 km. How many km will he have to cycle to reach his home straight? 1. 10 km 2. 5 km 3. 20 km 4. 25 km 58. Girish walks 8 km towards east and turns right and walks 3 km straight. Again he turns right and walks 12 km straight. Now how far is he from the starting point? 1. 5 km 2. 6 km 3. 8 km 4. 10 km 59. Ramesh walked 5 km towards east then he turned right and walked 8 km. He then turned left and walked 5 km. He again turned left and walked 8 km. At what distance is he now from the starting point? 1. 13 km 2. 10 km 3. 16 km 4. 20 km 60. A man walks 30 meters towards south. Then turning to his right he walks 30 meters. Then turning to his left he walks 20 m. Again turning to his left he walks 30 meters. How far is he from his starting position? 1. 30 m 2. 40 m 3. 50 m 4. 60m 61. Samir started from his police station on inspection duty. After traveling straight for a distance of four km, he turned left for the market and traveled straight for another 200 meters, and turned left and traveled straight for 600 meters. How far is Samir from the police station? 1. 3.4 km 2. 3.8 km 3. 4.4 km 4. 4.8 km 62. A boy rode his bicycle northwards, then turned left and moved 1 km and again turned left and rode 2 km. He found himself exactly on 1 km west of his starting point, How far did he ride northwards initially? 1. 1 km 2. 3 km 3. 2 km 4. 5 km 63. Deepu went 20 meters to the east, he turned left and walked 15 meters. He turned again right and went 35 meters. He again turned right and walked 15 meters. How far was he from his starting point? 1. 35 m 2. 50 m 3. 55 m 4. 60 m 64. From a point P, Samir started walking towards South and walked 40 meters. He turned towards his left and walked 30 meters and reached a point Q. The point Q is at what minimum distance and at what direction from the point P? 1. 50 m, south-west 2. 45 m, south-east 3. 50 m, south-east 4. 35 m, south-east 65. I traveled 35 km to the west, then turned right and traveled 7 km, then turned left and traveled 8 km, then turned back and traveled 11 km, then turned right and traveled 7 km. How far is he from the starting point? 1. 3 km 2. 6 km 3. 7 km 4. 9 km 66. Soni traveled 9 km to the west, then turned right and traveled 7 km, then turned left and traveled 8 km, then turned back and traveled 11 km, then turned right and traveled 7 km. How far is he from the starting point? 1. 3 km 2. 6 km 3. 7 km 4. 9 km Directions : A, B, C and D are standing on four corners of a square piece of plot as shown in the given figure. They start moving and the movements are explained in each of the questions. Read the questions and select the right alternative. 67. From the original position, D starts crossing the field diagonally. After walking half the distance he turns right, walks some distance and turns left. Which direction is D facing now? 1. South-east 2. North-west 3. South-west 4. North 68. B traveled straight to C, a distance of 10 km. He turned right and walked 7 km towards D, again he turned right and walked 8 km and then finally turned right and walked 7 km. How far is he from his original position? 1. 7 km 2. 8 km 3. 2 km 4. 3 km 69. A, B, C and D walk diagonally to opposite corners and from there B and C walk one and a half side anti clock-wise while A and D walk one side clock-wise along the sides. Where is D now? 1. At the north-west corner 2. At the north-east corner 3. At the south-west corner 4. At the north corner 70. A and D walk one and a half length of the side clockwise and anti-clockwise respectively. Which one of the following statements is true? 1. A is at midpoint between B and C and D at the corner originally occupied by A 2. A and D are both at the midpoint between C and D 3. A and D are both at the midpoint between B and C 4. None of these Directions: -) Seven Villages A, B, C, D, E, F and G are situated as follows: a) E is 2 km to the West of B W E S N C D A B b) F is 2 km to the North of A c) C is 1 km to the West of A d) D is 2 km to the South of G e) G is 2 km to the East of C f) D is exactly in the middle of B and E 71. Which two villages are farthest from one another? 1. F and E 2. G and E 3. D and C 4. F and B 72. How far is E and F as the Crow Flies? 1. 5 2. 26 3. 4 4. 20 73. Suman walks 15 meters towards west, then turns to her right and walks 15 meters and then turns to her left and walks 10 meters. Again she turns left and walks 15 meters. What is the shortest distance between her starting point and her present position? 1. 25 m 2. 35 m 3. 30 m 4. 20 m 74. Ashok started walking towards north. After walking 30 meters he turned left and walked 40 meters. He then turned left, and walked 30 meters. He again turned left and walked 50 meters. How far was he from his original position? 1. 12 m 2. 15 m 3. 10 m 4. 20 m 75. A rat runs 20‟ towards east and turns to right runs 10‟ and turns to right, runs 9 and again turns to left, runs 5‟ and then turns to left runs 12‟ and finally turns to left and runs 6‟. Now which directions is the rat facing? 1. East 2. North 3. West 4. South 76. Two towns A and B are 60 km apart. A school has to be built to serve 150 students of A, 50 students of town B. If the total distance to be traveled by all the 200 students is to be small as possible, then where is the school to be built? 1. In town B 2. 45 km from town B 3. In town A 4. 45 km from town A 77. I went 10 m to the east, then turned North and walked another 15 m, then I turned west and covered 12 m and then turned south and covered 15 m. How far am I from my house? 1. 0 m 2. 2 m 3. 3 m 4. 5 m 78. Ramesh started from a point A towards south and traveled 5 km, then he turned right and traveled 2 km, then he turned right and traveled 5 km, then he turned left and traveled 5 km. How far was he from point A? 1. 7 km 2. 17 km 3. 46.5 km 4. 60.5 km The question is not whether we will die, but how we will live. 79. I traveled 3 km southwards, then turned right and traveled 5 km. Then turned right and traveled 7 km. In which direction was I traveling last? 1. South 2. East 3. North 4. West 80. After walking 6 km, I turned right and covered a distance of 2 km, then turned left and covered a distance of 10 km. In the end, I was moving towards the North. From which direction did I start my journey? 1. North 2. South 3. East 4. West 81. Arun started walking positioning his back towards the sun. After some time, he turned left, then turned right and then towards the left again. In which direction is he going now? 1. East or South 2. West or North 3. North or South 4. South or West 82. A policeman goes straight seven kilometers eastwards, then turns right and goes straight three kilometers and turns right again and goes straight ten kilometers. In which direction is he from the starting point? 1. South-west 2. North-west 3. North-east 4. South-east 83. Sub-Inspector Jatin traveled from his police station straight for 400 meters. He then turned left and traveled 500 meters straight after which he turned left again and traveled for 400 meters straight. He then turned right and walked for another 600 meters straight. How far is he from the police station? 1. 1 km 2. 1.1 km 3. 1.4 km 4. 1.8 km 84. Rakesh is standing at a point. He walks 20 m towards the east and further 10 m towards the south, then he walks 35 m towards the west, and further 5 m towards the east. What is the straight distance in meters between his starting point and the point where he reached last? (approximately) 1. 12 2. 14 3. 10 4. 18 85. P, Q, R and S are playing cards, P and Q are partners, S faces toward north. If P faces towards west, then who faces towards south? 1. P 2. Q 3. S 4. R 86. Facing towards South, Ram started walking and after covering 40m he turned left and walked further 30 meters. How far is he from his starting position and in which direction? 1. 50 m South-west 2. 25 m South-west 3. 50 m South-east 4. 25 m South-east 87. Radha‟s school bus is facing north when she reaches her school. After starting from Radha‟s house, it turns right twice and then left before reaching the school. What direction was the bus facing when it left the bus stop in front of Radha‟s house? 1. South 2. North 3. East 4. West 88. Starting from point P satish walked 20 meters towards south. He turned left and walked 30 meters. He then turned left and walked 20 meters. He again turned left and walked 40 meters and reached at point Q. How far and in which direction is the point Q from the point P? 1. 20 m, west 2. 10 m, east 3. 10 m, west 4. 10 m, north 89. Facing towards south, Pramod walked 25 meters. He then turned to his right and walked 13 meters. He again turned right and walked 25 meters. How far was he from his original position and towards direction? 1. 20 m, east 2. 13 m, south 3. 20 m, north 4. 13 m, west 90. Starting from a point Raju walked 12 meters towards north he turned right and walked 10 m, he again turned right and walked 12 m then he turned left and walked 5 m. How far is he now and in which direction from the starting point? 1. 27 m towards east 2. 5 m towards east 3. 10 m towards west 4. 15 m towards west 91. Ram traveled 35 km from starting point towards south and then turned left and traveled 17 km and finally turned left again and traveled 35 km. How far was Ram from the starting point? 1. 17 km 2. 18 km 3. 35 km 4. 70 km 92. Somi traveled 9 km to the west then turned right and traveled 7 km, then he turned left and traveled 8 km, then turned back and traveled 11 km, then turned right and traveled 7 km. How far is he from the starting point? 1. 3 km 2. 6 km 3. 7 km 4. 9 km 93. A boy rode his bicycle northwards then turned left and moved 1 km and again turned left and traveled 2 km. He found himself correctly 1 km west of his starting point. How far did he ride northwards initially? 1. 1 km 2. 3 km 3. 2 km 4. 5 km 94. Ramesh started from a point A towards south and traveled 5 km, then he turned left and traveled 5 km, then he turned right and traveled 5 km. How far was he from point A? 1. 7 km 2. 17 km 3. 11 km 4. 5 km 95. Facing towards south Pramod walked 50 meters. He then turned to his right and walked 30 meters. He again turned right and walked 50 meters. How far was he from his original position and towards which direction? 1. 20 m, east 2. 30 m, south 3. 20 m, north 4. 30 m, west 96. Mohan starts from his home and walks 4 km straight, he turns towards his right and walks 2 km. He turns again to his right and walks 2 km again. If he is in north-west, then in which direction did he start in the beginning? 1. North-west 2. South-east 3. North-east 4. South-west 97. A goes 100 m to the south and then 100 m to the east to reach B‟s house. From there they together go to the market which is to the north-east of B‟s house. If the market be to the east of A‟s house, how far is it from his house? 1. 100 m 2. 200 m 3. 300 m 4. 400 m 98. From my house I went 15 km to the North, then I turned west and covered 10 km, then I turned south and covered 5 km and then turned east and covered 10 km. In which direction am I from my house? 1. West 2. East 3. North 4. South 99. A police-Inspector drove 30 km towards west and then 40 km towards South. From this place, he drove 60 km towards east and then 40 km towards north. At what distance is he from the starting point? 1. 30 km 2. 50 km 3. 60 km 4. 130 km 100. Mohit walks a distance of 5 km towards south, then turns to his right and walks 3 km. He again turns right and walks 5 km. He then turns to his left and walks 5 km. How far is he from the starting point and in what direction? 1. 5 km, west 2. 3 km, north 3. 3 km, east 4. 8 km, west 101. A man proceeding to the north turns to the right. After some time he takes a turn to the left and again to the left. Then he goes to his right and after some distance again turns towards his right. The direction in which he is now moving is ___________ 1. East 2. North 3. South 4. West 102. The time on Rita‟s watch is a quarter to three. If the minute hand point to north-east, in which direction does the hour hand point? 1. South-west 2. South-east 3. North-west 4. East- west 103. A man walks 7 miles eastwards, turns right and travels 3 miles and further turns right and travels 11 miles. How far is he from the starting point? 1. 5 miles 2. 3 miles 3. 6 miles 4. 8 miles 104. A and B start walking in opposite directions. A covers 3 miles and B 4 miles. Then A turns right and walks 4 miles and B turns left and walks 3 miles. How far each is from the starting point? 1. 4 miles 2. 6 miles 3. 8 miles 4. 5 miles 105. A man started walking from a point towards south. He turned right at right angles, then again right at right angles. In what direction was he ultimately walking? 1. East 2. West 3. North 4. South 106. Ravi went 10 m to the east, then turned north and walked another 5 m. Then he turned west and covered 15 m. How far is he from the starting point? (approximately) 1. 5 m 2. 2 m 3. 3 m 4. 7 m 107. A watch show 8.30. If the minute hand point towards east, in which direction will the hour hand point? 1. South-West 2. West 3. North-West 4. South-East 108. Venu walked 7 km towards west from Annapurna Studio. Then he took o 90 to his left and walked 4 km, again he had taken another left turn with o 90 and walked 2 km, then he turned to his right and walked towards south 1 km. Finally he walked 5 km towards east. How far is Venu from his starting point and in which direction? 1. 6 km South 2. 5 km North 3. 5 km South 4. 8 km North 109. Harish, Sai, Shanker and Raghu are in play ground. Harish stands South- west to shanker. Sai stands North-east to Harish and is between Harish and Shanker‟s way, but south to Raghu. Find in which direction Raghu to Shanker? 1. South 2. North-East 3. North-West 4. South-East 110. One evening, A was standing and facing a pole. The shadow of the pole fell exactly to his left. In which direction was he facing? 1. North 2. South 3. East 4. South-East 111. A clock is so placed that at 2 P.M. the minute hand points towards northwest. In which direction does the hour hand point at 6 P.M. 1. North-West 2. West 3. North-East 4. South-East 112. Ramana started from his college and walked 1 km forward, then he returned to his left and walked 1.5 km. Again he turned to his left and walked 1 km. Finally he walked 1.5 km towards his right. How far is he from his starting point? 1. 5 km 2. 2.5 km 3. 3.5 km 4.3km Coding – Decoding Examples Example1. In a certain code, PAPER is written as SCTGW. How is MOTHER written in that code? (a) POXJJT (b) ORVLGW (c) PQXKJV (d) PQVJGT Solution. PQXKJV. The letters at the odd positions are moved three, four and five steps forward, while the letters at the even positions are each moved two steps forward, to get the corresponding letters of the code. Example 2. In a certain code, SIKKIM is written as THLJJL. How is TRAINING written in that code? (a) SQBHOHOH (b) UQBJOHHO (c) UQBHOHOF (d) UQBJOHOH Solution. UQBHOHOF. The letters at the odd position are moved one step forward while the letters at the even positions are moved one step back to get the corresponding letters of the code. Example 3. If in a certain language. CALCUTTA is coded as GEPGYXXE, which word would be coded as FSQFCE? (a) BOMBYA (b) BOMYAB (c) BOMBAY (d) BOBAMY Solution. BOMBYA. Each letter of the word is four steps behind the corresponding letter of the code. Example 4. If D = 4 and COVER = 63 then BASIS = ? (a) 55 (b) 54 (c) 50 (d) 49 Solution. 50. In the given code A = 1, B = 2, C = 3 … so that, COVER = 3 + 15 + 22 + 5 + 18 = 63 BASIS = 2 + 1 + 19 + 9 + 19 = 50 Example 5. In a certain code, 15789 is written as XTZAL and 2346 is written as NPSU. How is 23549 written in that code? (a) NPTSL (b) NPTUL (c) NBTSL (d) PNTSL Solution. NPTSL. The numbers coded as 1 5 7 8 9 2 3 4 6 X T Z A L N P S U That is 2 as N, 3 as P, 5 as T, 4 as S and 9 as L. Thus 23549 coded as NPTSL. Example 6. If cloud is called white, white is called rain, rain is called green is called air, air is called blue and blue is called water, where will the birds fly? (a) Air (b) Cloud (c) Blue (d) Rain Solution. Blue. The birds fly in the „air‟ and „air‟ is called „blue‟. So the birds fly in the „blue‟. Example 7. In a certain code language, „dom pul ta‟ means „bring hot food‟; „pul fir sop‟ means „food is good‟ and „tak da sop‟ means „good bright boy‟, which of the following does mean „hot‟ in that language? (a) dom (b) pul (c) ta (d) can‟t determined Solution. Can‟t determined. The code for „food‟ from the first and second statements can be determined. To find the code for hot, we need the code for „bring‟ which can not be determined from the given information. Example 8. In a certain code, „37‟ means „which class‟ and „583‟ means „caste and class‟. What is the code for „Caste‟? (a) 3 (b) 7 (c) 8 (d) Either 5 or 8 Solution. Either 5 or 8. In the both statements, the common code digit is 3 and common word is „class‟ so „3‟ means „class‟. Thus in the second statement, either 5 or 8 stands for „caste‟. Exercise 1. IF LEARNING is written as MGDVSOUO then SURPRISE would be: (a) TWUTWOAL (b) TWUTWOZM (c) TWVUXPAN (d) TWUSVNZK 2. If SUNDAY is coded as XZCMTR then PAYMENT would be: (a) RPNDZOJ (b) QBZNFOU (c) SMDLXZO (d) TNEMYAP 3. If TAP is coded as SZO, then how is FREEZE coded? (a) EQDDYD (b) ESDFYF (c) GQFDYF (d) EQDFYG 4. In a certain code, FORGE is written as FPTJI. How is CULPRIT written in that code? (a) CXOSULW (b) CVNSVNZ (c) CVMQSTU (d) CSJNPGR 5. If victory is coded as YLFWRUB, how can success be coded? (a) VXFFHVV (b) VXEEIVV (c) VYEFIVV (d) VYEEHVV 6. In a certain code SOCIAL is written as TQFMER, then how you will code DIMPLE? (a) EKPTQK (b) EKPQPJ (c) EKPSPJ (d) EKPSOH 7. In a certain code SOCIAL is written as TQFMER, then how you will code DIMPLE? (a) wtzyv (b) twxyz (c) tqwvm (d) mtuvw 8. If PAINTER is written in a code language as NCGPRGP, then REASON would be written as : (a) PCYQMN (b) PGYQMN (c) PGYUMP (d) PGYUPM 9. If CIGARETTE is coded as GICERAETT. Then DIRECTION will be coded as : (a) RIDTCENOI (b) NORTECDII (c) IRDCTIONE (d) NOIETCRID 10. If DIAMOND is coded as VQYMKLV, how is FEMALE coded as: (a) UVNZOV (b) TUMYNU (c) TUMZOU (d) TVNYNV 11. If in a certain language, REMOTE is coded as ROTEME, which word would be coded as PNIICC? (a) PICCIN (b) PINCIC (c) PICNIC (d) PICINC 12. If in a certain code, COVET is written as FRYHW, which word would be written as SHDUO? (a) REPAY (b) PEARL (c) QUAKE (d) STINK 13. If PAINT is coded as 74128 and EXCEL is coded as 93596, then how would you encode ACCEPT? (a) 547978 (b) 554978 (c) 735961 (d) 455978 14. If ENGLAND is written as 1234526 and FRANCE is written as 785291, how is GREECE coded? (a) 832252 (b) 835545 (c) 381191 (d) 381171 15. If LINGER is 123456 and FORCE is 56789, then FIERCE is: (a) 345667 (b) 345677 (c) 456678 (d) 556789 16. If SHARP is coded 58034 and PUSH as 4658, then RUSH is coded as : (a) 3583 (b) 3685 (c) 3658 (d) 3568 17. If MASTER is coded as 411259, then POWDER will be coded as: (a) 765459 (b) 765439 (c) 765549 (d) 765439 18. In certain code language 35796 is written as 44887. How is 46823 written in that code? (a) 55934 (b) 55914 (c) 55714 (d) 57914 19. In a certain code language 24685 is written as 44887. How is 35791 written in that code? (a) 44880 (b) 46682 (c) 44682 (d) 44826 20. If AT = 20, BAT = 40 then CAT will be equal to: (a) 30 (b) 60 (c) 50 (d) 70 21. If ROSE is coded as 6821, CHAIR is coded as 73456 and PREACH is coded as 961473, what will be the code for SEARCH? (a) 246173 (b) 216473 (c) 214673 (d) 214763 22. If in a certain language, 943 is coded as BED, and 12448 is coded as SWEET, how is 492311 coded in that language? (a) EDSWBS (b) DSWTEE (c) EBWDSS (d) TSWBDD 23. If according to a certain code, PAINTER is written as 3528617, then TANRPEI is coded as? (a) 6587312 (b) 6583721 (c) 9385472 (d) 9385427 24. If PLANETS is written as 4823579, then SNLEPAT would be coded as: (a) 9385247 (b) 9384527 (c) 9385472 (d) 9385427 25. If water is called food, food is called is tree, tree is called sky, sky is called wall, on which of the following grows a fruit? (a) sky (b) tree (c) water (d) food 26. If sky is called sea, sea is called water, water is called air, air is called cloud and cloud is called river, then what do we drink when thirsty? (a) sky (b) water (c) air (d) sea 27. In a certain code language „389‟ means „run very fast‟ „964‟ means „come back fast‟ and „487‟ means „run and come‟. Which digit in the language means „come‟? (a) 9 (b) 4 (c) 7 (d) 8 28. In „nitco sco tingo‟ means „softer than flower”; „tingo rho mst‟ means „sweet flower fragrance‟ and „mst‟ sco tmp‟ means „sweet than smile‟, what would „fragrance‟ stand for? (a) rho (b) tmp (c) sco (d) mst 29. If „nso pir kli chn‟ stands for „Sapna‟ gets marriage gift? „ptr lnm wop chn‟ stands for „wife gives marriage gift‟, „tti wop nhi‟ stands for „he gives nothing‟, what would means „gives‟? (a) wop (b) ptr (c) nhi (d) chn 30. In a certain code language „bi nie pie‟ means „some good jokes‟; „nie bat tik; means „some real stories‟ and „pie lik tal‟ means „many good stories‟. Which word in that code means „jokes‟? (a) nie (b) pie (c) bi (d) None of these 31. In a certain code language, „Tom Kun Sub‟ means „Dogs are barking‟; „Kun Jo Mop; means „Dogs and horses‟ and „Must Tom Ko‟ means „Donkeys are mad‟. Which word in that language means „barking‟? (a) Kun (b) Sud (c) Tom (d) Ko 32. If „isn lto inm‟ stands for „neat and tidy‟; „qpr inm sen‟ stands for „small but neat‟ and „hsm sen rso‟ stands for „good but erratic‟, what would „but‟ stand for? (a) qpr (b) sen (c) inm (d) hsm 33. If „col tip mot‟ means „singing is appreciable‟; „mot baj min‟ means „dancing is good‟ and „tip nop baj‟ means singing and dancing‟. Which of the following means „good‟ is that code language? (a) min (b) baj (c) not (d) None of these Directions (Qs.34-37) : According to a certain code : „I received a letter,‟ we saw an aircraft‟. „John loves long letters‟, means „captain saw blue flag‟. „I like long one‟, means „we believe the captain‟. 34. What does the word „received‟ in the code mean? (a) we (b) saw (c) aircraft (d) blue 35. What word is coded as „believe”? (a) I (b) Like (c) Long (d) one 36. What does John mean? (a) aircraft (b) captain (c) blue (d) is 37. What will be the code for „The captain‟? (a) Long letter (b) Received one (c) Loves long (d) Long me 38. In a certain code language, „po ki top ma‟ means „usha is playing cards‟; „Kop ja ki ma‟ means „Asha is playing is tennis‟; „ki top sop ho‟ means „they are playing football; and „po sur kop ho‟ means „cards and tennis‟. Which word in that language means „Asha‟? (a) Kop (b) Top (c) Ja (d) Ki Directions (Qs. 39-41) : In a certain code, „il be pee‟ means „roses are blue‟; „sik hee means „red flowers‟ and „pee mit hee‟ means „flowers are vegetables‟. 39. How is „red‟ written in that code? (a) Be (b) Hee (c) Sik (d) None of these 40. How is „roses‟ written in that code? (a) il (b) Pee (c) Be (d) Pee 41. How is „vegetables are red flowers‟ written in this code? (a) Pee sik nut hee (b) Sik pee hee be (c) il sik mi thee (d) None of these Directions (Qs. 42-43) : According to certain code; „po be co fo‟ means „some students are sharp‟ „lo mo jo bo‟ means „many teachers are dull‟ „wo co lo zo‟ means „Dull students need training „mo zo ho po‟ means „some teachers need test‟. 42. The code for „many students‟ would be (a) Co mo (b) Co jo (c) Jo fo (d) Fo zo 43. The code „zo wo jo mo‟means (a) Some teachers need training (b) Some students need rest (c) Some teachers are sharp (d) Many teachers need training. Directions (Qs.44-45) : if according to a certain code : „mar tar gar zar‟ means „Can we start immediately‟. „har zar par dar‟ means „No you start tomorrow‟. „dar sar kar tar‟ means „Can you come here‟. „yar par mar sar‟ means „No we stay here‟. 44. What is the code for „stay‟? (a) Yar (b) Par (c) Mar (d) Sar 45. What does „dar‟ mean? (a) No (b) Can (c) You (d) Start 46. In a certain code, „467‟ means „leaves are green‟; „485‟ means „green is good‟ and „639‟ means „they are playing‟. Which digit stands for „leaves‟ in that code? (a) 4 (b) 6 (c) 7 (d) 3 47. In a certain code language, 479‟ means „fruit is sweet‟; „248‟ means „very sweet voice‟ and „637‟ means „eat fruit daily‟. Which digit stands for „is‟ in that code? (a) 9 (b) 7 (c) 4 (d) None of these. 48. In a certain code „786, means „study very hard‟. „958‟ means „hard work pays; and „645‟ means „study and work‟. Which of the following is the code for „very‟? (a) 8 (b) 6 (c) 7 (d) None of these 49. In a certain code language, „3a, 2b, 7c‟ means „truth is Eternal‟; „7c, 9a, 8b, 3a‟ means „Enmity is not Eternal and „9a, 4d, 2b, 8b‟ means „truth does not Peresh‟. Which of the following means „enemity‟ in that language: (a) 3a (b) 7c (c) 8b (d) 9a Directions (A) „134‟ means „you are well‟; (B) „758‟ means „they go home‟; (C) „839‟ means „we are home‟; 50. Which of the following represents „they‟ in that code language? (a) 5 (b) 7 (c) 3 (d) Data inadequate 51. In a certain code language CENTRAL is written as LARTNEC. How will SEMINAR be written in that code language? 1. NARIMES 2. MESIRAN 3. RANIMES 4. NARISEM 52. In a certain code language INACTIVE is written as VITCANIE. How will COMPUTER be written in that code language? 1. UTEPMOCR 2. ETUPMOCR 3. MOCPETUR 4. PMOCRETU 53. In a certain language KNIFL is coded as IFLKN, how is DOCTOR coded in that language? 1. ROTCOD 2. ROTDOC 3. CODTOR 4. TORDOC 54. In a certain code HUMIDITY is written as UHMIIDTY. How is POLITICS written in that code? 1. OPLIITCS 2. OPLITICS 3. POLIITCS 4. OPLIITSC 55. In a certain code language LEARNING is written as LGNINRAE. How will SURPRISE be written in that code language? 1. ESIRPRSU 2. RUSEPSIR 3. SESIRPRU 4. ESRIPRUS 56. In a certain code language TELEPHONE is written as ENOHPELET. How is ALIGATOR written in that code? 1. ROTAGIAL 2. ROTAGILA 3. ROTAGILE 4. ROTEGILA 57. In a certain code CALANDER is written as CLANAEDR. How is CIRCULAR written in that code? 1. ICCRLURA 2. CRIUCLRA 3. ICCRULRA 4. CRIUCALR 58. In a certain code MEDICAL is written as MEIDCAL. How would POLICE be written in that code? 1. PCELIO 2. POICLE 3. POILCE 4. PCELIO 59. In a certain code MOUNTAIN is written as OMNUATNI. How is READER written in that code? 1. ERDARE 2. ERADRE 3. REDAEL 4. RAEDER 60. In a code, EDITION is written as IDETNOI. How will MEDICAL be written in that code? 1. DEMILAC 2. LACIDME 3. DIEMCAL 4. CAMDILE 61. If VAIN is written as WBJO. Which word is written as UPOF? 1. TONE 2. TOMB 3. ROSE 4. ROPE 62. In a code language „ABHIJIT‟ is written as CEJLLLV. How is BROTHER written in that code? 1. DUQWJTH 2. DUQWTSH 3. DUQTWSH 4. DUQWJHT 63. In a certain code language PARENTS is written as RCTGPVU. How will CHILDREN be written in that code language? 1. EFJKCPCM 2. EJKNFTGP 3. EJKNFTPG 4. EJKNFPTG 64. If in a certain language GRASP is called as BMVNK, which word would be coded as CRANE? 1. FUDSJ 2. HWFSJ 3. HWFJS 4. XMVIZ 65. If QOSCFLBIO is the code for PORCELAIN, which word is coded as BKMOUSPP? 1. ALTOLROPY 2. ALLOTROPY 3. ALOTROLPY 4. None 66. If CANT is written as BZMS which word is written as JHKM? 1. MILK 2. LIKE 3. KITE 4. KILN 67. In a certain code GOODNESS is coded as HNPCODTR. How is GREATNESS coded in that code? 1. HQFZUODTR 2. HQFZUMFTR 3. HQFZUMFRT 4. HQFZSMFRT 68. If in a certain language SALE is coded as PAIE, how is CASUAL coded in that code? 1. FAVUDL 2. DBTVBM 3. ZAPUXL 4. BARUZK 69. If CANOE is coded as IFRRG, how is MUSIC written in that code? 1. SZWEL 2. SQWLE 3. SWZLE 4. SZWLE 70. If CAB is coded as WUV. How is DEAF coded in that language? 1. XYZU 2. XWUY 3. XYUZ 4. XZVU 71. If ROSE is coded as 6821, CHAIR is coded as 73456 and PREACH is coded as 961473. What will be the code for SEARCH? 1. 216473 2. 214637 3. 214673 4. 246173 72. If GIVE is coded as 5137 and BAT is coded as 924. How is GATE coded? 1. 5427 2. 5247 3. 5724 4. 2547 73. If HID is written ad B4C3B2. How will URN be written as? 1. C7B9B7 2. C3B9B7 3. C7B9B5 4. B9C3C7 74. If in a certain code SISTER is coded as 535301, UNCLE is coded as 84670 and BOY as 124, how is SON coded in that code? 1. 524 2. 643 3. 353 4. 846 75. If ROPE is coded as 6821 and CHAIR is coded as 73456 then what will be the code for CRAPE? 1. 73456 2. 76412 3. 77246 4. 76421 76. If MINJUR is coded as 312547 and TADA as 6898, how can MADURAI be coded? 1. 3498178 2. 389487 3. 3849781 4. 3894781 77. If in a certain code language A is coded as 1, B is coded as 2 and so on, how is BIDDIC coded in that code? 1. 294439 2. 294493 3. 294349 4. 249439 78. If FUN is written as B3C7B7 which word is written as B2C3B7? 1. PIN 2. RUN 3. DIN 4. PUN 79. If in a certain code TWENTY is written as 863985 and ELEVEN is written as 323039, how is TWELVE written in that code? 1. 863203 2. 823230 3. 823032 4. 863903 80. If in a certain language PRIVATE is coded as 1234567 and RISK is coded as 2398, how is RIVETS coded in that language? 1. 687543 2. 234769 3. 496321 4. 246598 Directions Calculate the value of each word by the following formula. All the consonants are coded as 2n-1 and vowels are coded as 3n+1, where n is the position of the letter? 81. CHIRU 1. 67 2. 152 3. 147 4. None 82. REASONING 1. 233 2. 234 3. 250 4. None 83. MATHS 1. 117 2. 116 3. 120 4. None 84. ARITHMETIC 1. 263 2. 231 3. 235 4. None 85. ICET 1. 80 2. 85 3. 88 4. 87 86. If rain is called water, water is called air, air is called cloud, cloud is called sky, sky is called sea, sea is called road, then where do the aero planes fly? 1. water 2. road 3. sea 4. cloud 87. If rain is called pink, pink is called cloud, cloud is called water, water is called breeze and breeze is called moon. With what do you wash your hands? 1. water 2. rain 3. breeze 4. room 88. If cushion is called pillow, pillow is called mat, mat is called bed sheet, and bed sheet is called cover. What can be spread on the floor? 1. cover 2. bed sheet 3. mat 4. pillow 89. If light means red, red means green, green means white, white means yellow. What is the colour of blood? 1. red 2. yellow 3. blue 4. light 90. If pen is called pencil, pencil is called scale, scale is called bag and bag is called book, which is used to carry the books? 1. scale 2. pen 3. book 4. bag Directions (Questions 41-43): In a certain code “il be pee” means “roses are blue”, “sik hee” means “red flowers” and “pee mi hee” means “flowers are vegetables”. 91. How is red written in that code? 1. hee 2. sik 3. be 4. Can‟t be determined 92. How is “roses” written in that code? 1. il 2. pee 3. be 4. Can‟t be determined 93. How is “vegetables are red flowers” written in this code? 1. sik pee hee be 2. il sik mi hee 3. pee sik mi hee 4. Can‟t be determined 94. In a certain language “pre not bis” means “smoking is harmful”, “vog dor not” means “avoid harmful habit”, and “dor bis yel” means “please avoid smoking. Which of the following means “habit” in that language? 1. vog 2. not 3. dov 4. bis 95. “bis” stand for 1. please 2. avoid 3. harmful 4. smoking 96. In a certain code “253” means “books are old”, “546” means “man is old”, “378” means “buy good books”. What does “are” mean in that code? 1. 2 2. 3 3. 4 4. 3 97. In a certain code “37” means “which claws” and “583” means “caste and claws”. What is the code for “caste”? 1. 3 2. 7 3. 8 4. Either 5 or 8 98. In a certain code „289‟ means „read from paper‟, „276‟ means „tea from field‟ and „85‟ means „wall paper‟. Which of the following is the code for „tea‟? 1. 2 2. 6 3. Either 7 or 6 4. Either 5 or 8 99. In a certain code language “123” means “how are you”, “423” means “how are they”, and “356” means “how is she”. In that code language 3 stands for which of the following? 1. how 2. are 3. you 4. she 100. In a certain code language “123” means “hot filter coffee”, “356” means “very hot day” and “589” means “day and night”. Which digit in that language means “very”? 1. 8 2. 6 3. 9 4. 5 101. In a certain code, MPOEPO means LONDON. What is CPNCBZ? 1. DQODCA 2. BOMBAY 3. MADRAS 4. RAJKOT 102. In a certain code, CLOCK means KCOLC. How is STEPS written in that code? 1. SPEST 2. SPSET 3. SPETS 4. SEPTS 103. In a certain code, GAMESMAN means AGMEMSAN. How is DISCLOSE written in that code? 1. IDSCOLSE 2. IDCSOLES 3. IDSCOLES 4. IDSCLOSE 104. In a certain code, PRACTICE is written PARTCCIE. How is TRAINS written in the same code? 1. TRAINS 2. TANRIS 3. TAIRNS 4. TARNIS 105. In a certain code, BAD is written as YZW, SAID is written as HZRW, then LOVE will be written as 1. WXMN 2. MRSU 3. BRTP 4. OLEV 106. In a certain code, GOLFER is written as H N M E F Q. HUNGER will be coded as 1. I T O F F Q 2. I V O H F S 3. I T O D F Q 4. T I D O Q F 107. In a certain code, GOLFER is written as IRPKKY, then decode HRVHK 1. FORTS 2. FORCE 3. FIRST 4. FEWER 108. In a certain code, ROUNDS is written as RONUDS. How is PLEASE written in that code? 1. LPAESE 2. PLAESE 3. LPAEES 4. PLASEE 109. In a certain code, SCALE is written as ELACS. How is CREAM written in that code? 1. MACER 2. MEARC 3. MERAC 4. MAERC 110. In a certain code, CHAIR is written as HAIRC. How is BRIDE written in that code? 1. RIDEB 2. BRIEB 3. EBRID 4. RIDBE 111. In a certain code, VACATE is written as AVACET. How is LITERATE written in that code? 1. ILETRAET 2. ILTEARTE 3. ILTREATE 4. ILETARET 112. In a certain code, RUSTIC is written as CSUITR. How is DUSTER written in that code? 1. RUSETD 2. CSUETR 3. RESTUD 4. RSUETD 113. In a certain code, QUIET is written as TXLHW. How is FLOAT written in that code? 1. TORDW 2. HNQCV 3. INRCW 4. IORDW 114. In a certain code, TRINOLI is written as SSHONMH. Write SICILY in the same code. 1. RJBJKA 2. RHJCZP 3. RJBJKZ 4. TJDJMZ 115. In a certain code, BANANA is written as ANANAB : write MELON in the same code. 1. KENDM 2. NFMPO 3. NPOKS 4. NOLEM 116. If HOBBY is coded as IOBY; LOBBY is coded as MOBY; code BOBBY. 1. BOBY 2. COBY 3. DOBY 4. COBBY 117. If SUCCESS is coded as TVDDFTT, then how will you code RETREAT? 1. SBUSFBS 2. SFUSFBS 3. SFUSFSB 4. SFUSFBU 118. If MAN is written as NZM, then GIRL will be written as 1. TRIO 2. RTIO 3. HJLM 4. GIKL 119. If SWEET is written as WSTEE, then BOOKS will be written as 1. OBOSK 2. OBSOK 3. OBKSO 4. BOSOK 120. If MALT is written as NBMU, then ZEBRA will be written as 1. AFCSB 2. ACFSB 3. YFCSB 4. AFSCB 121. If TABLE is coded as ABTEL, then STOOL is coded as 1. TOSLO 2.TOLSO 3. OTSLO 4. TOSOL 122. If SHIP is written as VKLS, then PENCIL will be written as 1. SHQFLO 2. RIPGHO 3. SHFQLO 4. SHQFOL 123. If ZAT is written as RAT, then MAT will be written as 1. RAT 2. SAT 3. BAT 4.TAT 124. If PAGES is written as GESPA, then TIGHT will be written as 1. GHITT 2. GHTTI 3. GHTIT 4. HGTTI 125. If SING is written as UKPI, then TAKE will be written as 1. VCMG 2. WDNH 3. VCGM 4. WDHN 126. If ARMY is written as HYTF, then SICK will be written as 1. ZRJP 2. ZPRJ 3. ZJPR 4. ZPJR 127. If COBRA is coded BOCAR, then GROUP will be coded as 1. ORPGU 2. OGRPU 3. ORTAU 4. ORGPU 128. If PAGES is written as APEGS, then TOUCH will be written as 1. OCTUCH 2. OTUCH 3. OTCUH 4. OTUHC 129. If SELF is coded as RDKE, then STATE will be coded as 1. RSZSD 2. RSZDS 3. RZSZD 4. RSZSC 130. If MOSCOW is written as JLPZLT, then LONDON will be written as 1. ILKALA 2. ILKALK 3. ILKLAK 4. ILKLKA 131. If NEWS is written as WENS, then MATE will be written as 1. TAME 2. META 3.MTAE 4. EATM 132. If ZEBRA is written as EZRBA, then BRISK will be written as 1. RBSIK 2. BRSKI 3. RBIST 4. RBSKB 133. If SELF is written as TELF, then COW will be written as 1. MOW 2. TOW 3. WOW 4. DOW 134. If NEW is written as WEN, then TWO will be written as 1. OWT 2. SOW 3. WTO 4. WTV 135. If WATCH is written as AWCTH, then TABLE will be written as 1. ATLBE 2. ATBLE 3. ATBEL 4. ELBAT 136. If MATCH is written as OCVEJ, then SCORE will be written as 1. UEQGT 2. UEQTG 3. UETQG 4. TDPFS 137. If WATER is written as XBUFS, then SALT will be written as 1. UCNV 2. TBMU 3. WZKS 4. WZSK 138. If PAGES is written as SEGAP, then STATE will be written as 1. ETATS 2. STTAE 3. ETSAT 4. TATSE 139. If WOLF is written as YQNH, then SENT will be written as 1. GUPV 2. GUVP 3. UGPT 4. UGPV 140. If REPORT is written as MZKJMO, then MODEL will be written as 1. GIXYF 2. GIXYT 3. HJYZG 4. GJYZG 141. If WFITE is written as YHKVG, then EXAM will be written as 1. GCZO 2. GYBO 3. GZCO 4. GZBO 142. If PAPER is written as REPAP, then ENGLISH will be written as 1. HSILGNE 2. HSLIGNE 3. HSLIGEN 4. HSLIENG Directions: If A = 5, B = 6, C = 7, D = 8 and so on, what do the following numbers or letters stand for 143. 22, 25, 8, 22, 5 1. Priya 2. Neema 3. Meena 4. Rudra 144. 6, 22, 19, 27, 18 1. Brown 2. White 3. Green 4. Black 145. 22, 5, 14, 5, 18 1. Rajan 2. Badal 3. Rajiv 4. Bimal 146. 6, 5, 22, 19, 8, 5 1. Cochin 2. Baroda 3. Madras 4. Bombay 147. 17, 19, 20, 9, 8 1. Plane 2. Moped 3. Motor 4. Tonga Directions: For the following questions, calculate value of each word by using the following formula: Consonants : (2 x position of the letter in alphabet) – 1 Vowels : (3 x position in alphabet) + 1 148. BREAD 1. 67 2. 62 3. 59 4. 65 149. FLUTE 1. 153 2. 157 3. 151 4. 149 150. CHANGE 1. 77 2. 79 3. 83 4. 80 151. In a certain code, PAN is written as 31 and PAR is written as 35; code PAT in the same pattern. 1. 30 2. 37 3. 39 4. 41 152. If BLOOD is coded as 24113, BURST is coded as 20678; code ROBUST. 1. 620781 2. 612078 3. 678102 4. 610732 153. If CINEMA is written as 395541, then PICTURE will be written as 1. 16932021185 2. 79311295 3. 2967694 4. 7932395 154. If BALL is coded as 211212, how will you code the word LATE? 1, 121205 2. 122195 3. 123205 4. 101205 155. If MEALS is coded as 13511219, how will you code the word WATER? 1. 13120518 2. 23120518 3. 23120519 4. 23121518 156. If CABLE is coded as 312125, how will you code the BUTTER? 1. 22120201518 2. 22120202319 3. 2212020518 4. 32120212128 157. If LETTER is coded as 1252020518, how will you code the word VOWEL? 1. 2215234 2. 221523512 3. 221523513 4. 2115235 158. If TERM is coded as 722914, how will you code the word RECT? 1. 92247 2. 92237 3. 92217 4. 92238 159. If CAP is coded as 242611, how will you code the word POT? 1. 11127 2. 11137 3. 11128 4. 11138 160. If FIVE is coded as 2118522, how will you code NIKE? 1. 13181622 2. 13181722 3. 12181622 4. 12181722 161. If DATE is coded as 2326722, how will you code ZEAL? 1. 1222615 2. 1222515 3. 1242615 4. 1242516 162. If COME is coded as 24121422, how will you code MEAN? 1. 14222614 2. 14212614 3. 14222613 4. 14212613 163. If MATHS is coded as 14267198, how will you code PHYSICS? 1. 11192818228 2. 11192818248 3. 11193818238 4. 11193818238 164. If MALE is coded as 25132417, how will you code SEAL? 1. 5161324 2. 5161234 3. 5171324 4. 5171424 165. If ADVENTURE is coded as ERUTNEVDA, how is GREEN coded in that language? 1. NEERG 2. ENEGR 3. GEREN 4. NEEGR 166. In a certain code JODHPUR is written as RUJODHP, how is CANDIDATE written in that code? 1. TECANDIDA 2. TECANDIAD 3. ETCANDIDA 4. ETCANDIAD 167. If PEOPLE is coded as PLPOEE, how is TREND coded? 1. TREDN 2. DNERT 3. TRDNE 4. TNERD 168. In a certain code language STUDENT is written as TUTDNES. How will SOURCES be written in that code language? 1. SUORCES 2. SUORECS 3. SOURSEC 4. SOUCRES 169. In a certain code HUMIDITY is written as UHIMIDTY. How is POLITICS written in that code? 1. OPILITCS 2. OPLITCS 3. POLITISC 4. OPLITISC 170. In a certain code GIGANTIC is written as GIGTANCI. How is MIRACLES written in that code? 1. RIMLASCE 2. RIMLACSE 3. RMLIASCE 4. RIMLSCAE 171. In a certain code JUDICIAL is written as a JUDICILA. How will GLORIOUS be written? 1. GLOORSIU 2. GLOOIRSU 3. GOLOIRSU 4. GOLORSIU 172. In a certain code MAN is written as SANM and WORD is written as SORDW. How would SALE be written in that code? 1. SEALS 2. LEASS 3. LEASAS 4. SALES 173. In a certain code INSTITUTION is written as NOITUTITSNI. How is PERFECTION written in that code? 1. NOICTEFREP 2. NOITCEFERP 3. NOITCEFREP 4. NOITCEFRPE 174. If REACH is written as TGCEJ which word is written as VQYGT? 1. STAND 2. SOWER 3. TOAST 4. TOWER 175. In a certain code SENSITIVE is written as QHLVGWGYC. How is MICROSOFT written in that code? 1. KGAPMQMDT 2. OKETQUQHV 3. KLAUMVMIR 4. KLAUMUMIR 176. If CURE is written as BTQD. How will MAIL be written in that code? 1. LZGS 2. LZKH 3. LZHK 4. LYHK 177. If SKIP is written as VHLM. How is NAME written as 1. QXBP 2. QXPB 3. XQPB 4. QXOB 178. If the word NATION is written as OCWMTT, how the word COUNTRY would be written in that code? 1. DQXRYXF 2. DQXRYFX 3. DQXRXYF 4. DPXRYXF 179. In a certain code TABLE is written as WDEOH. How would SKY be written in that code? 1. VNB 2. TBN 3. BNY 4. NYB 180. In a certain language BLEMISH is coded as AODPHVG, how is CHAPTER coded in that code? 1. DEBOUTDR 2. BKZSSHQ 3. CAHTPRE 4. BKZSSOH 181. If in a certain language CASUAL is coded as GEWYEP, how is PEOPLE coded in that code? 1. SHRSOH 2. TISTPI 3. SIRTOI 4. THSTOI 182. In a certain language TRIANGLE is coded as SQHZMFKD. Which word would be coded as DWZLOKD? 1. EXAMPEL 2. EXAMFL 3. EXAMPLE 4. NONE 183. If in a certain code, COVET is written as FRYHW, which word would be written as SHDUO? 1. QUAKE 2. REPAY 3. REAPL 4. PEARL 184. If LOSE is coded as 1357 and GAIN is coded as 2468, then the figures 84615 stand for ____? 1. SNAIL 2. LANES 3. NAILS 4. NALIS 185. In a certain code RIPPLE is written as 613382 and LIFE is written as 8192. How is PILLER written in that code? 1. 318826 2. 318286 3. 618826 4. 328816 186. If PALE is coded as 2134. EARTH is coded as 41590, how is PEARL coded in that language? 1. 29530 2. 24153 3. 25413 4. 25430 187. If CASE is coded as 5231, CHAIR is coded as 58206, and TEACH is coded as 71258. What does 586037 stand for? 1. CHRSIT 2. CHASTE 3. CHEESE 4. CHRIST 188. If PLAY is coded as 8123 and RHYME is coded as 49367. How is MALE coded? 1. 6198 2. 6395 3. 6217 4. 6271 189. In a certain code RIPSLE is written as 613082 and WIFE is written as 4192, how is PEWSLE written in that code? 1. 324082 2. 698241 3. 416328 4. 356124 190. In a certain code language 24685 is written as 33776. How is 35791 written in that code? 1. 44882 2. 44880 3. 46682 4. 44828 191. If HORN is written as B4C5B9B7 which word is written as B3C7B7B2? 1. FUND 2. HIND 3. FERN 4. FILM 192. If MATH is coded as E8A0G13C5. Which word is written as A2J5C1B3? 1. COME 2. CONE 3. CODE 4. CAVE Directions: In a particular language every r th letter is coded as (14-r) th letter for r=1,2,3…….13 and for r=14, 15…..26. r th letter is coded as (40-r) th letter. 193. What is the code for ICET? 1. EKIT 2. EKTI 3. FKIT 4. ELIT 194. What is the code for RANK? 1. VMCZ 2. VNCZ 3. VMCY 4. VMZC 195. What is the code for MATHS? 1. AMTFV 2. AMTFU 3. ANTFU 4. AMTUF 196. What is the code for „CODE‟? 1. KZII 2. KZJL 3. KYJI 4. KZIJ 197. If sand is called air, air is called rock, rock is called well, well is called ruby, ruby is called table, table is called gauge, gauge is called bangle and bangle is called bed then from where a woman can draw water? 1. bed 2. gauge 3. ruby 4. well 198. If bat is called racket, racket is football, football is shuttle, shuttle is judo, judo is carom. What is cricket played with? 1. racket 2. football 3. bat 4. shuttle 199. If black means white, white means red, red means yellow, yellow means blue, blue means green, green means violet and violet means orange. What is the colour of the sky? 1. blue 2. yellow 3. orange 4. green 200. If paper is called eraser, eraser is called bag, bag is called scale, scale is called pencil, pencil is called paper. What will a person write with? 1. scale 2. pencil 3. paper 4. eraser 201. If banana is apple, apple is grape, grape is mango, mango is nuts, nuts is guava. Which of the following is yellow fruit? 1. mango 2. nuts 3. grapes 4. banana 202. If lead is called stick, stick is called nib, nib is called needle, needle is called rope, rope is called thread, what will be fixed in a pen to write with it? 1. stick 2. needle 3. thread 4. lead 203. If air is called water, water is called green, green is called dust, dust is called yellow and yellow is called cloud, where do fish live in? 1. air 2. water 3. green 4. dust 204. If sky is called sea, sea is called water, water is called air, air is called cloud and cloud is called river, then what do you drink in thirst? 1. sky 2. air 3. water 4. river 205. If wall is called window, window is called door, door is called floor, floor is called roof and roof is called ventilator, on what will a person stand? 1. window 2. wall 3. floor 4. roof 206. If paper means wood, wood means straw, straw means grass, grass means rubber, rubber means cloth, then the furniture made up of? 1. cloth 2. straw 3. paper 4. wood Directions In a certain code language “ in jee loo” means “you did it”, “joo ip an” means “how are things”, “loo sam” means “you sing” and “an pee joo” means “things are sweets”. 207. Which of the following is the code for how? 1. joo 2. ip 3. am 4. joo 208. What is the code for “you sing sweet” 1. loo sam an 2. loo pee joo 3. pee sam loo 4. loo ip pee 209. Which of the following is the code for “it”? 1. in 2. jee 3. loo 4. Can‟t be determined 210. If 9144 means CHENNAI, 9122 means MUMBAI, 9111 means DELHI, then how do you code HYDERABAD? 1. 9133 2.9155 3. 9140 4. 9177 Series and Sequences Number Series: 1. 2, 3, 5, 7, 11, _____, 17 1. 9 2. 15 3. 13 4. 14 2. 21, 32, 45, 60, _____, 96, 117, 140 1. 75 2. 73 3. 74 4. 77 3. 1, 2, 5, 10, 17, 26, 37, ______ 1. 51 2. 50 3. 49 4. 65 4. 43, 44, 48, 57, 73, _____ 1. 98 2. 97 3. 87 4. 99 5. 13, 17, 21, 25, _______ 1. 28 2. 31 3. 27 4. 29 6. 2, 2, 4, 12, 48, ________ 1. 96 2. 250 3. 240 4. 230 7. 1, 2, 10, 37, _______ 1. 101 2. 100 3. 102 4. 103 8. 291, 170, _____, 40, 15, 6 1. 76 2. 112 3. 89 4. 100 9. 21, 23, 26, ____, 35 1. 28 2. 30 3. 37 4. 29 10. 10, 12, 16, 24, 40, 72, 136, ____ 1. 272 2. 382 3. 264 4. 292 11. 1, 5, 11, 19, 29, ____, 55 1. 45 2. 39 3. 41 4. 47 12. 6, 10, 18, 34, ______ 1. 44 2. 55 3. 66 4. 80 13. 1, 8, 16, 25, _______ 1. 30 2. 35 3. 40 4. 50 14. 5, 10, 17, 26, 37, 50, ___ 1. 64 2. 82 3. 65 4. 101 15. 37, 38, 34, 43, 27, 52, ____ 1. 16 2. 64 3. 74 4. 18 16. 10, 14, 22, 38, 70, ____ 1. 130 2. 134 3. 140 4. 142 17. 10, 11, 13, 16, 20, 25, ____ 1. 30 2. 31 3. 32 4. 33 18. 10, 15, 40, 165, ___ 1. 700 2. 725 3. 760 4. 790 19. 21, 29, 43, 55, 73, ____ 1. 88 2. 89 3. 90 4. 101 20. 2, 6, 6, 14, 30, 62, ______, 254 1. 142 2. 128 3. 126 4. 132 21. 4, 8, 7, 14, 12, 24, 19, ____, 28 1. 12 2. 38 3. 36 4. 24 22. 2, 7, 9, 3, 8, 11, 4, 9, 13, _____, 10, 15 1. 4 2. 7 3. 5 4. 6 23. 3, 9, 5, 25, 7, 49, 9, ______ 1. 81 2. 64 3. 100 4. 121 24. 8, 8, 9, 9, 11, 10, 14, 11. 1. 15 2. 18 3. 17 4. 12 25. 1, 8, 9, _____, 25, 216, 49 1. 64 2. 60 3. 70 4. 75 26. 3, 4, 15, 16, ______, 36, 63, 64 1. 30 2. 25 3. 34 4. 35 27. 1, 3, 1, 9, 1, 81, 1, _____ 1. 243 2. 324 3. 6561 4. 5641 28. 2, 4, 7, 14, 17, 34, 37, _____ 1. 74 2. 76 3. 47 4. 72 29. 20, 18, 19, 16, 18, 14, _____ 1. 16 2. 17 3. 15 4. 13 30. 3, 12, 4, 16, 5, 20, 6, _______ 1. 30 2. 36 3. 24 4. 18 31. 5, 20, 6, 24, 7, 28, _____ 1. 8 2. 9 3. 32 4. 10 32. 5, 4, 10, 8, 15, 12, 20, _____, 25 1. 13 2. 18 3. 15 4. 16 33. 8, 24, 12, ____, 18, 54 1. 28 2. 46 3. 36 4. 48 34. 10, 15, 20, 30, 40, 60, 80, ____ 1. 90 2. 100 3. 110 4. 120 35. 6, 42, 12, 35, 18, 28, 24, 21, __ , 14, 36, 7 1. 30 2. 35 3. 36 4. 18 36. 2, 9, 30, ____, 282 1. 90 2. 91 3. 92 4. 93 37. 1, 4, 12, 2, 5, 15, 3, 6, 18, 4, ______ 1. 21 2. 7 3. 5 4. 6 38. 2, 8, 4, 3, 18, 6, 4, 32, 8, _______50, 10 1. 7 2. 6 3. 5 4. 9 39. 1278, _____, 314, 152, 70, 28 1. 634 2. 636 3. 632 4. 656 40. 7, 5, 2, 14, 3, 1, 2, 6, 8, 5, 3, 24, 6, 2, 4, ___ 1. 10 2. 36 3. 12 4. 24 41. 2, 3, 6, 3, 4, 12, 4, 5, 20, 5, 6, ___ 1. 35 2. 30 3. 25 4. 35 42. 5, 7, 12, 6, 8, 14, 7, _____, 16, 8, 10, 18 1. 8 2. 10 3. 6 4. 9 43. 5, 2, 11, 6, 3, 12, 7, 4, 13, ____ 1. 8 2. 9 3. 10 4. 11 44. 3, 4, 12, 6, 2, 9, 18, 3, 6, ___, 24, 12, 2 1. 3 2. 8 3. 4 4. 9 45. 51, 17, 3, 16, 48, 12, 4, 10, 40, ____, 5, 13, 65 1. 9 2. 7 3. 6 4. 8 46. 3, 4, 10, 33, 136, ____, 4116 1. 136 2. 685 3. 32 4. 680 47. 4, 5, 9, 20, 5, 6, 11, 30, 6, 7, _____, 42 1. 12 2. 11 3. 13 4. 8 48. 50, 50, 60, 40, 70, 30, 80, 20, 90, 10, 100, ____ 1. 10 2. 20 3. 0 4. 5 49. 200, 300, 212, 288, 236, 264, 284, 216, __, __ 1. 380, 120 2. 188, 360 3. 388, 178 4. 380, 130 50. 0, 4, 6, 3, 7, 9, 6, ?, 12 1. 8 2. 10 3. 11 4. 14 51. 21, 32, 45, 60, _____, 96, 117, 140 1. 75 2. 73 3. 74 4. 77 52. 1, 2, 5, 10, 17, 26, 37, ______ 1. 51 2. 50 3. 49 4. 65 53. 2, 9, 30, ____, 282 1. 90 2. 91 3. 92 4. 93 54. 43, 44, 48, 57, 73, _____ 1. 98 2. 97 3. 87 4. 99 55. 13, 17, 21, 25, _______ 1. 28 2. 31 3. 27 4. 29 56. 2, 2, 4, 12, 48, ________ 1. 96 2. 250 3. 240 4. 230 57. 1, 2, 10, 37, _______ 1. 101 2. 100 3. 102 4. 103 58. 291, 170, _____, 40, 15, 6 1. 76 2. 112 3. 89 4. 100 59. 21, 23, 26, ____, 35 1. 28 2. 30 3. 37 4. 29 60. 10, 12, 16, 24, 40, 72, 136, ____ 1. 272 2. 382 3. 264 4. 292 61. 1, 5, 11, 19, 29, ____, 55 1. 45 2. 39 3. 41 4. 47 62. 6, 10, 18, 34, ______ 1. 44 2. 55 3. 66 4. 80 63. 1, 8, 16, 25, _______ 1. 30 2. 35 3. 40 4. 50 64. 5, 10, 17, 26, 37, 50, ___ 1. 64 2. 82 3. 65 4. 101 65. 37, 38, 34, 43, 27, 52, ____ 1. 16 2. 64 3. 74 4. 18 66. 3, 4, 10, 33, 136, ____, 4116 1. 136 2. 685 3. 32 4. 680 67. 10, 14, 22, 38, 70, ____ 1. 130 2. 134 3. 140 4. 142 68. 10, 11, 13, 16, 20, 25, ____ 1. 30 2. 31 3. 32 4. 33 69. 10, 15, 40, 165, ___ 1. 700 2. 725 3. 760 4. 790 70. 21, 29, 43, 55, 73, ____ 1. 88 2. 89 3. 90 4. 101 71. 2, 3, 5, 7, ? 1. 17 2. 15 3. 11 4. 19 72. 1, 5, 11, 19, 29, 41, ? 1. 49 2. 51 3. 55 4. 59 73. 11, 32, 53, 74, 95, 116, ? 1. 137 2. 125 3. 120 4. 138 74. 2, 5, 9, 10, 13, 17, 18, 21, 25, 26, ? 1. 27 2. 28 3. 29 4. 30 75. 3, 5, 9, 15, 23, 33, 45, ? 1. 59 2. 60 3. 61 4. 62 76. 0, 1, 8, 27, 64, ? 1. 91 2. 125 3. 128 4. 256 77. 2, 4, 7, 11, 16, ? 1. 20 2. 21 3. 22 4. 23 78. 5, 14, 27, 44, 65, ? 1. 88 2. 90 3. 109 4. 130 79. 1, 4, 10, 22, 46, ? 1. 48 2. 68 3. 82 4. 94 80. 3, 5, 9, 17, 33, ? 1. 48 2. 49 3. 63 4. 65 81. 1, 4, 9, 16, 25, ? 1. 30 2. 31 3. 32 4. 36 82. 17, 13, 11, 7, 5, 1, ? 1. 2 2. - 1 3. 0 4. 1 83. 30, 24, 19, 15, 12, ? 1. 8 2. 9 3. 10 4. 11 84. ? , 24 1 , 36 1 , 54 1 , 81 1 1. 32 3 2. 15 1 3. 16 1 4. 18 1 85. 2, 6, 11, 17, ?, 32 1. 22 2. 24 3. 28 4. 23 86. 3, 7, 15, ?, 63 1. 31 2. 42 3. 35 4. 34 87. 128, 110, 90, ?, 44 1. 56 2. 72 3. 68 4. 70 88. 7, 15, 29, 59, 117, ? 1. 235 2. 233 3. 234 4. 335 89. 6, 8, 9, 12, 14, 18, ? 1. 19 2. 21 3. 23 4. 25 90. 5, 6, 10, 19, 35, ? 1. 50 2. 55 3. 60 4. 71 91. 999, 727, 509, 339, ? 1. 211 2. 208 3. 120 4. 205 92. 5, 14, 41, 122, 365, ? 1. 1194 2. 1094 3. 1095 4. 1093 93. 17, 19, 15, 23, 7, 39, ? 1. 18 2. 9 3. - 25 4. 25 94. 3, 5, 8, 13, 20, ? 1. 29 2. 31 3. 33 4. 39 95. 3, 6, 12, 15, 30, 33, ? 1. 50 2. 60 3. 44 4. 66 96. 0, 2, 6, ?, 20, 30, 42 1. 8 2. 10 3. 12 4. 14 97. 5, 7, 11, 13, 17, 19, 23, 25, ? 1. 25 2. 27 3. 29 4. 31 98. 1, 2, 9, ?, 65, 126 1. 28 2. 82 3. 99 4. 108 99. 97, 86, 73, 58, 45, ? 1. 54 2. 55 3. 34 4. 56 100. 3, 5, 7, 9, ? 1. 11 2. 12 3. 13 4. 14 101. 1, 4, 9, 16, ? 1. 18 2. 23 3. 25 4. 36 102. 3, 10, 19, 30, 43, ? 1. 60 2. 58 3. 55 4. 50 103. 5, 6, 14, 45, 184, ? 1. 952 2. 925 3. 529 4. None 104. 5, 7, 11, 19, 35, ? 1. 60 2. 62 3. 67 4. 70 105. 2, 2, 4, 12, 48, ? 1. 240 2. 420 3. 480 4. 220 106. 8, 9, 20, 63, ? 1. 100 2. 252 3. 256 4. 120 107. 7, 8, 12, 21, ? 1. 42 2. 25 3. 37 4. 35 108. 1, 5, 19, 81, ? 1. 162 2. 231 3. 411 4. 352 109. 3, 7, 15, 31, ? 1. 52 2. 45 3. 60 4. 63 110. 3, 8, 18, 33, ? 1. 52 2. 53 3. 60 4. 63 111. 43, 60, 94, 145, ? 1. 213 2. 201 3. 190 4. 205 112. 0, 2, 6, ?, 20, 30, 42 1. 13 2. 15 3. 12 4. 14 113. 3, 6, 18, 72, ? 1. 108 2. 360 3. 164 4. 320 114. 215, 182, 149, 116, ? 1. 83 2. 73 3. 58 4. 92 115. 4, 9, 13, 22, 35, ? 1. 57 2. 70 3. 63 4. 75 116. 2, 4, 7, 11, 16, ? 1. 18 2. 20 3. 22 4. 25 117. 11, 13, 17, 19, 23, 29, 31, 37, 41, ? 1. 43 2. 47 3. 51 4. 53 118. 2, 6, 12, 20, 30, 42, 56, ? 1. 60 2. 64 3. 70 4. 72 119. 11, 12, 17, 18, 23, 24, ? 1. 12 2. 29 3. 30 4. 35 120. 5, 6, 8, 11, ?, 20, 26 1. 15 2. 17 3. 14 4. 16 121. 840, 168, 42, 14, 7, ____ 1. 1 2. 7 3. 9 4. 12 122. 13, 32, 24, 43, 35, ?, 46, 65, 57, 76 1. 45 2. 52 3. 54 4. 55 123. 0, 2, 3, 5, 8, 10, 15, 17, 24, 26, ? 1. 28 2. 30 3. 32 4. 35 124. 15, 14, 16, 13, 17, ? 1. 18 2. 19 3. 15 4. 12 125. 17, 18, 14, 15, 11, ? 1. 12 2. 15 3. 17 4. 19 126. 3, 5, 5, 19, 7, 41, 9, ? 1. 71 2. 61 3. 72 4. 69 127. 3, 2, 6, 8, 18, 40, 72, 240, ? 1. 360 2. 320 3. 440 4. 432 128. 4, 6, 6, 15, 8, 28, 10, ? 1. 36 2. 39 3. 45 4. 38 129. 23, 32, 49, 94, 73, ? 1. 64 2. 87 3. 95 4. 37 130. 67, 61, 59, 53, 47, ? 1. 43 2. 41 3. 37 4. 31 131. 5, 8, 9, 14, 16, 23, 26, ? 1. 29 2. 33 3. 35 4. 39 132. 3, 6, 8, 16, 19, ? 1. 35 2. 38 3. 21 4. 36 133. 6, 3, 12, 6, 18, ? 1. 9 2. 12 3. 24 4. 36 134. 5, 9, 6, 11, 7, ? 1. 13 2. 15 3. 17 4. 19 135. 0.1, 0.9, 0.01, 0.09, ?, 0.009 1. 0.01 2. 0.005 3. 0.001 4. 0.0101 136. 1, 2, 3, 6, 9, 18, ?, 54 1. 18 2. 36 3. 81 4. 27 137. 1, 2, 7, 7, 13, 12, ? 1. 19 2. 18 3. 12 4. 14 138. 2, 3, 10, 15, 26, 35, 50, 63, ? 1. 80 2. 82 3. 83 4. 84 139. 6, 24, 12, ?, 18, 8, 24 1. 4 2. 8 3. 16 4. 6 140. 1, 0, 3, 2, 5, 4, ? 1. 7 2. 6 3. 5 4. 4 141. 4, 2, 5, 1, 6, ? 1. 5 2. 2 3. 4 4. 0 142. 0, 2, 6, 6, 12, 10, ? 1. 12 2. 14 3. 15 4. 18 143. 50, 50, 60, 40, 70, 30, 80, 20, 90, 10, 100, ____ 1. 10 2. 20 3. 0 4. 5 144. 200, 300, 212, 288, 236, 264, 284, 216, __, __ 1. 380, 120 2. 188, 360 3. 388, 178 4. 380, 130 145. 0, 2, 3, 5, 8, 10, ? 1. 9 2. 11 3. 13 4. 15 146. 8, 24, 12, ____, 18, 54 1. 28 2. 46 3. 36 4. 48 147. 10, 15, 20, 30, 40, 60, 80, ____ 1. 90 2. 100 3. 110 4. 120 148. 6, 42, 12, 35, 18, 28, 24, 21, __ , 14, 36, 7 1. 30 2. 35 3. 36 4. 18 149. 5, 20, 6, 24, 7, 28, _____ 1. 8 2. 9 3. 32 4. 10 150. 5, 4, 10, 8, 15, 12, 20, _____, 25 1. 13 2. 18 3. 15 4. 16 151. 1, 8, 9, _____, 25, 216, 49 1. 64 2. 60 3. 70 4. 75 152. 3, 4, 15, 16, ______, 36, 63, 64 1. 30 2. 25 3. 34 4. 35 153. 1, 3, 1, 9, 1, 81, 1, _____ 1. 243 2. 324 3. 6561 4. 5641 154. 2, 4, 7, 14, 17, 34, 37, _____ 1. 74 2. 76 3. 47 4. 72 155. 20, 18, 19, 16, 18, 14, _____ 1. 16 2. 17 3. 15 4. 13 156. 3, 12, 4, 16, 5, 20, 6, _______ 1. 30 2. 36 3. 24 4. 18 157. 8, 8, 9, 9, 11, 10, 14, 11 1. 15 2. 18 3. 17 4. 12 158. 2, 6, 6, 14, 30, 62, ______, 254 1. 142 2. 128 3. 126 4. 132 159. 4, 8, 7, 14, 12, 24, 19, ____, 28 1. 12 2. 38 3. 36 4. 24 160. 2, 7, 9, 3, 8, 11, 4, 9, 13, _____, 10, 15 1. 4 2. 7 3. 5 4. 6 161. 3, 9, 5, 25, 7, 49, 9, ______ 1. 81 2. 64 3. 100 4. 121 162. 14, 60, 28, 45, ?, 30, 56 1. 40 2. 35 3. 36 4. 42 163. 7, 5, 2, 14, 3, 1, 2, 6, 8, 5, 3, 24, 6, 2, 4, ___ 1. 10 2. 36 3. 12 4. 24 164. 1, 4, 12, 2, 5, 15, 3, 6, 18, 4, ______ 1. 21 2. 7 3. 5 4. 6 165. 2, 8, 4, 3, 18, 6, 4, 32, 8, _______50, 10 1. 7 2. 6 3. 5 4. 9 166. 1278, _____, 314, 152, 70, 28 1. 634 2. 636 3. 632 4. 656 167. 2, 3, 6, 3, 4, 12, 4, 5, 20, 5, 6, ___ 1. 35 2. 30 3. 25 4. 35 168. 5, 7, 12, 6, 8, 14, 7, _____, 16, 8, 10, 18 1. 8 2. 10 3. 6 4. 9 169. 5, 2, 11, 6, 3, 12, 7, 4, 13, ____ 1. 8 2. 9 3. 10 4. 11 170. 3, 4, 12, 6, 2, 9, 18, 3, 6, ___, 24, 12, 2 1. 3 2. 8 3. 4 4. 9 171. 51, 17, 3, 16, 48, 12, 4, 10, 40, ____, 5, 13, 65 1. 9 2. 7 3. 6 4. 8 172. 4, 5, 9, 20, 5, 6, 11, 30, 6, 7, _____, 42 1. 12 2. 11 3. 13 4. 8 173. 1, 7, 11, 13, 11, ? 1. 12 2. 7 3. 9 4. 10 174. 1, 2, 3, 5, 4, 5, 9, 14, 13, 14, 27, ? 1. 80 2. 82 3. 40 4. 41 175. 1, 4, 9, ?, 8, 27 1. 1 2. 4 3. 6 4. 2 176. 8, 17, 9, 21, 12, 27, 15, ?, 21 1. 18 2. 16 3. 36 4. 10 177. 1, 3, 4, 8, 15, 27, ? 1. 37 2. 55 3. 50 4. 44 178. 1, 2, 4, 7, 13, 24, 44, ? 1. 62 2. 81 3. 73 4. 69 179. 1, 1, 1, 2, 4, 8, 3, 9, ? 1. 18 2. 17 3. 15 4. 27 130. 10, 40, 90, 61, 52, 63, ? 1. 54 2. 94 3. 14 4. 72 Letter Series 1. AZXBVTCR _______ 1. P, D 2. E, O 3. Q, E 4. O, X 2. C-3, E-5, G-7, I-9, _______ 1. X-24, M-21 2. K-11, M-13 3. O-15, X-14 4. M-18, K-14 3. C, e, G, i, K, _____ 1. O 2. m 3. k 4. U 4. BA, YZ, DC, WX, _______ 1. DE 2. EF 3. FE 4. FG 5. A, C, E, G, I, _____ 1. J, L 2. K, N 3. K, M 4. L, N 6. ACE, FHJ, KMO, PRT, _____ 1. TVX 2. RTU 3. UWY 4. ZBG 7. ADG, GJM, MPS, ____, YBE 1. SVX 2. SYX 3. SWZ 4. SVY 8. AK, CM, EO, GQ, ______ 1. JT 2. IS 3. JP 4. HR 9. SJA, TKB, ULC, VMD, WNE, _____ 1. XPF 2. XNF 3. XOG 4. XOF 10. QIA, SKC, UME, ______ 1. XOH 2. WOG 3. TLD 4. VPG 11. AJQ, BHR, CLS, DMT, ENU, ______ 1. VOF 2. IOT 3. FOV 4. FOW 12. EIMQ, FJNR, GKOS, _____ 1. IMQU 2. KOSW 3. HLPT 4. HLPU 13. ABCDE, FGHIJ, KLMNO, PQRST, UVWXY, _______ 1. ABCDE 2. ZABCD 3. ZYXWV 4. None 14. YUSP; UROL; QNKH, ______ 1. MIGD 2. MJFC 3. MJGD 4. MKHE 15. J Z I Y H _____ 1. A 2. X 3. U 4. Z 16. A Z B Y C ______ 1. A 2. W 3. Y 4. None 17. Z Y X A B C W V U D E F T S R G H _____ 1. L 2. M 3. R 4. P 18. P Q U R Q Q U R R Q U R ______ 1. I 2. R 3. V 4. Z 19. P Q U R Q U R N Q U R _______ 1. M 2. N 3. O 4. Q 20. Z A S G S F Z J Z _____ 1. Z 2. I 3. O 4. Q 21. A C F J O ______ 1. U 2. B 3. V 4. W 22. AB, DC, EF, HG, ____ 1. I 2. V 3. W 4. N 23. D F I M R _____ 1. V 2. X 3. W 4. Y 24. B E I _____ 1. W 2. M 3. N 4. Z 25. DMP, FLN, HKL, JJJ, ______ 1. MII 2. LIH 3. III 4. MIF 26. A, Z, D, X, G, V, J, T, M, ____ 1. R, P 2. S, N 3. P, R 4. N, S 27. B, D, G, K, P, _____ 1. S 2. V 3. T 4. W 28. MKP, WSZ, KGN, ____ 1. LIP 2. MIP 3. TMQ 4. HLE 29. C4X, F9U, I 16R, ____ 1. L 25P 2. L 25 O 3. L 27 P 4. None 30. EJOT, DHLP, CFIL, ___ 1. BDFH 2. BHLM 3. DEIJ 4. DGKC 31. S2E, U6D, W21C, _____ 1. Y66B 2. Y44B 3. Y88D 4. Z88D 32. 2A11, 4D13, 12G17, _____ 1. 36 I 19 2. 48 J 21 3. 36 J 21 4. 48 J 23 33. 2Z5, 7Y7, 14X9, 23W11, 34V13, ___________ 1. 27U24 2. 47U15 3. 45U15 4. 47V14 34. J2Z, K4X, I7V, ______, H16R, M22P 1. I 11 T 2. L 11 S 3. L 12 T 4. L 11 T 35. 3F, 6G, 11I, 18L, ______ 1. 21O 2. 25N 3. 27P 4. 27Q 36. D-4, F-6, H-8, J-10, _____, ______ 1. K-12, M-13 2. L-12, M-14 3. L-12, N-14 4. K-12, M-14 37. A D E H I L _________ 1. MP 2. MN 3. MO 4. MQ 38. AZBYCXD____ 1. E 2. W 3. R 4. F 39. A G L P S _____ 1. X 2. Y 3. W 4. U 40. R U X A D _______ 1. E 2. F 3. G 4. I 41. C E I K O Q _____ 1. R 2. S 3. T 4. U 42. Z X V T R P _____ 1. Q 2. R 3. S 4. N 43. CD, GH, KL, OP, ST, _____ 1. RS 2. QR 3. GH 4. WX 44. XD, WC, ____, YA 1. XY 2. CD 3. OP 4. ZB 45. C G K O S A E I M Q E I M Q ___ 1. W 2. X 3. V 4. U 46. ACF acf G______ _______ 1. IL, giL 2. JL, giL 3. IL, giL 4. LL, gli 47. Z X V z x v U ____ ______ 1. Ust UST 2. SQ usq 3. USQO 4. USTrs 48. accce, ACCCE, _______ _______ 1. GJJJK, gjjjjjk 2. giiik, GIIIK 3. GIIIK, ghhk 4. None 49. CFL, EIK, GLJ, IOI, __ 1. KRH 2. KRJ 3. JRH 4. KQH 50. A, CD, GHI, ___, VUWXY 1. LMNO 2. MNO 3. NOPQ 4. MNOP 51. A/2, B/4, C/6, D/8, ________ 1. E/16 2. F/32 3. F/12 4. E/10 52. ZXVTR ______ 1. O 2. N 3. K 4. P 53. B, A, Z, D, C, Y, F, E, _____ 1. W 2. X 3. U 4. G 54. A, E, J, O, T, ______ 1. U 2. Y 3. W 4. Z 55. AG, CI, MS, R___ 1. V 2. U 3. X 4. Y 56. AG, BH, CI, ______ 1. DJ 2. DI 3. EL 4. HM 57. AGM, BHN, CIU, DJP, ______ 1. EPR 2. EKP 3. EMS 4. EKQ 58. CJQ, DKR, ELS, FMT, ______ 1. GNU 2. GOV 3. GNW 4. HOV 59. GPW, FOV, ENU, _______, CLS, BKR 1. DMT 2. DKR 3. DMR 4. DLT 60. NIFA, OJGB, PK___ 1. HD 2. LC 3. HC 4. TU 61. YMA, ZNB, AOC, ____ 1. BND 2. CPC 3. BPQ 4. BPD 62. AGPU, BHQV, CIRW, ____ 1. DOSX 2. DJSY 3. DJSX 4. DISX 63. XSNI, TOJE, _____ 1. LGBZ 2. PKFA 3. HCYU 4. JGBX 64. A E I L P _____ 1. V 2. W 3. N 4. T 65. A C E D F ______ 1. H 2. J 3. E 4. W 66. A J E B U Q I Y E P A ______ 1. J 2. K 3. W 4. Y 67. B C D Y X W F G H U T S ________ 1. C 2. D 3. F 4. J 68. G I J J L M M O P P _________ 1. M 2. R 3. N 4. O 69. A D B E C F D _______ 1. W 2. G 3. U 4. U 70. W U S Q O _____ 1. O 2. N 3. M 4. W 71. B C F G J K ____ 1. P 2. O 3. M 4. N 72. B, F, K, Q, _____ 1. X 2. R 3. T 4. Y 73. A, B, D, G, ____, P 1. J 2. I 3. K 4. L 74. POQ, SRT, VUW, _____ 1. XYZ 2. XZY 3. YXZ 4. YZX 75. AD, EH, IL, ______, QT 1. MP 2. MN 3. LM 4. OM 76. ADG, HKN, _____ 1. ORU 2. VXZ 3. JLN 4. BEG 77. AZ, CX, FU, _____ 1. KP 2. JQ 3. IR 4. IV 78. CDE, HIJ, OPQ, XYZ, _____ 1. IJK 2. JKL 3. KLM 4. LMN 79. CDE, IJK, RST, DEF, _____ 1. RST 2. STU 3. GRS 4. PQR 80. C4X, F9U, I16R, _____ 1. K25P 2. L25P 3. L25O 4. L27P 81. OPQ, WXY, ______, RST, EFG 1. HIJ 2. IJK 3. KLM 4. LMN 82. CD, HI, MN, _____ 1. QS 2. RS 3. OP 4. PQ 83. AU, BY, CZ, _______ 1. BC 2. KL 3. MN 4. DX 84. C F I L O _____ 1. P 2. Q 3. R 4. S 85. E G J L O Q ____ 1. S 2. R 3. U 4. T 86. A I P V A E _____ 1. F 2. G 3. H 4. I 87. I M Q U Y C _____ 1. C 2. D 3. F 4. G 88. X U S P N K ____ 1. I 2. L 3. M 4. Q 89. T Q N K H _____ 1. I 2. J 3. S 4. E 90. D I L Q T Y B G _____ 1. H 2. I 3. O 4. J 91. X U S P N K I ____ 1. J 2. K 3. M 4. F 92. D F I M R ____ 1. S 2. U 3. M 4. X 93. B D G I L N ____ 1. O 2. Q 3. S 4. U 94. D I L Q T Y B G _ 1. H 2. J 3. R 4. I 95. T S Q N J ______ 1. S 2. E 3. K 4. L 96. S P L G _____ 1. R 2. S 3. U 4. A 97. B E I N T _____ 1. R 2. S 3. U 4. A 98. B F K Q ______ 1. R 2. S 3. W 4. X 99. R T P R N P ____ 1. Q 2. L 3. S 4. F 100. W T P M I F B ____ 1. W 2. P 3. F 4. Y 101. X W V U T S ____ 1. R 2. T 3. E 4. X 102. AD, EH, IL, ______, QT, UX 1. AY 2. VB 3. CW 4. MP 103. AY, BZ, CW, _____ 1. EF 2. GH 3. MN 4. DX 104. BC, FG, JK, ____, RS, VW 1. LM 2. OP 3. QR 4. NO 105. AI, BJ, CK, ____ 1. LM 2. GH 3. QR 4. DL 106. Z W S P L I E____ 1. D 2. F 3. G 4. B 107. AC, EG, BD, FH, IK, _____ 1. LM 2. OP 3. IJ 4. JL 108. ABC abc DEF _____ 1. ghi 2. GHI 3. ABC 4. def 109. AGMS, agms, _____ 1. ABCD 2. abcd 3. BHNT 4. bhnt 110. CYD, FTH, IOL, LJP, ______ 1. OFT 2. LET 3. OEK 4. OET 111. BXF, DVI, FTL, HRO, _____ 1. JPL 2. KPL 3. JOL 4. JPR 112. ZGL, XHN, VIQ, TJU, _____ 1. QKZ 2. RKY 3. RLZ 4. RKZ 113. BXJ, ETL, HPN, KLP, _______ 1. NHR 2. MHQ 3. MIP 4. NIR 114. AaD, BeF, DiH, _____, KuL 1. FmI 2. GoJ 3. HlK 4. GiJ 115. OAL, MZN, KBP, IYR, _______ 1. GCT 2. QXT 3. QXJ 4. GET 116. BY, IQ, NK, QG, ____ 1. RF 2. TF 3. RE 4. SE 117. DKM, FJP, HIS, JHV, _____ 1. HGY 2. IGZ 3. IGY 4. LGY 118. AZ, IY, OW, SS, ____ 1. QA 2. KU 3. OU 4. UK 119. AX, BY, CX, ____ 1. EF 2. GH 3. IJ 4. DW 120. GHJM__V 1. T 2. S 3. R 4. Q 121. AYD, BVF, DRH, ______, KGL 1. FMI 2. GMJ 3. HLK 4. GLJ 122. MHZ, NIW, OKT, PNQ, _______ 1. RRN 2. QRN 3. QRM 4. QQN 123. LXF, MTJ, NPN, OLR, ___ 1. PHV 2. PIU 3. PJW 4. PKX 124. shg, rif, qje, pkd, _____ 1. ole 2. olc 3. nmc 4. nlb 125. FLP, INS, LPV, ________ 1. ORY 2. UXZ 3. VXY 4. SVW 126. DEF, HIJ, MNO, _______ 1. STU 2. RST 3. RSV 4. SRQ 127. U, O, I, ____, A 1. E 2. C 3. S 4. G 128. A, B, D, G, ____ 1. M 2. L 3. K 4. H 129. Z, U, Q, ____, L 1. I 2. K 3. M 4. N 130. A, C, F, H, ____, M 1. L 2. K 3. J 4. I 131. AZ, CX, FU, ______ 1. IR 2. IV 3. JQ 4. KP 132. AZ, GT, MN, _____, YB 1. KF 2. RX 3. SH 4. TS 133. BF, CH, _____, HO, LT 1. DN 2. EL 3. EK 4. None 134. AD, EH, IL, _____, QT 1. LM 2. MN 3. MP 4. OM 135. CAT, FDW, IGZ, _______ 1. KJA 2. KTC 3. LHD 4. LJC Number Analogy: 1. 29 : 31 :: 37 :_______ 1. 47 2. 43 3. 38 4. 41 2. 26 : 126 :: 37 :_____ 1. 195 2. 186 3. 217 4. 205 3. 2 : 16 :: 3: _______ 1. 243 2. 81 3. 27 4. 729 4. If 7 : 2=27, 3 : 4=21 then 5 : 6 = ? 1. 33 2. 35 3. 20 4. 15 5. 48 : 80 ::_______: 576 1. 18 2. 24 3. 48 4. 68 6. 52:76::_____:536 1. 196 2. 322 3. 488 4. 702 7. 56 : 182 ::______: 992 1. 552 2. 600 3. 702 4. 756 8. 3:11::7:_______ 1. 22 2. 29 3. 18 4. 51 9. 324 : 162 1. 64:36 2. 2:1 3. 22:10 4. 134:112 10. 6 : 18 :: 4 :____ 1. 12 2. 6 3. 8 4. 16 11. 21 : 3 :: 574 :____ 1. 23 2. 82 3. 97 4. 113 12. 1 : 1 :: 25 :_______ 1. 26 2. 125 3. 240 4. 625 13. 121 : 12 :: 25 : ? 1. 1 2. 2 3. 6 4. 7 14. 42 : 20 :: 64 :______ 1. 51 2. 52 3. 53 4. 54 15. 7584 : 5362 :: 4673 :________ 1. 2367 2. 2451 3. 2531 4. None 16. 25 : 37 :: 49 :______ 1. 41 2. 56 3. 60 4. 65 17. 25 : 125 :: 36 :_____ 1. 180 2. 206 3. 216 4. 318 18. 14 :9 :: 26 :______ 1. 12 2. 13 3. 15 4. 31 19. 8 : 28 :: 27 :______ 1. 8 2. 28 3. 64 4. 65 20. 583 : 293 :: 488 :_________ 1. 291 2. 378 3. 487 4. 581 21. 7 : 56 :: 9 :_______ 1. 63 2. 81 3. 90 4. 99 22. 9 : 8 : 16 :_____ 1. 27 2. 18 3. 17 4. 14 23. 8 : 81 :: 64 :______ 1. 125 2. 137 3. 525 4. 625 24. 17 : 52 :: 1 :_________ 1. 3 2. 4 3. 5 4. 51 25. 9 : 80 :: 100 :_______ 1. 901 2. 1009 3. 9889 4. 9999 26. 12:144 1. 22:464 2. 20:400 3. 15:135 4. 10:140 27. 27 : 9 1. 64:8 2. 125:5 3. 135:15 4. 729:81 28. 5 : 35 1. 7:77 2. 9:45 3. 11:55 4. 3:24 29. 8 : 256 1. 7:343 2. 9:243 3. 10:500 4. 5:75 30. 6 : 39 ::____: 333 1. 22 2. 15 3. 18 4. None 31. 5 : 130 ::______: 1010 1. 8 2. 9 3. 10 4. None 32. 4 : 60 ::_____: 504 1. 8 2. 7 3. 6 4. None 33. 6 : 10 ::____: 1342 1. 120 2. 132 3. 170 4. None 34. 125 : 216 :: 1331 :______ 1. 145 2. 1728 3. 289 4. None 35. 81 : 729 :: 144 :_____ 1. 1131 2. 1331 3. 1728 4. None 36. 196 : 256 :: 324 :_____ 1. 400 2. 200 3. 361 4. None 37. 121 : 169 :: 361 :_______ 1. 400 2. 529 3. 180.5 4. None 38. 125 : 343 :: 343 :___ 1. 1331 2. 1719 3. 1000 4. None 39. 5 : 120 :: 8 :______ 1. 512 2. 504 3. 510 4. None 40. 123 : 14 :: 234 :____ 1. 25 2. 27 3. 29 4. None Directions In each of the following questions a pair of numbers which are having a certain relation between them are given to the left of sign : : while one number is given on another side of : : Choose the best alternative which is having the same relation with this number as the numbers of the given pair bear. 41. 4 : 8 : : 8 : ? 1. 32 2. 10 3. 12 4. 24 42. 32 : 4 :: 200 : ? 1. 20 2. 25 3. 10 4. 30 43. 7 : 49 :: 15 : ? 1. 200 2. 625 3. 225 4. 210 44. 144 : 13 :: 225 : ? 1. 15 2. 14 3. 13 4. 16 45. 64 : 7 :: 121 : ? 1. 8 2. 9 3. 10 4. 11 46. 4 : 10 :: 25 : ? 1. 37 2. 30 3. 42 4. 36 47. 16 : 64 :: 49 : ? 1. 323 2. 56 3. 373 4. 343 48. 11 : 19 :: 31 : ? 1. 37 2. 43 3. 39 4. 47 49. 14 : 9 :: 26 : ? 1. 12 2. 13 3. 15 4. 31 50. 27 : 65 :: 1 : ? 1. 8 2. 9 3. 10 4. 7 51. 853 : 963 :: 844 : ? 1. 921 2. 873 3. 651 4. 861 52. 20 : 8000 :: 30 : ? 1. 12000 2. 15000 3. 27000 4. 30000 53. 8 : 72 :: 12 : ? 1. 156 2. 200 3. 144 4. 120 54. 9 : 8 :: 16 : ? 1. 27 2. 18 3. 17 4. 114 55. 12 : 37 :: 2 : ? 1. 6 2. 8 3. 7 4. 10 56. 10 : 99 :: 12 : ? 1. 144 2. 143 3. 141 4. 145 57. 81 : 91 :: 100 : ? 1. 110 2. 131 3. 111 4. 120 58. 30 : 42 :: 56 : ? 1. 72 2. 68 3. 84 4. 76 59. 7 : 342 :: 9 : ? 1. 344 2. 801 3. 999 4. 728 Directions: Each of the following questions consists of a pair of numbers that have a certain relationship to each other, followed by four other pairs of numbers given as alternatives. Select the pair in which the numbers are similarly related as in the given pair. 60. 8 : 15 1. 24 : 36 2.49 : 64 3. 35 : 48 4. 99 : 121 61. 5 : 100 1. 4 : 48 2. 4 : 64 3. 3 : 18 4. 9 : 81 62. 3 : 24 1. 2 : 8 2. 5 : 119 3. 4 : 62 4. 7 : 49 63. 12 : 21 1. 18 : 90 2. 28 : 56 3. 41 : 24 4. 17 : 71 64. 8 : 12 1. 18 : 27 2. 16 : 23 3. 20 : 30 4. 12 : 18 65. 5 : 30 1. 4 : 20 2. 7 : 21 3. 8 : 72 4. 2 : 4 66. 81 : 9 1. 12 : 3 2. 18 : 6 3. 62 : 8 4. 56 : 7 67. 72 : 14 1. 18 : 90 2. 52 : 10 3. 35 : 18 4. 50 : 20 68. 64 : 512 1. 7 : 49 2. 9 : 81 3. 6 : 216 4. 25 : 625 69. 8 : 32 1. 6 : 28 2. 5 : 15 3. 16 : 128 4. 12 : 144 70. 12 : 30 1. 56 : 89 2. 30 : 56 3. 19 : 29 4. 42 : 58 71. 72 : 83 1. 51 : 72 2. 23 : 31 3. 42 : 53 4. 20 : 30 Directions Choose the best number which is similar to the numbers given in the following given set. 72. 539, 278, 458 1. 368 2. 549 3. 637 4. 873 73. 126, 168, 147 1. 189 2. 104 3. 125 4. 963 74. 284, 362, 188 1. 482 2. 354 3. 823 4. 611 Directions (Questions 35-40): Choose the set of numbers from the four alternatives sets, that is similar to the given set in the question. 75. (5 8 13) 1. (3 4 5) 2. (6 13 22) 3. (7 10 14) 4. (2 5 9) 76. (5 7 9) 1. ( 6 6 8) 2. (7 8 9) 3. (8 5 4) 4. (4 7 8) 77. (7 24 25) 1. (6 35 36) 2. (9 40 42) 3. (5 11 13) 4. (11 60 61) 78. (63 8 3) 1. (1 2 1) 2. (80 9 4) 3. (225 15 4) 4. (8 4 2) 79. (16 9 4) 1. (25 36 49) 2. (64 49 36) 3. (25 36 16) 4. (36 9 49) 80. (2 3 6) 1. (5 2 9) 2. (4 2 8) 3. (3 3 8) 4. (4 3 9) Letter Analogy Find out the correct letter pair from the alternative given in answer choices below, to donate the same relationship among the group of letters as established between the sets at the top (question pair). 1. APA : EQE ::_____:________ 1. BQB: FGF 2. CDC: GHG 3. LML: NON 4. IRI: OSO 2. AP: EQ::_____:______ 1. AB:CD 2. EF: IK 3. LM:NO 4. IR:OS 3. JAJ: KEK::_______:_______ 1. BAB: DED 2. FGI: HIJ 3. KEK: LIL 4. LIL: MOM 4. AZB: CYD::___:______ 1. EXF: GWH 2. EFG: HIJ 3. EFG: HIK 4. EZF: CYH 5. I:V::N:_______ 1. H 2. X 3. T 4. W 6. V:N::Z:_____ 1. X 2. I 3. T 4. M 7. V:X::H:_______ 1. Y 2. T 3. I 4. Z 8. PS:DG::_____:_________ 1. CE:TR 2. KM:OQ 3. EH:TW 4. FH:JL 9. BC:GH::___:______ 1. RT:XY 2. ST:UV 3. OP:QR 4. ST:XY 10. JK:QR::_______:______ 1. ST:UV 2. WX:ZY 3. CF:JL 4. BC:IJ 11. CD:GH::LK:____:________ 1. DC 2. EG 3. AB 4. JI 12. XY: PQ::MN:_______ 1. TS 2. MO 3. QP 4. BC 13. MN:OP::RS:_______ 1. BH 2. HI 3. MO 4. UW 14. YZ:XY::AB:_______ 1. ML 2. BD 3. PR 4. PQ 15. DC:HG::ML:_________ 1. OP 2. NM 3. BA 4. PQ 16. TS:LK::BA:______ 1. DE 2. FE 3. GI 4. RP 17. AB:DE::_____:_______ 1. GH:JK 2. HI:RS 3. GH:KL 4. ED:BA 18. I:T::___:______ 1. W:X 2. M:V 3. L:N 4. L:X 19. b:d::p:_______ 1. a 2. o 3. q 4. d 20. F:P::E:_______ 1. F 2. G 3. B 4. W 21. RAGDE:EDGAR::________:_____ 1. LUKE:MATTHEWS 2. GANDHI:HDNADI3. EGROEG:GEORGE 4. POLITE:COURTESY 22. AF:IK::LQ:_____ 1. MO 2. RS 3. TV 4. TU 23. FED:MKI::PON:_____ 1. VUY 2. WUS 3. TVU 4. TVM 24. AYBZ:CWDX::EUFV:______ 1. GSHT 2. GHST 3. SHGT 4. MVGT 25. ACEG:IKMO::KMOQ:_________ 1. SWVY 2. SUWY 3. STVW 4. SWTM 26. ZWT:ROL::IFC:_______ 1. AXU 2. AYU 3. ZUT 4. AWT 27. ABD:EFH::IJL:______ 1. MNP 2. MPN 3. NMP 4. NMT 28. FHJ:LNP::RTV:________ 1. ZXB 2. XZT 3. XZB 4. VTM 29. DE:45::BC:________ 1. 23 2. 24 3. 25 4. 26 30. ABE:8::FBD:______ 1. 14 2. 13 3. 15 4. 12 31. 987:IHG::654:______ 1. FDE 2. FED 3. EFD 4. DEF 32. K 11 J : :: : T 20 R ________ 1. 7 10 2. 10 18 3. 8 11 4. 10 15 33. Z Y T : : 26 25 20 : _______ 1. S 19 2. R 17 3. 8 16 4. 19 20 34. LXM:12X13::UXW:_______ 1. 21X20 2. 21X23 3. 20X23 4. 23X10 35. ZYB:XWD::UTG:_________ 1. ISR 2. SRI 3. IRS 4. None 36. ABX:DEU::GHR:_______ 1. JKO 2. JOK 3. KOJ 4. OKJ 37. ? : DURXQG :: WOULD : TLRIA 1. ARMOUR 2. SHROUD 3. SHOULD 4. AROUND 38. ? : YBVLKA :: WOULD : TLRIA 1. BEYOND 2. NORMAN 3. BYGONE 4. MATTER 39. LJH : KKI :: CIA : ? 1. BJB 2. BBB 3. CBZ 4. BBZ 40. DRIVEN : EIDRVN :: BEGUM : ? 1. BGMEU 2. MGBEU 3. UEBGM 4. BGMUE Directions: Find out the correct letter pair from the alternative given in answer choices below, to donate the same relationship among the group of letters as established between the sets at the top (question pair). 41. ZA:YB::XC:______ 1. YZ 2. NM 3. BC 4. WD 42. ABCD:WXYZ::EFGH:_____ 1. STVU 2. STOU 3. STUE 4. STUV 43. AD:BE::CF:___ 1. DE 2. BC 3. DG 4. FG 44. ACDE:OGHI::ESTU:____ 1. EPQU 2. ABCD 3. OGHK 4. XYZE 45. BAC:DEF::____:NOP 1. GHI 2. JHI 3. GIH 4. HIJ 46. CG:EI::FJ:_____ 1. JK 2. IJ 3. LM 4. GK 47. ACF:EDG::IEH:______ 1. OFI 2. GHI 3. LMN 4. EIJ 48. AEZ:EIY::IOX:_____ 1. UYZ 2. AEX 3. EIX 4. OUW 49. AZB:BYC::CXD:___ 1. DWE 2. DEF 3. DFG 4. DMN 50. BACE:DACE::FACE:_________ 1. HASE 2. LACE 3. CASE 4. HACE 51. ZYB:XWD::TSH:________ 1. QFR 2. RFQ 3. RQF 4. None 52. ADG:ZWT::IKN:________ 1. RPM 2. PMR 3. MRP 4. PRM 53. NQS:TWY::KHF:_______ 1. NLQ 2. QNL 3. LQN 4. None 54. PNR:KMI::XZV:_______ 1. DAE 2. AED 3. EAD 4. None 55. ACEG:DFHJ::_______:ZXVT 1. WUSQ 2. SQOM 3. USQO 4. YWUS 56. KcaC:CacK::XgmF: ______ 1. GmeF 2. FmgX 3. EgmX 4. EmgF 57. QIOK:MMKO::YAWC:______ 1. USGA 2. UESG 3. VUES 4. SUEG 58. ACEG:ZXVT::IKMO:_____ 1. YACE 2. RPLN 3. SQOM 4. RPNL 59. PNDY:QMEX::JRSF:______ 1. KQRE 2. KSTE 3. KSRE 4. KQTE 60. POLITE:ETILOP::_____:______ 1. ELPMIS; SIMPLE 2. DRAOG; BOARD 3. CHART; TRAHC 4. SINGLE; ELGNIS 61. RT:WZ:______:_____ 1. AC:RU 2. AB:PW 3. PR:LM 4. TU:WX 62. Z:N::____:_______ 1. H:T 2. X:E 3. M:N 4. T:V 63. IJ:KL::_____:______ 1. AB:PQ 2. AD:GH 3. LM:OP 4. MN:OP 64. AZ:BY::____:______ 1. CX:BW 2. CW:DY 3. CX:DW 4. CZ:DY 65. LLAMS:SMALL::_____:_________ 1. CORK:KROC 2. BARK:KRAB 3. TREE:EERT 4. SRENID:DINERS 66. CBA:FED::______:_______ 1. IJH:MNL 2. BCA:FGH 3. MCA:JKO 4. IHG:KLJ 67. FED:IHG::________:______ 1. ACB:GIJ 2. TSR:WVW 3. IJK:LMO 4. DEF:IGH 68. CEH:IKN::_____:_______ 1. CDF:IJK 2. OQT:UWZ 3. EFH:KMN 4. BCE:GIJ 69. CDF:GHJ::____:_____ 1. BQB:FGF 2. CDC:GHG 3. KLM:OQR 4. PQR:STU 70. 17 IH : 27 NM : 31 PO :_______ 1. GM 16 2. GT 14 3. GV 16 4. GF 13 71. AEI:MQU::XBF:_______ 1. JNR 2. NJP 3. STV 4. MNO 72. XUR:OLI::FCZ:_______ 1. WTQ 2. WQT 3. WTM 4. TWC 73. RPQ:OMN::JIH:_____ 1. GFE 2. GEF 3. GTB 4. GBT 74. A:Z::B:_____ 1. X 2. Y 3. W 4. U 75. ADH:BEI::KTO:______ 1. LUR 2. LUP 3. MUR 4. MUP 76. ABY:BCX::GHS:________ 1. HIR 2. IRH 3. RIH 4. None 77. CXDW:HSIR::KPLO:______ 1. KPQj 2. KQjP 3. PKQj 4. JKQP 78. BCYX:DEWV::GHTS:_______ 1. IJRQ 2. JIRQ 3. RIQJ 4. None 79. ADF:JMO::DGI:_____ 1. TQO 2. ORT 3. ZXV 4. PON 80. BYDW:FUHS::AZCX:_____ 1. EVGT 2. FVGT 3. EGVT 4. FGVT 7. NUMBER RANKING 1. In a number series given below count each 5 which is not immediately preceded by 3 but is immediately followed by 7. How many such 5‟s are there? 5 7 3 3 5 7 3 5 7 7 5 3 5 7 5 7 2 3 5 7 5 3 7 5 3 5 7 7 3 5 3 5 5 7 1. 1 2. 2 3. 3 4. 4 2. How many numbers are there which are divided by 3 and followed by the numbers divided by 2 in the given series? 3 4 5 9 6 1 5 3 2 4 5 3 4 3 4 9 2 5 1. 1 2. 2 3. 3 4. 6 3. How many 5‟s are there in the following number sequence which are immediately followed by 3, but not immediately preceded by 7? 8 9 5 3 2 5 3 8 5 5 6 8 7 3 3 5 7 7 5 3 6 5 3 3 5 7 3 8 1. 1 2. 2 3. 3 4. 4 4. How many such 7‟s are there in the following number sequence which are immediately followed by 4 but not immediately preceded by 8? 8 7 4 4 7 8 4 7 4 7 8 4 8 8 7 7 4 8 7 4 7 4 8 8 7 7 7 9 4 8 7 7 4 1. 2 2. 3 3. 4 4. 5 5. How many 8‟s are there in the following number series which are exactly divisible by its immediately preceding and immediately succeeding numbers? 7 8 3 8 4 8 1 2 8 5 4 8 1 4 8 3 8 8 2 4 8 2 8 5 8 4 8 5 1. 4 2. 2 3. 5 4. 3 6. How many numbers are there in the given series, which are not preceded by 5 but followed by 4? 1 5 7 9 6 7 9 5 4 3 2 1 0 9 1. 1 2. 2 3. 3 4. 4 7. How many 3‟s are there in the following number sequence which are immediately preceded by 6 but not immediately followed by 7? 2 3 7 4 3 5 6 3 7 4 6 3 8 9 6 3 5 1 8 3 7 2 4 2 8 6 3 9 1. 1 2. 2 3. 3 4. 4 8. In the following number series how many 7‟s are there which are immediately followed by 5 also immediately preceded by 6? 7 5 7 6 8 7 5 6 7 5 6 8 6 7 5 7 5 7 7 1. 1 2. 2 3. 3 4. None 9. How many 3‟s are there in the given series that are exactly followed by 1 and also immediately preceded by 2? 3 2 3 1 4 3 1 2 3 1 2 4 2 3 1 3 1 3 3 1. 2 2. 3 3. 4 4. 5 10. How many prime numbers are there which are an odd number and preceded by an even number? 3 2 4 2 7 5 4 9 7 8 5 5 6 3 3 5 4 2 3 9 6 2 7 1 2 3 6 1. 9 2. 7 3. 8 4. 5 11. How many 8‟s are there in the following sequence which are immediately followed by 6 but not immediately preceded by 9? 6 8 9 7 6 8 6 9 8 6 2 8 6 9 8 6 8 9 8 1. 3 2. 1 3. 2 4. None 12. In the following series of numbers, find out how many times 1, 3 and 7 have appeared together, 7 being in the middle and 1 and 3 on either side of 7. 2 9 7 3 1 7 3 7 7 1 3 3 1 7 3 8 5 7 1 3 7 7 1 7 3 9 0 6 1. 3 2. 4 3. 5 4. More than 5 13. How many 4‟s immediately preceded by 5 but not immediately followed by 7 are there in the following series of numbers? 5 4 8 7 4 9 5 4 7 7 4 5 5 4 6 5 4 7 5 4 7 3 2 4 7 1. 2 2. 3 3. 4 4. 5 14. How many even numbers are there which are not followed by even but preceded by even number? 3 2 5 4 4 7 6 5 2 6 7 6 9 8 4 7 5 4 8 5 6 2 1 1 2 4 8 1. 5 2. 6 3. 4 4. 7 15. Four of the following five are alike in a certain way and so form a group. Which is the one that does not belonging to the group? 1. 81081 2. 18081 3. 18018 4. 80801 16. How many 7‟s are there in the following numbers sequence which are immediately preceded by 5 but not immediately followed by 3? 3 7 5 7 4 5 7 3 9 7 8 5 7 7 8 9 7 1 5 7 6 5 7 4 3 7 5 7 3 8 1. 1 2. 2 3. 3 4. 4 17. How many 8‟s are there in the following number sequence which are preceded by 7 but not immediately followed by 4? 2 3 8 2 5 7 8 3 7 8 4 6 9 8 4 3 2 7 8 9 5 7 8 1 5 2 9 1. One 2. Two 3. Three 4. Four 18. In a row of children, Hari is eleventh from the left and Manjula is seventeenth from the right. When they exchange their places, Hari will be thirteenth from the left. Which of the following will be the new position of Manjula from right? 1. Eleventh 2. Twenty-ninth 3. Twenty-first 4. Nineteenth 19. How many numbers are there which are divisible by 3 and are preceded by 3 but not followed by 2? 3 6 2 2 9 3 6 7 5 3 9 8 7 2 2 3 3 9 3 3 2 3 6 4 3 8 7 1. 5 2. 4 3. 9 4. 1 20. Which of the following will be the third digit of the number from your right end of the third number after the numbers are arranged in descending order? 4 6 9 7 , 6 9 8 9 , 5 3 9 2 , 7 5 1 8 , 6 2 1 5 , 5 9 4 2 1. 1 2. 5 3. 2 4. 4 21. Kapil ranked thirteenth from the top and twenty-six from the bottom among those who have passed in the annual examination in a class. If six students have failed in the annual examination, what was the total number of students in that class? 1. 45 2. 38 3. 44 4. 50 22. In a row of boys, Anil is 15 th from the left and Vishakh is 7 th from the right. If they interchange their positions, Vishakh becomes 15 th from the right. How many boys are there in the row? 1. 21 2. 22 3. 29 4. Can‟t be determined 23. Samir‟s rank is tenth from the top in his class. Prabir, who is 15 th from the end is lower in rank than Samir by ten. How students are there in Samir‟s class. 1. 32 2. 31 3. 38 4. 34 24. How many even numbers are there which are divisible by a prime number and preceded by an odd number and followed by a prime number? 3 4 7 5 8 2 7 9 8 2 6 7 4 5 3 8 2 8 4 5 6 2 7 2 2 3 2 1. 6 2. 7 3. 9 4. 8 25. In a row of children, Shibu is 5 th from the left and Ravi is 6 th from right. When they exchange position, Shibu will be 13 th from the left. What will be Ravi‟s position from the right? 1. 4 th 2. 5 th 3. 13 th 4. 14 th 26. Madhav ranks thirteenth in a class of thirty-one. What is his rank from the last? 1. 19 2. 17 3. 18 4. 20 27. In the following series how many such odd numbers are there which are divisible by 3 or 5, then followed by odd numbers and again followed by even numbers? 12 19 21 3 25 18 35 20 22 21 45 46 47 48 9 50 52 54 55 56 1. 3 2. 1 3. 2 4. None 28. How many 6‟s present in the following sequence of number which are preceded by 1 but not followed by 9? 9 6 1 2 3 1 6 8 3 4 1 6 9 0 5 7 1 6 4 3 2 2 6 5 1. 1 2. 2 3. 3 4. 4 29. How many such 5‟s are there in the following number sequence which are immediately followed by „3‟ but not immediately preceded by „7‟? 8 9 5 3 2 5 3 8 5 5 6 8 7 3 3 5 7 7 5 3 6 5 3 3 5 7 3 8 1. 1 2. 2 3. 3 4. 4 30. How many 6‟s are there in the following sequence which are immediately followed by „3‟ and immediately preceded by „7‟? 6 3 3 7 7 6 6 3 7 3 7 6 7 3 7 6 3 3 6 6 7 7 3 6 7 3 1. 1 2. 2 3. 3 4. None 31. How many 8‟s are present in the following sequence of number which are preceded by 9 but not followed by 6? 2 1 9 8 5 4 3 9 8 7 0 9 8 6 8 9 3 9 8 1 2 9 1. 1 2. 2 3. 3 4. 4 32. In the series given below, how many 8‟s are there which are exactly divisible by its immediately preceding as well succeeding numbers? 2 8 3 8 2 4 8 2 4 8 6 8 2 8 2 4 8 3 8 2 8 6 1. 1 2. 2 3. 3 4. 4 33. In a row of 16 boys, when Prakash was shifted by two places towards the left, he became 7 th from the left end. What was his earlier position. 1. 7 th 2. 8 th 3. 9 th 4. 10 th 34. How many 5‟s immediately preceded by 9 but not immediately followed by 2 are there in the following series? 5 2 8 5 9 2 1 0 5 6 1 6 5 4 2 1 5 9 5 8 2 7 9 5 2 1 1. 1 2. 2 3. 4 4. 6 35. How many 6‟s are there in the following number series which are either preceded by 4 or following by 7? 3 1 2 9 6 4 7 6 4 6 7 2 9 7 6 4 4 6 7 1. 1 2. 2 3. 3 4. 4 36. In the following series of numbers, how many times have the figures 9, 1 and 8 appeared together 1 being in the middle and 9 and 8 being on either side of 1? 2 1 9 8 1 9 8 3 7 1 9 7 8 1 2 9 1 9 8 1 8 2 1 2 1. 1 2. 6 3. 3 4. 4 37. How many vowels are there which are followed by prime number and preceded by even number? 5 i 6 o a t 9 7 e 5 u 4 t n 3 a 6 e 7 i 11 e a 3 1. 1 2. 2 3. 5 4. None 38. How many consonants are there which are followed by even number and preceded by vowels? a 1 b 2 c 3 d 4 e f 8 g h i 7 8 9 j k 3 l m 5 k 0 7 a b 1 o n 3 1. 1 2. 2 3. 7 4. None 39. How many prime numbers are there which are followed by vowels but not preceded by consonants? 5 i 6 o a t 9 7 e 5 u 4 t n 3 a 6 e 7 i 11 e a 3 1. 1 2. 2 3. 5 4. None 40. How many composite numbers are there which are not followed by vowels but preceded by consonants? a 1 b 2 c 3 d 4 e 5 f 6 g 7 h 8 i 9 j 0 k 1 l 2 m 3 n 4 o 5 p 6 q 7 r 8 s 9 1. 1 2. 2 3. 3 4. 4 “Intellectuals solve problems, geniuses prevent them.” 1. How many 1‟s are there in the following sequence which are immediately preceded by 9 but not immediately followed by 7? 7 1 0 1 1 7 1 8 9 1 7 1 2 1 3 1 4 5 7 1 3 9 1 7 1. one 2. two 3. three 4. four 2. How many 9‟s are there in the following sequence which are preceded by 6 but not immediately followed by 3? 6 9 3 7 6 9 6 3 9 6 4 6 9 4 7 6 6 6 9 3 6 7 6 9 2 9 6 1. 2 2. 3 3. 4 4. 5 3. Nikhil ranks 15 in the class of 35. What is his rank from the last? 1. 20 2. 22 3. 19 4. 21 4. How many 7‟s are there in the following sequence which are immediately preceded by 5 but not immediately followed by 3? 3 7 5 7 4 5 7 3 9 7 5 8 7 7 8 9 7 1 5 7 6 5 7 4 3 7 5 7 3 8 1. One 2. Two 3. Three 4. Four 5. Hamilton is 5 months younger to Simon while Bob is 3 months younger to Auden. When Shetty was born Bob was 2 months old. Auden is 5 years old and Hamilton is 6 years old. Who among the following is the oldest? 1. Simon 2. Bob 3. Auden 4. Shetty 6. How many odd numbers are there in the following series, which are followed by 1 and preceded by 2? 1 3 2 0 0 4 5 6 8 8 9 1 0 2 3 1 5 0 2 1 3 5 1 6 0 1. 1 2. 2 3. 4 4. 6 7. If the position of the first and the sixth digits of the sequence of numbers 5 3 1 7 6 8 9 2 0 4 are interchanged, the second and seventh and so on, which number would be sixth from the right end? 1. 3 2. 1 3. 6 4. 4 8. How many 7‟s immediately preceded by 6 but not immediately followed by 4 are there in the following series? 7 4 2 7 5 4 3 6 7 5 3 5 7 8 4 3 7 6 7 2 4 1 6 7 4 3 1. 1 2. 2 3. 4 4. 6 9. In a row of boys, if Arun who is 12 th from left and Ajay 8 th from right inter change their positions. Ajay becomes 14 th from the right end. How many boys are there in that row? 1. 25 2. 24 3. 26 4. 21 10. How many 8‟s are in the following number sequence which are not preceded by 7 but immediately followed by 4? 8 7 4 7 8 4 7 7 8 4 7 7 8 8 4 7 4 8 4 7 8 8 8 4 4 7 8 4 4 4 8 8 4 7 8 7 4 1. One 2. Two 3. Three 4. Four 11. How many 7‟s are there in the following sequence which are immediately preceded by 1‟s and not immediately followed by 3‟s? 9 8 5 1 7 3 1 7 6 5 6 3 7 7 1 4 6 1 7 5 9 3 1 7 4 4 6 1 7 3 3 7 8 1 7 2 1. 1 2. 2 3. 3 4. 4 12. How many 2‟s are there in the following number sequence which are immediately preceded by 3 but not immediately followed by 0? 3 3 2 2 3 2 2 3 0 3 2 0 2 3 3 2 2 3 0 3 2 0 3 3 2 2 0 3 2 0 3 2 3 1. One 2. Five 3. Three 4. Four 13. Ravi ranked 13 th from the top and 26 th from the bottom among those who passed in the annual examination in a class. If 6 students have failed in the examination, what was the total number of students in the class? 1. 45 2. 44 3. 47 4. 46 14. In the following series of numbers, find out how many times 1, 3 and 7 have appeared together, 7 being in the middle and 1 and 3 on either side of 7. 2 9 7 3 1 7 3 7 7 1 3 3 1 7 3 8 5 7 1 3 7 7 1 7 3 9 0 6 1. 3 2. 4 3. 5 4. More than 5 15. How many 5‟s preceded by 6 and not immediately followed by 8 are there in the following series? 5 8 2 5 6 8 3 6 5 5 3 5 5 8 8 3 5 6 5 2 8 0 6 5 8 3 1. 1 2. 2 3. 4 4. 6 16. How many 3‟s are there in the following number sequence which are immediately preceded by 6 but not immediately followed by 7? 2 3 7 4 3 2 6 3 7 4 6 3 8 9 6 3 5 1 8 3 7 2 4 2 8 6 3 9 1. One 2. Two 3. Three 4. Four 17. In the given series how many times it is that the sum of two consecutive numbers is 8. 1 8 3 7 4 7 1 9 4 2 6 4 8 3 7 1. 2 2. 4 3. 6 4. 7 18. In a row of girls Sunitha is 12 th from the left and 9 th from the right. How many girls are there in the row? 1. 21 2. 20 3. 22 4. 19 19. How many 6‟s are there in the following sequence which are immediately preceded by 8 but not immediately followed by 4? 4, 7, 5, 6, 9, 1, 6, 8, 4, 7, 3, 4, 8, 6, 3, 9, 6, 7, 8, 6, 4, 7, 3, 5, 8, 6, 1 1. 3 2. 4 3. 5 4. 2 20. Below in the given a number series 1 8 5 7 2 9 8 4 3 6 2 7 5 1 8 9 4 3 6 5 0 How many instances are there in which an even number is followed by two odd numbers? 1. Three 2. One 3. Two 4. None 21. How many 8‟s are present in the following sequence of number which are preceded by 5 but not immediately followed by 3? 5 8 3 7 5 8 6 3 8 5 4 5 8 4 7 6 5 5 8 3 5 8 7 5 8 2 8 5 1. 3 2. 4 3. 5 4. 7 22. How many even numbers are there in the following series, which are followed by an odd number and preceded by an even number? 4 1 5 7 2 5 8 4 9 6 8 2 5 4 1 3 2 9 1. 1 2. 2 3. 3 4. None of these 23. In a row of 30 boys when Prasad shifted right by 3 places he became 15 th place from the right. What was his position from left before he shifted? 1. 12 2. 13 3. 11 4. 10 24. Kesav ranks thirteenth in a class o twenty six. What is his rank from the last? 1. 13 2. 14 3. 15 4. 16 25. How many 6‟s are there in the following number sequence each of which is immediately followed by an even number and immediately preceded by an odd number? 3 6 2 5 6 3 2 6 3 2 6 2 7 6 4 6 5 8 6 7 6 4 2 6 8 1. 1 2. 2 3. 3 4. 4 26. How many 4‟s immediately preceded by 5 but not immediately followed by 7 are there in the following series of number? 5 4 8 7 4 9 5 4 7 7 4 5 5 4 6 5 4 7 5 4 7 3 2 4 7 1. 2 2. 3 3. 4 4. 5 27. At a parking place 36 vehicles are parked in a single row. After the first car there is one scooter after the second car there are two scooters and after the third car there are three scooters so on. Work out the number of scooters in the second half of the row. 1. 10 2. 12 3. 18 4. 17 28. How many 3‟s are present in the following sequence of number which are preceded by 2 but not followed by 4? 1 2 3 4 2 3 1 4 4 3 2 2 3 1 2 3 1 4 3 1 2 3 4 1. 4 2. 5 3. 6 4. None 29. In a row of boys, Sumit is fifteenth from the left and seventh from the right. How many boys are there in the row? 1. 21 2. 27 3. 29 4. 31 30. In a certain series given below count each 5 which is not immediately preceded by 3 but immediately followed by 7. How many such 5‟s are there? 1 5 7 3 5 7 4 7 3 7 2 5 6 5 8 5 7 4 5 6 5 5 7 1 5 7 7 5 5 1. 1 2. 2 3. 3 4. 4 31. Ajay‟s position in a row is thirteenth from the front side and sixth from the back side. How many persons are standing in that row? 1. 17 2. 18 3. 19 4. 20 32. How many 7‟s immediately preceded by 6 but not immediately followed by 4 are there in the following series? 7 4 2 7 6 4 3 6 7 5 3 5 7 8 4 3 7 6 7 2 4 0 6 7 4 3 1. 1 2. 2 3. 4 4. 6 33. How many 2‟s are there in the following series, which are immediately preceded by 9 but not followed by 7? 7 5 2 4 2 9 2 7 2 9 2 5 4 2 5 7 2 9 1 2 7 1. 1 2. 2 3. 34 4. 0 34. Some students are sitting in a single row. John is sitting 14 th from the left and Joseph is 7 th from the right. What is the total number of the students? 1. 21 2. 20 3. 19 4. Can‟t be determined 35. What will be the middle digit of the middle number after the following numbers are arranged in descending order? 268, 197, 678, 129, 259 1. 6 2. 9 3. 2 4. 5 36. How many 7‟s are there in the following sequence which are preceded by 4 but not immediately followed by 2? 4 7 2 7 2 3 5 9 7 4 7 5 2 4 7 9 4 7 8 4 7 1 1. 1 2. 2 3. 3 4. 4 37. How many 7‟s are there in the following series, which are immediately preceded by 5 and followed by 4? 1 5 7 3 4 7 5 7 4 8 5 7 4 3 2 1 7 7 1 5 7 9 1 7 4 1. 2 2. 4 3. 3 4. None of these 38. Vijay ranks seventh from the top and 28 th from the bottom in a class. How many students are there in the class? 1. 34 2. 35 3. 36 4. 37 39. How many 8‟s are there in the following sequence which are immediately preceded by 6 but not immediately followed by 5? 6 8 5 7 8 5 4 3 6 8 1 9 8 5 4 6 8 2 9 6 8 1 3 6 8 5 3 6 1. One 2. Two 3. Three 4. Four 40. Rasheed ranked 17 th from the top and 36 th from the bottom among those who have passed in the annual examination in a class. If six students have failed in the annual examination, what was the total number of students in that class? 1. 59 2. 60 3. 61 4. 58 Letter Ranking 1. How many b‟s between „a‟ and „e‟ are there in the following series? a b e a e a e a b e a b e a b e a b e b b b e a b e e a b e 1. 5 2. 6 3. 7 4. 8 2. How many 0‟s are followed by a vowel in the following? a e i o u a e i o u a e i o u o a o a o i a e a b c 1. 1 2. 3 3. 4 4. 6 3. Find the total number of c s followed by a vowel in the following. a b c a b c a c a c b c b c c c d e e c e a c e a c e a c e 1. 4 2. 6 3. 7 4. 8 4. How many n s are there before d in the following. n d n d n d n d n n d d d n d c d n d n d n d n d c d 1. 3 2. 4 3. 5 4. 10 5. How many p s are there which has „f‟ before in the following? f p f p p c f f f p f p f p f p p f f p p p f f f p f p f p f p p f f p f 1. 12 2. 7 3. 6 4. 8 6. How many c s are there between two consonants in the following. a b c d c d c e c e c f c o c i c j c k c c k 1. 3 2. 4 3. 5 4. 6 Directions (Questions 7-11): Study the following letter-number sequence and answer the questions below. 9 J 7 K Q N P 8 H I X Y 5 C 6 D 4 G 3 F E 2 A B 1 7. Which of the following element will be the fifth to the left of nineteenth element from your right? 1. K 2. 7 3. Y 4. J 8. Four of the following five are similar on basis of their position in the above sequence and hence form a group. Which one does not belong to that group? 1. 97KP 2. QP8X 3. 7QNH 4. N8HY 9. If every second element is dropped in the above sequence starting from Q (Q is dropped first), which of the following will be eighth element to the left of the 12 th element from your left? 1. 7 2. 8 3. K 4. N 10. If every sixth element from left starting from N is replaced by Archana, Rekha, Sima and Neetu (N is replaced by Archana), what will be the position of Rekha from your right? 1. 12 th 2. 13 th 3. 14 th 4. 15 th 11. If the first twelve elements in the above sequence is written in reverse order, then which element will be fifth to the left of twentienth element from your left? 1. 8 2. P 3. Q 4. N 12. In the following colour sequence, R stands for Red, Y for Yellow, G for green, B for Blue and W for white. If the sequence is continued, which colour will come next? B B R B R W B R W G B R W G Y B R B R W B R W 1. Yellow 2. White 3. Blue 4. Green 13. In the following series, count those „N‟ which are followed by „X‟ but „X‟ is not followed by „T‟. How many such N‟s are there? N X N T Q M N T M X N X C N Q M N N X Q N X T X N A M X N X M 1. 2 2. 4 3. 5 4. 7 14. Five newly born babies were weighed by the doctor. In her resort she pointed out that the child A is lighter than the child B. The child C is lighter than the child D. The child B is lighter than the child D but heavier than the child E. Which child is the heaviest? 1. E 2. D 3. C 4. B 15. How many A‟s are there in the following sequence which are immediately followed by B as well as immediately preceded by Z? A M B Z A N A A B Z A B A Z B A P Z A B A Z A B 1. Three 2. Nil 3. One 4. Two 16. The result of a class was declared. The boy X stood 5 th in the class. The girl Y was 8 th from the last. The position of the boy Z was 6 th after X and in the middle of X and Y. Work out total number of the students in the class? 1. 23 2. 29 3. 25 4. 26 17. In the following sequence count each N which is immediately followed by X but X is not immediately followed by T. How many such N‟s are there? N X N T Q M N X T M X N X C N Q M N N X Q N X T X N A M N X M 1. 2 2. 4 3. 5 4. 7 Directions (Questions 18-37): Each of the following questions is based on the following alphabet series: A B C D E F G H I J K L M N O P Q R S T U V W X Y Z 18. Which of the following letters will be sixth to the right of the eighteenth letter from the left after reversing the second half of the English Alphabet. 1. X 2. P 3. O 4. N 19. If the letters of the English Alphabet interchange positions, so that A takes the place of Z and Z takes the place of A, B takes place of Y and Y takes the place of B and so on, what will be the 4 th letter from the right? 1. D 2. N 3. O 4. L 20. If the English Alphabet is arranged in reverse order, which letter will be the eighth letter to the left of the seventh letter counting from the right end? 1. P 2. O 3. N 4. Q 21. Which letter should be sixth to the right of the sixteenth letter from the left if the second half of the English Alphabet is reversed? 1. R 2. V 3. J 4. U 22. Which letter will be the sixth to the right of the eleventh letter from the right end of the English Alphabet? 1. K 2. V 3. J 4. U 23. Which letter will be the seventh to the left of the fourteenth letter from the right end of the English Alphabet? 1. E 2. F 3. T 4. S 24. In the English Alphabet which letter is seventh to the right of fifteenth letter from the right end? 1. S 2. T 3. R 4. H 25. Which letter will be the tenth to the left of the eighteenth letter from the left end, of the English Alphabet? 1. H 2. Y 3. A 4. There is no such letter 26. Which letter will be midway between the eighteenth letter from the left end and tenth letter from the right end of the English Alphabet? 1. Q 2. R 3. K 4. No letter 27. If the English Alphabets were written in the reverse order, which will be the sixth letter to the left of the tenth letter from the right? 1. W 2. P 3. D 4. K 28. If the English Alphabets were written in the reverse order, which would be the fourth letter to the right of the fifteenth letter from the left? 1. G 2. H 3. I 4. S 29. Which letter will be the tenth to the right of the eighteenth letter from the right end of the English Alphabets? 1. S 2. T 3. P 4. There is no such letter 30. What will be the seventh letter to the right of the eleventh letter from the right if the letters of the English Alphabets were arranged in reverse order? 1. D 2. W 3. E 4. V 31. Which letter will be the eighth to the right of the seventeenth letter from the right end of the English Alphabets? 1. R 2. B 3. K 4. Q 32. What will be the third letter to the left of the fourth letter starting from your right after every third letter is cancelled? 1. Q 2. J 3. R 4. V 33. Which letter will be midway between the fourteenth letter from the left and nineteenth letter from the right end of the English Alphabet? 1. I 2. K 3. M 4. G 34. Which letter is mid-way between the ninth letter from the right and eighth letter from the left in the English Alphabets? 1. N 2. O 3. L 4. M 35. If the English Alphabet is written in the reverse order which will be the letter to the immediate left of M? 1. N 2. L 3. O 4. K 36. Which letter is mid-way between eighth letter from the right and the seventh letter from the left in the English Alphabet? 1. G 2. L 3. M 4. N 37. Which is the first letter to the right of the letter which is immediately before the ninth letter from the left in the English Alphabet? 1. I 2. H 3. G 4. J 38. In the following series, how many times have the alphabets A, M, Z come consecutively where in the M is the middle with A and Z being on any of the sides of M? Z N A L M Z A B M Y Z M A Y M A Z A M B N L M A Z Y 1. 6 2. 4 3. 1 4. 2 39. In the following series, count those „N‟ which are followed by X but X is not followed by T. How many such N‟s are there? N X N T Q M N T M X N X C N Q M N N X Q N X T X N A M X N X M 1. 2 2. 4 3. 5 4. 7 40. How many Z are there in the following series which are immediately preceded by A but not immediately followed by T? A Z T U V T Z A S T A Z O V T U Z A T A Z S T V 1. One 2. Two 3. Three 4. Four 41. How many B‟s are there in the following series which are immediately followed by E? C E B E C D P B E B F E B E D F E B C E F C A E 1. Three 2. One 3. Two 4. None Directions Study the following letter-number arrangement and answer the questions given below. A 4 B D 2 C N O T 6 9 V L 3 Q P K 7 J H 5 8 M S E 42. If the above letter-number arrangement is written in reverse order, which letter/number will eighth to the right of L? 1. R 2. 3 3. 2 4. None 43. Which of the following will come in place of question mark (?) in the following sequence with reference to the above arrangement? BCN DNO ___?___ CT6 1. 2OT 2. 2TO 3. TO2 4. None 44. If it is possible to make a meaningful word with the third, the eighth, the tenth and the twenty sixth letters from your left in above given series, which of the following will be the first letter of that word. If no such word can be made, give X as the answer. If more than one such word can be made give M as the answer. 1. N 2. B 3. T 4. X 45. Which of the following be third to the right of the fifteenth letter/number from you right? 1. P 2. Q 3. L 4. 3 46. If every alternate letter/number is dropped I the above arrangement, beginning with dropped A as first letter, which of the following will be the letter 6 th from left? 1. L 2. 3 3. V 4. Q Directions Study the following letter-number sequence and answer the questions given below them. P K 4 M D A 8 S T 3 E J R 6 Q N L H B 7 U G C Z F 47. Which letter/number is the seventh to the right of the fifth letter/number from your left? 1. 6 2. J 3. R 4. E 48. If every fourth letter/number is dropped starting from of the above letter- number sequence, which of the following letter/number will be the eighth from your right? 1. Q 2. 2 3. L 4. E 49. Which letter/number will be midway between the sixth letter/number from your right and twelth letter/number from our left? 1. Q 2. 6 3. N 4. J 50. Which letter/number will be seventh to the left of the sixteenth letter/number from your left? 1. C 2. T 3. S 4. 2 Directions: Study the following sequence (letters, numbers and symbols) and answer the questions given below them: N O P 4 + * E M K † 5 $ S L A Z • = @ H T B J 6 F Y 51. Which letter/number/symbol will be midway between the fifteenth sign from your left and eighteenth letter from your right? 1. 5 2. S 3. L 4. $ 52. Which letter/number/symbol is the fifth to the right of the sixteenth sign from your left? 1. T 2. 5 3. B 4. Z 53. Which of the following will be the ninth sign to the right of twenty-fourth position from your right? 1. $ 2. A 3. S 4. L Directions Answer the following questions based on the series given below. A b C d E 1 f G h i j 2 k l M n O 3 p Q r S t 4 u v W x y 5 z 54. What is the middle letter/digit in the series given above? 1. 3 2. O 3. n 4. Q 55. What would be the answer to the above question, if even numbers were removed from the series? 1. Same as in above question 2. One letter to the left of the answer of 1 3. One letter to the right of the answer of 1 4. Can‟t be uniquely determined 56. If the second half of the series (excluding n) above was written in reverse order, what would be the 8 th letter/digit to the right of the 16 th letter from the right? 1. U 2. v 3. 4 4. x 57. If no reversing was done in above question, what would be the answer of above question? 1. Same as in above question 2. One letter to the left of the answer of question 3 3. One letter to the right of the answer of question 3 4. Can‟t be uniquely determined Directions Study the following letter-number sequence and answer the question given below. A 2 C D 5 F G H 9 K M P 1 3 L E B S U N 8 O I R V T X Z 58. If every alternate starting from your left hand side replaces digits of a clock with 1 replaced A, which letter/number will replace 6 of the clock? 1. F 2. K 3. M 4. I 59. If the first half of the letter number sequence is written in the reverse order, which letter/number will be fourth to left of eighteenth letter/number from your right? 1. H 2. G 3. E 4. F 60. If every alternate position is dropped starting from G in the above letter-number sequence, then how many letters-numbers will be left? 1. 18 2. 16 3. 15 4. 17 61. Which letter will be the sixth to the left of seventh letter from the right end? 1. B 2. L 3. E 4. T Directions Study the following letter-number series and answer the questions given below: H P 9 G A M T 4 B K R 7 N D Y J 3 S C E Q 8 62. Which letter-number is seventh to right of ninth letter number from your left? 1. 9 2. P 3. Y 4. J 63. If every fourth letter/number (starting from A) is dropped from the given letter sequence. Which of the following will be eighth letter/number from your right? 1. 4 2. K 3. 7 4. R 64. If the first half of the above sequence is written in the reverse order which of the following will be the ninth letter/number to the right of sixteenth letter/number from your right? 1. Q 2. 3 3. Y 4. J 65. If it is possible to make a meaningful word with the first, the second, the fourth, the fifth and the eleventh letters of the above sequence, write the middle letter of that word. If it is not possible to make such a word write M as your answer. 1. A 2. H 3. P 4. G 66. If the alternate letters in the following alphabet starting from A are changed into small letter leaving the rest in capitals. Which of the following represents the second month after June? A B C D E F G H I J K L M N O P Q R S T U V W X Y Z 1. AugusT 2. AUgUsT 3. augusT 4. August 67. If by arranging the letters of the word UTLSO, the name of a flower is formed. Which of the following pairs represents the first and the last letters of the word so formed? 1. TO 2. OS 3. LS 4. TS 68. How many pairs of letters are there in the word PEPURCUSSION which have as many letters between them in the word as in the alphabet and that too in the same order? 1. One 2. Two 3. Three 4. Nil Directions Study the following letter series and answer the questions given below them. A B C D E F G H I J K L M N O P Q R S T U V W X Y Z 69. Which letter is sixth to the right of fifteenth letter from your left? 1. L 2. J 3. K 4. U 70. If every third letter is dropped starting from C from the given alphabet which of the following will be the third letter to the left of ninth letter from your left? 1. H 2. Q 3. I 4. U 71. Which letter will be midway between the seventh letter from your left and twelth letter from your right? 1. M 2. J 3. K 4. L Directions Study the following letter-number sequence and answer the questions given below: C Z 4 S R K N H O P X A 9 M J 5 Q T E 6 L U B 3 D V 72. If every third letter/number is dropped in the above sequence starting from S (S is dropped first), which of the following will be 5 th letter/number to the left of 15 th position from your left? 1. 9 2. M 3. J 4. 5 73. If every 4 th position starting from N is replaced by Lata, Nita, Rita, Mili and Priya (N becomes Lata), what will be the position of Priya in the above sequence counting from your right? 1. Third 2. fifth 3. seventh 4. fourth 74. How many p‟s are there in the following letter sequence which are immediately preceded by r but not immediately followed by q. q p r p n p r q r p t r p u q r p q r t s p r s r p q s t q r p q 1. 9 2. 3 3. 2 4. 5 75. How many u‟s are there which are immediately followed by v and also immediately preceded by w? u w u v v u w u v u w u v u w u w u v v u w v u u v w u v u w v u v u w u v u v v u w v u 1. 9 2. 7 3. 6 4. 5 76. How many x‟s are there not immediately preceded by y but immediately followed by z in the following series? x y x z x z z y x y y x x z x y x z x y x y z x x z y z z x z y x z 1. 9 2. 7 3. 4 4. 5 77. How many b‟s are there not immediately preceded by c and not immediately followed by a in the following series? a b c a c a c b b c a c b b b b c c a a c a b c b a c b a c a b c a b c b a c c a a c b b c b a c b a 1. 9 2. 12 3. 8 4. 6 78. How many m‟s are there immediately preceded by 2 but not immediately followed by 3 in the following series? m 2 m 2 3 3 2 m 3 m 2 m 2 3 m 2 m 3 3 m 2 2 m 3 m 2 2 m 3 m 3 m m 2 m 3 2 m 3 2 m 3 m 2 m 2 m m 2 m 3 2 m 3 1. 2 2. 3 3. 4 4. 1 79. How many vowels are there which are followed by vowels and preceded by consonants? o e m u v m n o i k l o o u u v a e m o o e w i o e i e o u o u b i a e i d a i a v v o i 1. 9 2. 8 3. 7 4. 6 80. 45D____9____IJ____7F___ 1. E, 10, 8, G 2. E, 10, 6, G 3. E, 10, 5, G 4. F, 10, 6, G Odd Man Out (Numbers) Directions: In each of the following numbers series, one term is wrong which is given in one of the four alternatives provided after each series. Find this term. 1. 3, 5, 10, 12, 24, 26, 48, 54 1. 12 2. 24 3. 26 4. 48 2. 1. 3, 4, 3, 7, 8, 13, 12, 25 1. 8 2. 13 3. 12 4. 25 3. 2, 5, 11, 20, 30, 47, 65 1. 20 2. 30 3. 47 4. 65 4. 1, 5, 2, 18, 13, 38, 42 1. 18 2. 13 3. 38 4. 42 5. 7, 8, 18, 13, 38, 42 1. 18 2. 13 3. 38 4. 42 6. 1. 7, 8, 18, 57, 228, 1165, 6996 1. 8 2. 18 3. 57 4. 228 7. 1. 3, 7, 15, 27, 63, 127, 255 1. 7 2. 15 3. 27 4. 63 8. 1. 19, 26, 33, 46, 59, 74, 91 1. 26 2. 33 3. 46 4. 59 9. 1. 2880, 480, 92, 24, 8, 4, 4 1. 2880 2. 480 3. 92 4. 24 10. 1. 445, 221, 109, 46, 25, 11, 4 1. 221 2. 109 3. 46 4. 25 11. 2, 3, 13, 37, 86, 167, 288 1. 3 2. 13 3. 37 4. 86 12. 2, 5, 12, 27, 58, 120, 248 1. 5 2. 12 3. 27 4. 120 13. 232, 120, 64, 36, 22, 16, 11.5 1. 120 2. 64 3. 36 4. 16 14. 568, 276, 136, 64, 28, 10, 1 1. 276 2. 136 3. 64 4. 28 15. 875, 2.75, 8, 18, 40, 85, 176 1. 2.75 2. 8 3. 18 4. 40 16. 3, 5, 12, 38, 154, 914, 4634 1. 5 2. 12 3. 38 4. 914 17. 696, 340, 168, 80, 36, 14, 3 1. 340 2. 168 3. 80 4. 36 18. 634, 314, 164, 74, 34, 14, 4 1. 314 2. 164 3. 74 4. 34 19. 4, 5, 14, 39, 103, 169, 290 1. 5 2. 14 3. 39 4. 103 20. 2, 3, 6, 12, 45, 157.5, 630 1. 3 2. 6 3. 12 4. 45 21. 5, 27, 61, 122, 213, 340, 509 1. 27 2. 61 3. 216 3. 340 22. 3, 10, 19, 31, 43, 58, 75 1. 10 2. 19 3. 31 4. 43 23. 720, 120, 24, 8, 2, 1, 1 1. 1 2. 2 3. 24 4. 8 24. 1, 4, 7, 11, 16, 22, 29 1. 1 2. 4 3. 22 4. 11 25. 58, 57, 54, 50, 42, 33, 22 1. 57 2. 54 3. 50 4. 42 26. 1, 6, 11, 22, 33, 46, 61 1. 6 2. 1 3. 46 4. 11 27. 3, 18, 38, 78, 123, 178, 243 1. 123 2. 178 3. 3 4. 38 28. 89, 78, 86, 80, 85, 82, 83 1. 78 2. 86 3. 80 4. 85 29. 3, 10, 29, 60, 127, 18, 345 1. 10 2. 29 3. 60 4. 127 30. 1. 17, 19, 23, 29, 33, 37, 41 1. 17 2. 19 3. 23 4. 33 31. 27, 26, 28, 25, 29, 24, 31 1. 24 2. 29 3. 31 4. 28 32. 2, 8, 20, 44, 92, 184, 380 1. 380 2. 184 3. 92 4. 44 33. 25, 26, 24, 29, 27, 36, 33 1. 24 2. 25 3. 29 4. 33 34. 1160, 584, 296, 148, 80, 44, 26 1. 80 2. 26 3. 44 4. 148 35. 60, 48, 38, 28, 24, 20, 18 1. 18 2. 20 3. 24 4. 28 36. 144, 132, 125, 113, 105, 93, 84, 72, 61, 50, 39 1. 93 2. 84 3. 50 4. 61 37. 1, 2, 5, 10, 21, 42, 85, 171 1. 21 2. 42 3. 85 4. 171 38. 1. 3, 9, 18, 54, 108, 314, 648, 1944 1. 314 2. 108 3. 54 4. 18 39. 3, 9, 18, 54, 108, 314, 648, 1944 1. 314 2. 108 3. 54 4. 18 40. 1, 3, 10, 29, 74, 172, 382 1. 10 2. 29 3. 74 4. 172 41. 3, 8, 15, 24, 34, 48, 63 1. 15 2. 24 3. 34 4. 48 42. 11, 12, 14, 17, 20, 26, 32 1. 32 2. 26 3. 20 4. 17 43. 2200, 2100, 2000, 1600, 1200, 700, 100 1. 2000 2. 2100 3. 100 4. 700 44. 2, 9, 28, 65, 126, 216, 344 1. 2 2. 28 3. 65 4. 216 45. 5, 15, 30, 135, 405, 1215, 3645 1. 3645 2. 1215 3. 405 4. 30 46. 112, 114, 120, 124, 132, 142, 154 1. 114 2. 120 3. 124 4. 132 47. 5, 11, 23, 47, 96, 191, 383 1. 11 2. 23 3. 47 4. 96 48. 3, 4, 5, 9, 22.5, 67.5, 270, 945 1. 4.5 2. 9 3. 22.5 4. 270 49. 380, 188, 92, 48, 20, 8, 2 1. 188 2. 92 3. 48 4. 20 50. 7, 9, 17, 42, 91, 172, 293 1. 9 2. 17 3. 42 4. 91 Directions : In each of the following numbers series, one term is wrong. Find this term. 51. 1. 242 2. 483 3. 362 4. 482 52. 1. 192 2. 141 3. 291 4. 451 53. 1. 1234 2. 1243 3. 4567 4. 3456 54. 1. 972 2. 281 3. 527 4. 549 55. 1. 8 2. 4 3. 16 4. 17 56. 1. 9 2. 6 3. 15 4. 19 57. 1. 52163 2. 25631 3. 34424 4. 33442 58. 1. 315 2. 207 3. 711 4. 325 59. 1. 3, 7, 5, 11 2. 11, 17, 19, 23 3. 3, 29, 7, 5 4. 2, 4, 3, 5, 7 60. 1. 14 2. 7 3. 28 4. 36 61. 1. 63852 2. 52638 3. 85361 4. 28751 62. 1. 3795 2. 9359 3. 5937 4. 3745 63. 1. 11, 3, 3, 17 2. 14, 5, 3, 47 3. 71, 7, 3, 17 4. 37, 14, 19, 7 64. 1. 936 2. 945 3. 864 4. 954 65. 1. 35, 24 2. 79, 68 3. 57, 46 4. 35, 79 66. 1. 67, 19 2. 71, 11 3. 41, 19 4. 89, 41 67. 1. 5, 13, 17 2. 29, 1, 5 3. 17, 17, 1 4. 15, 5, 5 68. 1. 65, 83 2. 83, 47 3. 34, 79 4. 65, 23 69. 1. 3535 2. 7595 3. 9575 4. 7395 70. 1. 49 2. 140 3. 98 4. 97 71. 1. 98765 2. 98756 3. 987654 4. 9876543 72. 1. 37037x3 2. 37037x6 3. 37037x9 4. 37037x4 73. 1. 121 2. 12321 3. 123321 4. 12345321 74. 1. 876321 2. 387315 3. 349416 4. 372164 75. 1. 6 2. 8 3. 11 4. 15 76. 1. 11 2. 13 3. 15 4. 17 77. 1. 53 2. 63 3. 72 4. 81 78. 1. 6 2. 7 3. 9 4. 12 79. 1. 27 2. 64 3. 125 4. 343 80. 1. 4 2. 9 3. 16 4. 36 81. 1. 385 2. 572 3. 671 4. 427 82. 1. 121 2. 132 3. 143 4. 152 83. 1. 6 2. 18 3. 12 4. 7 84. 1. 18 2. 6 2. 12 4. 9 85. 1. 7 2. 17 3. 37 4. 9 86. 1. 24 2. 12 3. 36 4. 27 87. 1. 14 2. 28 3. 21 4. 41 88. 1. 4 2. 16 3. 25 4. 55 89. 1. 9 2. 25 3. 36 4. 78 90. 1. 115 2. 98 3. 78 4. 89 91. 1. 189 2. 199 3. 178 4. 235 92. 1. 63 2. 45 3. 81 4. 38 93. 1. 385 2. 572 3. 671 4. 427 94. 1. 35 2. 49 3. 50 4. 63 95. 1. 21 2. 39 3. 51 4. 83 96. 1. 27 2. 125 3. 729 4. 1321 97. 1. 6 2. 12 3. 18 4. 7 98. 1. 15 2. 27 3. 24 4. 28 99. 1. 51 2. 144 3. 64 4. 121 100. 1. 10 2. 26 3. 24 4. 21 101. 1. 43 2. 53 3. 63 4. 73 102. 1. 324 2. 244 3. 136 4. 352 103. 1. 515 2. 875 3. 380 4. 876 104. 1. 699 2. 789 3. 682 4. 798 105. 1. 688 2. 686 3. 376 4. 867 106. 1. 369 2. 879 3. 789 4. 785 107. 1. 6 2. 18 3. 12 4. 7 108. 1. 579 2. 885 3. 696 4. 398 109. 1. 986 2. 689 3. 995 4. 963 110. 1. 821 2. 731 3. 533 4. 862 111. 1. 724 2. 364 3. 643 4. 736 112. 1. 756 2. 686 3. 843 4. 884 113. 1. 21 2. 69 3. 81 4. 83 114. 1. 37 2. 49 3. 132 4. 154 115. 1. 10 2. 11 3. 15 4. 16 116. 1. 11 2. 13 3. 15 4. 17 117. 1. 372164 2. 376821 3. 318951 4. 319446 118. 1. 7851 2. 6432 3. 5789 4. 1325 119. 1. 1532 2. 8749 3. 4268 4. 5846 120. 1. 7487 2. 5963 3. 8218 4. 6596 121. 1. 263 2. 111 3. 242 4. 383 122. 1. 325 2. 236 3. 178 4. 639 123. 1. 11 2. 13 3. 17 4. 39 124. 1. 7 2. 11 3. 13 4. 14 125. 1. 5 2. 17 3. 23 4. 9 126. 1. 7 2. 5 3. 1 4. 16 127. 1. 27 2. 19 3. 11 4. 8 128. 1. 539 2. 638 3. 731 4. 751 129. 1. 221 2. 351 3. 691 4. 784 130. 1. 13901 2. 87901 3. 90980 4. 89901 131. 1. 781 2. 258 3. 608 4. 341 132. 1. 5760 2. 6750 3. 7650 4. 8089 133. 1. 2 2. 16 3. 56 4. 128 134. 1. 2468 2. 2648 3. 4826 4. 6482 135. 1. 392 2. 326 3. 414 4. 248 136. 1. 2345 2. 3456 3. 5467 4. 5678 137. 1. 28 2. 65 3. 126 4. 215 138. 1. 150 2. 175 3. 200 4. 250 139. 1. 232 2. 431 3. 612 4. 813 140. 1. 140 2. 240 3. 360 4. 480 141. 1. 49 2. 63 3. 77 4. 81 142. 1. 144 2. 168 2. 196 4. 256 143. 1. 124 2. 235 3. 789 4. 510 144. 1. 369 2. 468 3. 942 4. 279 145. 1. 134 2. 256 3. 679 4. 532 146. 1. 976 2. 843 3. 732 4. 698 147. 1. 8743 2. 7521 3. 8310 4. 1897 148. 1. 2 2. 3 3. 5 4. 7 149. 1. 3 2. 5 3. 7 4. None 150. 1. 11 2. 13 3. 19 4. None 151. 1. 11 2. 21 3. 31 4. 41 152. 1. 11 2. 31 3. 41 4. None 153. 1. 12 2. 25 3. 37 4. 49 154. 1. 8 2. 64 3. 28 4. 125 155. 1. 751 2. 734 3. 981 4. 853 156. 1. 21 2. 36 3. 49 4. 56 157. 1. 48 2. 12 3. 36 4. 59 158. 1. 8314 2. 2709 3. 1315 4. 2518 159. 1. 381 2. 552 3. 729 4. 903 160. 1. 7 2. 15 3. 31 4. 57 161. 1. 119 2. 136 3. 147 4. 153 162. 1. 9611 2. 7324 3. 2690 4. 1754 163. 1. 99 2. 89 3. 79 4. 59 164. 1. 71 2. 73 3. 79 4. None 165. 1. 73 2. 83 3. 93 4. 103 166. 1. 121 2. 169 3. 225 4. 289 167. 1. 121 2. 529 3. 361 4. None 168. 1. 576 2. 676 3. 900 4. None 169. 1. 729 2. 676 3. 343 4. 216 170. 1. 729 2. 676 3. 625 4. 576 171. 1. 30 2. 56 3. 132 4. 182 172. 1. 30 2. 130 3. 350 4. 1342 173. 1. 21-49 2. 24-64 3. 25-54 4. 81-36 174. 1. 3-4 2. 16-26 3. 26-24 4. 27-22 175. 1. 48-134 2. 40-110 3. 18-48 4. 30-80 176. 1. 3-4 2. 4-7 3. 5-12 4. 20-21 177. 1. 7-18 2. 9-26 3. 11-36 4. 13-42 178. 1. 22, 4, 5 2. 34, 4, 8 3. 37, 4, 9 4. 54, 4, 13 179. 1. 6-15 2. 21-43 3. 25-51 4. 29-59 180. 1. 56-8 2. 121-17 3. 147-21 4. 168-24 181. 1. 24-21 2. 46-32 3. 62-23 4. 84-24 182. 1. 81-63 2. 24-48 3. 21-15 4. 13-39 183. 1. 252 2. 420 3. 600 4. 702 184. 1. 21 2. 63 3. 39 4. 83 185. 1. 385 2. 427 3. 671 4. 473 186. 1. 47, 59 2. 42, 29 3. 57, 69 4. 73, 61 187. 1. 7 2. 15 3. 31 4. 57 188. 1. 12 2. 16 3. 56 4. 128 189. 1. 3-5 2. 13-17 3. 19-25 4. 23-29 190. 1. 8-27 2. 125-126 3. 343-512 4. 1009-1331 191. 1. 13-156 2. 12-144 3. 15-180 4. 16-176 192. 1. 49-7 2. 36-9 3. 64-8 4. 121-11 193. 1. 13-21 2. 19-27 3. 15-23 4. 16-24 194. 1. 10-20 2. 30-40 3. 40-50 4. 50-60 195. 1. 140-45 2. 110-35 3. 100-30 4. 80-25 196. 1. 13-31 2. 45-54 3. 16-61 4. 71-88 197. 1. 21-6 2. 28-42 3. 42-12 4. 84-24 198. 1. 45-27 2. 30-18 3. 20-10 4. 15-12 199. 1. 72-45 2. 51-24 3. 46-20 4. 32-13 200. 1. 8-27 2. 125-216 3. 343-512 4. 1009-1331 201. 1. 15-46 2. 12-37 3. 9-28 4. 8-33 202. 1. 9-3 2. 1/2-1/8 3. 1/3-1/12 4. 24/6 203. 1. 32-13 2. 46-20 3. 51-24 4. 72-45 204. 1. 3-11 2. 8-16 3. 5-13 4. 14-24 205. 1. 28-4 2. 56-8 3. 35-5 4. 63-7 206. 1. 2-8 2. 3-27 3. 4-32 4. 5-125 207. 1. 56-8 2. 121-17 3. 147-21 4. 168-24 208. 1. 49-7 2. 36-9 3. 64-8 4. 121-11 209. 1. 8-20 2. 18-45 3. 16-40 4. 14-28 210. 1. 45 2. 126 3. 109 4. 207 211. 1. 324 2. 523 3. 442 4. 343 212. 1. 6589 2. 4323 3. 2341 4. 9673 213. 1. 80-25 2. 140-45 3. 120-35 4. 100-30 214. 1. 10-20 2. 30-40 3. 40-50 4. 50-40 215. 1. 7-3 2. 11-7 3. 13-9 4. 17-8 216. 1. 54-28 2. 34-17 3. 42-21 4. 22-11 217. 1. 49 2. 64 3. 48 4. 100 218. 1. 83-75 2. 58-50 3. 49-42 4. 25-17 219. 1. 70-80 2. 54-62 3. 28-32 4. 21-24 220. 1. 42-4 2. 36-6 3. 32-2 4. 15-5 221. 1. 71, 7, 3, 17 2. 67, 71, 3, 5 3. 41, 5, 3, 47 4. 37, 14, 19, 7 222. 1. 95-82 2. 69-56 3. 55-42 4. 48-34 223. 1. 80-9 2. 64-8 3. 36-6 4. 49-7 224. 1. 3-5 2. 5-3 3. 6-2 4. 7-3 225. 12-144 2. 13-156 3. 15-180 4. 16-176 226. 1. 23-29 2. 19-25 3. 13-17 4. 3-5 227. 1. 73-61 2. 57-69 3. 42-29 4. 47-59 228. 1. 0 2. 3 3. 8 4. 17 229. 1. 441 2. 163 3. 153 4. 522 230. 1. 240 2. 132 3. 1956 4. 563 231. 1. 30 2. 6 3. 12 4. 18 232. 1. 403 2. 202 3. 431 4. 853 233. 1. 31 2. 41 3. 51 4. 61 234. 1. 11 2. 21 3. 26 4. 31 235. 1. 51 2. 64 2. 121 3. 144 236. 1. 8 2. 64 3. 27 4. 729 237. 1. 62 2. 27 3. 81 4. 54 238. 3, 5, 12, 39, 154, 772, 4634 1. 5 2. 12 3. 39 4. 154 239. 376, 188, 88, 40, 16, 4, -2 1. 188 2. 88 3. 40 4. 16 240. 444, 300, 200, 136, 87, 84, 80 1. 300 2. 200 3. 136 4. 87 241. 2, 3, 12, 37, 86, 166, 288 1. 3 2. 12 3. 37 4. 66 242. 4, 9, 19, 43, 90, 185, 376 1. 9 2. 19 3. 43 4. 90 243. 49, 48, 45, 42, 33, 24, 13 1. 48 2. 45 3. 42 4. 33 244. 3, 3, 6, 16, 72, 360, 2160 1. 3 2. 6 3. 16 4. 72 245. 3, 7, 15, 27, 63, 127, 255 1. 7 2. 15 3. 27 4. 63 246. 3, 4, 8, 16, 33, 58, 94 1. 4 2. 8 3. 16 4. 33 247. 1, 6, 16, 26, 76, 156, 316 1. 6 2. 16 3. 26 4. 76 248. 1, 3, 7, 17, 31, 63, 127 1. 1 2. 7 3. 63 4. 17 249. 48, 47, 44, 40, 32, 23, 12 1. 47 2. 32 3. 40 4. 44 250. 24, 23, 21, 18, 14, 9, 5 1. 5 2. 9 3. 14 4. 18 251. 12, 20, 32, 42, 56, 72, 90 1. 20 2. 32 3. 42 4. 56 252. 12, 19, 14, 21, 28, 23, 18 1. 14 2. 18 3. 21 4. 28 253. 49, 48, 45, 42, 33, 24, 13 1. 48 2. 45 3. 42 4. 33 254. 3, 3, 6, 16, 72, 360, 2160 1. 3 2. 6 3. 16 4. 72 255. 3, 7, 15, 27, 63, 127, 255 1. 63 2. 7 3. 15 4. 27 256. 3, 4, 8, 16, 33, 58, 94 1. 4 2. 8 3. 16 4. 33 257. 6, 16, 26, 76, 156, 316 1. 6 2. 16 3. 26 4. 76 258. 11, 15, 17, 19, 23, 25 1. 19 2. 11 3. 15 4. 17 259. 1, 4, 3, 9, 5, 36 1. 9 2. 11 3. 15 4. 17 260. 2, 5, 11, 22, 32, 47 1. 11 2. 32 3. 47 4. 22 Odd Man Out (Letters): Directions : Four Groups of letters are given; three of them are alike in a certain way while one is different. Choose the odd one. 1. 1. DAG 2. KIN 3. ROU 4. YVB 2. 1. KQW 2. GMS 3. HNS 4. CIO 3. 1. ACEG 2. CEGI 3. GIKM 4. LNOR 4. 1. AFKP 2. BGMQ 3. CHMR 4. DINS 5. 1. ABBC 2. PQQR 2. HIIJ 4. WYYZ 6. 1. YZAB 2. EFGH 3. MNOP 4. VWXZ 7. 1. Bde 2. XPD 3. HQU 4. MKV 8. 1. SIT 2. LIP 3. FAN 4. OUT 9. 1. RUX 2. GJM 3. YBE 4. NPS 10. 1. BDH 2. IKP 3. QSW 4. TVZ 11. 1. NPM 2. IJL 3. QSZ 4. BHK 12. 1. VXZ 2. ACF 3. PRU 4. GIL 13. 1. BAC 2. POQ 3. STV 4. YXZ 14. 1. CDE 2. JKL 3. PQS 4. TUV 15. 1. ZAYB 2. XCWD 3. VEUF 4. TSGH 16. 1. A 2. U 3. Y 4. O 17. 1. IRJQ 2. UFVE 3. SHTG 4. NMOK 18. 1. HKNP 2. KNQT 3. MPSV 4. PSVY 19. 1. OVCI 2. RYFM 3. KRYF 4. MTAH 20. 1. LPVD 2. KOUC 3. BFLV 4. OSYG 21. 1. SUWYA 2. LJNPR 3. KMOQS 4. BDFHJ 22. 1. VTOJE 2. USNID 3. UPKEA 4. SQLGB 23. 1. WHEAT 2. TRAIN 3. PROUD 4. DRIVER 24. 1. MONDAY 2. TUESDAY 3. FRIDAY 4. HOLIDAY 25. 1. HSRI 2. MVUN 3. OLKP 4. PJQX 26. 1. STUA 2. RQPA 3. MLKA 4. HGFA 27. 1. XGEZ 2. PCAQ 3. LKIN 4. DWUF 28. 1. BDYW 2. CEXZ 3. DFYW 4. EGXV 29. 1. UAZF 2. SCXH 3. RDWJ 4. KBPG 30. 1. ABCD 2. EGIK 3. ACDF 4. CFIL 31. 1. BdEg 2. KmNP 3. PrSu 4. TwXz 32. 1. BCD 2. KMN 3. QRS 4. GHI 33. 1. BDGK 2. JLOS 3. NPSW 4. MORU 34. 1. DkUZ 2. LPuB 3. FoMY 4. UXeN 35. 1. APE 2. EQI 3. IOR 4. OSU 36. 1. XW 2. FG 3. ML 4. PO 37. 1. VT 2. MQ 3. PR 4. FG 38. 1. HGF 2. XWV 3. NML 4. OPQ 39. 1. PRT 2. MOQ 3. GEC 4. TVX 40. 1. VWY 2. QRT 3. LMO 4. JKL 41. 1. BHE 2. DJG 3. SYV 4. PUS 42. 1. JOT 2. OUT 3. FED 4. DIN 43. 1. PUT 2. END 3. OWN 4. ARM 44. 1. FAA 2. OFF 3. ATT 4. IFF 45. 1. BEJMRU 2. PSXAFI 3. WZEHMP 4. ZCHKQT 46. 1. TSRQ 2. MLKJ 3. YXWV 4. HGFD 47. 1. BAT 2. HAT 3. RAT 4. EAT 48. AZ 2. BY 3. CX 4. None 49. 1. BGL 2. MRV 3. JOT 4. AFK 50. 1. BGO 2. NRP 3. HLJ 4. QUS Directions: Four Groups of letters are given; three of them are alike in a certain way while one is different. Choose the odd one. 51. 1. GECA 2. NLJH 3. USQP 4. BZXV 52. 1. DHLP 2. CGKO 3. BFJN 4. AEIL 53. 1. AIOV 2. BIPW 3. CJQX 4. DKRY 54. 1. EDCBA 2. JOHGF 3. ONMLK 4. TSRQP 55. 1. BHLR 2. AGKQ 3. DJNT 4. EJOX 56. 1. CHM 2. HMR 3. RWB 4. LPU 57. 1. EWZQ 2. OSLS 3. GFKD 4. VSPM 58. 1. ACEG 2. IKMO 3. TVWY 4. FHJL 59. 1. UTSR 2. IHGE 3. NMLK 4. ZYXW 60. 1. BCDE 2. PQRS 3. WXYZ 4. STUW 61. 1. OFF 2. IFF 3. ATT 4. UXY 62. 1. CEI 2. QSX 3. JLP 4. QSW 63. 1. ZAB 2. IJK 3. YZA 4. STV 64. 1. XUW 2. DAC 3. PMN 4. HEG 65. 1. BIF 2. GMJ 3. DKH 4. PWD 66. 1. ADG 2. PSV 3. SUW 4. CFI 67. 1. EBA 2. XUT 3. TQP 4. JFE 68. 1. ACE 2. PRT 3. UWY 4. MNO 69. 1. ABD 2. FGI 3. LMO 4. STU 70. 1. DCBA 2. MNOP 3. HGFE 4. LKJI 71. 1. BFIK 2. DHKM 3. PRVX 4. MQTV 72. 1. DCBA 2. MNOP 3. HGFE 4. LKJI 73. 1. PCAQ 2. LKIN 3. XGEZ 4. DWUF 74. 1. MRSN 2. HWXI 3. KQSP 4. ZFGA 75. 1. LPWG 2. XBIS 3. FJQB 4. MQXH 76. 1. ADIP 2. RUZG 3. ORWF 4. PSXE 77. 1. CJTG 2. NUER 3. QXHW 4. PWHT 78. 1. EFGIK 2. CDFIM 3. BCEHL 4. ABDGK 79. 1. USAGE 2. USUAL 3. UKASE 4. URINE 80. 1. AUDIO 2. ARISE 3. AWAKE 4. VIDEO 81. 1. PENAL 2. IDHNI 3. RUUD 4. KRTSINSA 82. 1. ALMZ 2. BTUY 3. CPQX 4. DEFY 83. 1. EDKL 2. LMST 3. NMUV 4. QPRS 84. 1. PRVX 2. MQTV 3. DHKM 4. BFIK 85. 1. XZCG 2. OQTX 3. IMNQ 4. EGJN 86. 1. XYVZ 2. QPMR 3. KJHL 4. DCAE 87. 1. RSXY 2. NOUV 3. MNST 4. DEJK 88. 1. BD 2. IK 3. PN 4. SU 89. 1. POCG 2. KLIZ 3. BUDX 4. FQMV 90. 1. CFIL 2. PSVX 3. JMPS 4. ORUX 91. 1. FCGDE 2. TRQPS 3. KJHMF 4. KHGJI 92. 1. DE 2. PQ 3. TU 4. MO 93. 1. BD 2. MP 3. NQ 4. HK 94. 1. BCD 2. NPR 3. KLM 4. RQP 95. 1. RTW 2. QOM 3. IKG 4. IKM 96. 1. BEH 2. CFI 3. DGJ 4. EHL 97. 1. EBA 2. XUT 3. TQP 4. JFE 98. 1. BYX 2. LPO 3. EVU 4. FUT 99. 1. RJN 2. XTP 3. MIE 4. ZWR 100. 1. EBD 2. IFH 3. QNO 4. YVX 101. 1. RVCNZ 2. LPWGT 3. GTHSYB 44. FUJQOL 102. 1. aBC 2. BaC 3. abC 4. BCa 103. 1. BD 2. CE 3. DF 4. FG 104. 1. ZW 2. YV 3. XV 4. WT 105. 1. ABC 2. BCd 3. CDe 4. Efh 106. 1. bacd 2. figh 3. lomn 4. qrst 107. 1. T 2. H 3. K 4. S 108. 1. HEARS 2. DEARS 3. ERROR 4. FEARS 109. 1. BATU 2. ZYSU 3. SRPN 4. IJSU 110. 1. RNJ 2. XTP 3. MIE 4. ZWR 111. 1. DAL 2. TQS 3. LIK 4. XTW 112. 1. GTSH 2. BYXC 3. ETUF 4. LONM 113. 1. BEFJ 2. DFGJ 3. KNQS 4. QTUY 114. 1. KOM 2. SWV 3. BFD 4. GKI 115. 1. LKHG 2. VUQP 3. XWTS 4. FEBA 116. 1. DEJK 2. MNST 3. RSXY 4. NOUV 117. 1. YXVU 2. QPNM 3. LKHG 4. FECB 118. 1. QPTS 2. AZDC 3. KJNM 4. SRWV 119. 1. PLHD 2. QMIE 3. VRNJ 4. VQNI 120. 1. ACE 2. FHI 3. KMO 4. PRT 121. 1. AKEW 2. PNTO 3. LCUF 4. HJMX 122. 1. AJKL 2. IXYZ 3. OFGH 4. VCBA 123. 1. AOT 2. CPA 3. REB 4. TIW 124. 1. ECA 2. JHF 3. OMK 4. UXY 125. 1. WVU 2. NML 3. HGF 4. DBA 126. 1. CDE 2. JKL 3. PQS 4. TUV 127. 1. AD 2. BE 3. CF 4. EF 128. 1. AZ 2. BY 3. CX 4. DU 129. 1. AN 2. BO 3. CP 4. ES 130. 1. OpRs 2. TuWx 3. FgHi 4. LNOp Odd Man Out (Words): Directions: Four of the following five are alike in a certain way and so form a group. Which is the one that does not belong to the group. 1. 1. Rupee 2. Lira 3. Coin 4. Dinar 2. 1. Jovial 2. Sad 3. Lively 4. Cheerful 3. 1. Helicopter 2. Aircraft 3. Steamer 4. Chariot 4. 1. Rain 2. Mist 3. Fog 4. Cloud 5. 1. Algebra 2. Geometry 3. Mathematics 4. Trigonometry 6. 1. Niece 2. Mother 3. Aunt 4. Son 7. 1. Tooth 2. Chin 3. Nose 4. Ear 8. 1. Lame 2. Dwarf 3. Fat 4. Tail 9. 1. Ostrich 2. Crow 3. Eagle 4. Vulture 10. 1. Carnatic 2. Kuchipudi 3. Kathak 4. Manipuri 11. 1. Ditch 2. Canal 3. Channel 4. Drive 12. 1. Auroville 2. Wembly 3. Cenotaph 4. Pentagon 13. 1. President 2. Prime Minister 3. Governor 4. Chief Justice 14. 1. Dictionary 2. Magazine 3. Newspaper 4. Library 15. 1. City 2. Town 3. Village 4. Home 16. 1. Pond 2. River 3. Canal 4. Stream 17. 1. Blacksmith 2. Goldsmith 3. Tailor 4. Sailor 18. 1. Large 2. Big 3. Sizable 4. Light 19. 1. Passenger 2. Driver 3. Captain 4. Pilot 20. 1. Diamond 2. Topaz 3. Ruby 4. Pearl 21. 1. Calf 2. Cub 3. Piglet 4. Hireling 22. 1. Different 2. Separate 3. Distinct 4. Similar 23. 1. Cripple 2. Help 3. Disable 4. Weaken 24. 1. Horse 2. Goat 3. Bullock 4. Cat 25. 1. Where 2. Near 3. Beside 4. Above 26. 1. Ears 2. Hands 3. Fingers 4. Eyes 27. 1. Eagle 2. Vulture 3. Ostrich 4. Swan 28. 1. Sofa 2. Bed 3. Divan 4. Chair 29. 1. Snake 2. Lizard 3. Turtle 4. Whale 30. 1. Mercury 2. Venus 3. Moon 4. Jupiter 31. 1. April 2. May 3. July 4. September 32. 1. Half 2. Should 3. Could 4. Gold Directions In this type of questions, 4 or 5 pairs of words have been given. Except one pair, others bear a common relationship. Find the pair which is different. 33. 1. Broom : Sweep 2. Soap : Clean 3. Spoon : Feed 4. Knife : Sword 34. 1. Newspaper : Editor 2. Film : Director 3. Stamps : Philatelist 4. Book : Author 35. 1. Mother : Daughter 2. Father : Son 3. Uncle : Aunt 4. Uncle : Nephew 36. 1. Soft : Wool 2. Hard : Stone 3. Smooth : Glass 4. Gentle : Tender 37. 1. Bank : Manager 2. College : Principal 3. Navy : Commander 4. Post office : Post man 38. 1. Paper : Pen 2. Garden : Flower 3. Wood : Saw 4. Nail : Hammer 39. 1. Twigs : Nest 2. Wood : Furniture 3. Pitcher : Pottery 4. Gold : Ornaments 40. 1. Tailor : Clothes 2. Chef : Food 3. Author : Book 4. Scale : Length 41. 1. Indigo 2. Orange 3. Pink 4. Green 42. 1. Eagle 2. Kiwi 3. Emu 4. Penguin 43. 1. Arrow 2. Spear 3. Bullet 4. Sword 44. 1. Brick 2. Heart 3. Club 4. Spade 45. 1. Uttar Pradesh 2. Delhi 3. Maharashtra 4. Sikkim 46. 1. Jockey 2. Rook 3. Bishop 4. Pawn 47. 1. Wise 2. Arrogance 3. Rude 4. Honest 48. 1. Agra 2. Manali 3. Kulu 4. Darjeeling 49. 1. Table-tennis 2. Foot-ball 3. Badminton 4. Cricket 50. 1. Afghanistan 2. Mongolia 3. China 4. Bangladesh 51. 1. Khajuraho 2. Dilwara 3. Madurai 4. Ellora 52. 1. Goblin 2. Imp 3. Goblet 4. Gnome 53. 1. Goldsmith 2. Carpenter 3. Tailor 4. Teacher 54. 1. Economics 2. Physics 3. Chemistry 4. Botany 55. 1. Sesame 2. Mustard 3. Rapeseed 4. Cashewnut 56. 1. Assassinate 2. Murder 3. Kills 4. Kidnap 57. 1. Hanger 2. Platform 3. Dock 4. Park 58. 1. Shoulder 2. Foot 3. Elbow 4. Arm 59. 1. Laos 2. India 3. Bolivia 4. Afghanistan 60. 1. Cap 2. Veil 3. Turban 4. Helmet 61. 1. Ass 2. Cow 3. Rhinoceros 4. Lion 62. 1. Wheat 2. Mustard 3. Rice 4. Gram 63. 1. Biscuits 2. Bread 3. Chocolate 4. Pastry Directions In this type of questions, 4 or 5 pairs of words have been given. Except one pair, others bear a common relationship. Find the pair which is different. 64. 1. Husband : Wife 2. Dog : Cat 3. Chief Minister : M.L.A.4. Crow : Cuckoo 65. 1. Spain : Madrid 2. Japan : Singapur 3. India : Delhi 4. U.S.A : Washington 66. 1. Error : Blunder 2. Crime : Sin 3. Famous : Renowned 4. Lion : Lioness 67. 1. Snake : Hiss 2. Lion : Roar 3. Birds : Chirp 4. Frog : Bleat 68. 1. Farmer : Plough 2. Butcher : Chopper 3. Author : Book 4. Jockey : Tack 69. 1. Sheep : Lamb 2. Horse : Pony 3. Man : Woman 4. Dog : Puppy 70. 1. Steel : Utensil 2. Bronze : Statue 3. Duralumin : Aircraft 4. Iron : Rails 71. 1. Pituitary 2. Pancreas 3. Thalamus 4. Adernal 72. 1. Pellagra 2. Goitre 3. Scurvy 4. Anaemia 73. 1. Arrow 2. Axe 3. Knife 4. Dagger 74. 1. Metre 2. Furlong 3. Acre 4. Mile 75. 1. Pupil 2. Iris 3. Cornea 4. Medulla 76. 1. Sucrose 2. Ptyalin 3. Analyse 4. Pepsin 77. 1. Potassium 2. Silicon 3. Zirconium 4. Gallium 78. 1. Almond 2. Turmeric 3. Pepper 4. Cuminseed 79. 1. Hepatitis 2. Tetanus 3. Cancer 4. Conjectivitis 80. 1. Autocracy 2. Bereaucracy 3. Democracy 4. Diplomacy Analytical Reasoning Arrangements: 1. In a row of girls of sheetal who is 10 th from the left and Lina who is 9 th from the right change their seats. Sheetal becomes 15 th from the left. How many girls are there in a row? 1. 16 2. 23 3. 32 4. 25 2. Five boys are so standing that they from a circle. Ajay is between Ramesh and Dominic, Soloman is to the left of Babu. Ramesh is to the left of Soloman. Who is the right of Ajay? 1. Dominic 2. Soloman 3. Babu 4. Ramesh 3. In a row of 16 boys when Prakash was shifted by two places towards the left, he became 7 th from the left end. What was his earlier position from the right end of the row? 1. 12 th 2. 10 th 3. 14 th 4. 8 th 4. Five boys are sitting in a row. A is on the right of B, E is on the left of B, but to the right of C. If A is on the left of D. Who is sitting in the middle. 1. E 2. B 3. A 4. C 5. Some boys are sitting in row. P is sitting 14 th from the left and Q is 7 th from the right. If there are four boys between P and Q, how many boys are there in the row? 1. 19 2. 21 3. 25 4. 23 6. If (i) six persons, A, B, C, D, E and F are standing in a circle, not necessarily in the same order. (ii) B is between F and C. (iii) A is between E and D and (iv) F is to the left of D, which of the following is between A and F? 1. B 2. C 3. D 4. E 7. In a row of boys, Anil is 15 th from the left and Vishakh is 7 th from the right. If they interchange their positions. Vishakh becomes 15 th from the right. How many boys are there in the row? 1. 21 2. 25 3. 29 4. Can‟t be determined 8. Five persons were playing card game sitting in a circle all facing the center. Mukund was to the left of Rajesh, Vijay was to the right of Anil and between Anil and Nagesh. Who was to the right of Nagesh? 1. Rajesh 2. Vijay 3. Anil 4. Mukund 9. In front of a camera, Mr. X is sitting to the left of that man, who is at the center of the row, but Mr. X is to right of Mr. Y . Mr. P is to the right of Mr. Z and Mr. R is the right of Mr. P. Mr. R is second from the man, sitting at the center. Who is sitting at the center of the row? 1. Mr. X 2. Mr. Y 3. Mr. Z 4. Mr. R 10. A ranks fifth in a class. B is eighth from the last. If C is sixth after A and just in middle of A and B, how many students are there in the class? 1. 25 2. 26 3. 23 4. 24 11. Suresh is 7 ranks ahead of Ashok in the class of 39. If Ashok‟s rank is 17 th from the last, what is Suresh‟s rank from the start? 1. 15 2. 14 3. 24 4. 16 12. In a row of children Munni is nirth from the left of Tunni is thirteenth from the right. When they exchange places, Munni will be seventeenth from the left. Which of the following will be the new position of Tunni from the right? 1. 20 th 2. 7 th 3. 21 st 4. 9 th 13. Some boys are sitting in a row, P is sitting 14 th from the left and Q is seventh from the right. If there are four boys between P and Q, how many boys are there in the row? 1. 19 2. 21 3. 25 4. 23 14. In a row of trees, one tree is the 9 th from either end of the row. How many trees are there in the row? 1. 17 2. 19 3. 16 4. 18 15. In a certain class, Rakesh is 29 th from the top and mohan is 16 th from the bottom in the alphabetical arrangements of names. If they have 7 boys between them what is the number of students in the class? 1. 52 2. 45 3. 36 4. 35 16. Rakesh ranks seventh in a class of twenty. What is his rank from the last? 1. 15 th 2. 13 th 3. 14 th 4. 8 th 17. Of the five villages: 1) Phulwade is smaller than Dhanwade 2) Ambawade is bigger than Khelwade 3) Sonewade is bigger than Dhanwade but is not as big as Kelwade. Which is biggest village? 1. Ambawade 2. Phulwade 3. Dhanwade 4. Kelwade 18. It (A) Ashok is taller than Suresh (B) Raju is taller than Ashok (C) Chandu is shorter than Suresh, then chandu is __________ 1. taller than ashok 2. As tall as suresh 3. taller than suresh 4. shorter than Ashok 19. Five boys Rakesh, Anil, Mahesh, Suresh and Manjit are sitting in a circle. A) Anil is sitting between Rakesh and Suresh B) To Manjit‟s right suresh is seated. Who is seated to Mahesh‟s left? 1. Anil 2. Suresh 3. Manjit 4. Rakesh 20. Four girls are swimming in a stream. 1) Harjeet is further ahead of Manjula 2) Neena is behind Manjula 3) Ruchi is between Manjula and Neena. Who is second from the last? 1. Neena 2. Manjula 3. Ruchi 4. Harjeet 21. Five poles are standing in a row. M is on the left of N, O is on the right of P, which is on the right of N. If L is on the left of M, which pole is in center? 1. L 2. M 3. N 4. O 22. Five boys are sitting in a row. Sanjay is just on the one side of Pradeep but not just on any side of Timur. Kailash is just on one side of Ramesh who is sitting left of all and Timur is not sitting just on any side of Kailash who are sitting on either side of Sanjay? 1. Kailash & Pradeep 2. Ramesh & Pradeep 3. Only Pradeep 4. Pradeep & Timur 23. Six families A, B, C, D, E and F are living in houses in a row. B has F and D as neighbours, E has A and C as neighbours. A does not live next to D. Who are F‟s next door neighbours? 1. B and E 2. B and D 3. B and C 4. Data Insufficient 24. Sudha is taller than Pushpa but shorter than Malati. Geeta is shorter than Vinu and Vinu is not as tall as Pushpa. Who should be in the middle if they stand in a row according to height? 1. Pushpa 2. Malati 3. Sudha 4. Geeta 25. Among five friends, Manish is taller than Harish, but not as tall as Jayesh. Jayesh is taller than Vijay and Sharad. Vijay is shorter than Harish but taller than one who is shortest among them. Who is the fourth in the descending order of their heights? 1. Manish 2. Harish 3. Sharad 4. Can‟t be determined 26. If Shirish is taller than Charu but shorter than Raju and Charu is just as tall as Dilip but taller than Ashok, then Dilip is _______ 1. Just as tall as Shirish 2. Shorter than Charu 3. Taller than Raju 4. Taller than Ashok 27. While going to the school, Anil was behind Sunil and Rohit was ahead of Madan. Ramesh was in between Anil and Rohit. Who was leading? 1. Anil 2. Sunil 3. Rohit 4. Madan 28. Priti scored more than Rahul. Yamuna scored as much as Divya. Lotika scored less than Manju. Rahul scored more than Yamuna. Manju scored less than Divya. Who scored the lowest? 1. Yamuna 2. Manju 3. Lotika 4. Rahul 29. Two ladies and two men are playing bridge – a card game and seated at north, east, south and west of a table. No lady is facing east. Persons sitting opposite to each other are not of the same sex. One man is facing south. Which directions are the ladies facing? 1. East & West 2. South & East 3. North & West 4. North East 30. P, Q, R, S, and T are sitting in a row. Q is between P and T. To find out who among them is in the middle, which of the following information given in the statements A and B is/are sufficient? A. P is left of Q and right of S B. R is at the right end 1. Only (B) is sufficient 2. Only (A) is sufficient 3. Either (A) or (B) is sufficient 4. Both (A) and (B) together are needed Directions (Questions 31-34): Read the following information carefully and answer the questions given below: Six boys A, B, C, D, E and F are marching in a line. They are arranged according to their height, the tallest are being at the back and the shortest in front. F is between B and A E is shorter than D but taller than C who is taller than A E and F have two boys between them A is not the shortest among them all 31. Where is E? 1. Between A & B 2. Between C & A 3. Between D & C 4. In front of C 32. Who is the tallest? 1. B 2. D 3. F 4. A 33. If we start from the shortest which boy is fourth one in the line? 1. E 2. A 3. D 4. C 34. Who is the shortest? 1. C 2. D 3. B 4. F Directions (Questions 35-37): Study the following information carefully and answer the questions given below. i. Five courses A, B, C, D and E each of one month duration are to be taught from January to May one after the other not necessarily in same order by lecturers, P, Q, R, S and T. ii. P teaches course B but not in the month of April or May iii. Q teaches course A in the month of March iv. R teaches in the month of January but does not teach course C or D 35. Which course is taught by S? 1. C 2. E 3. Either C or D 4. D 36. Which lecture‟s course immediately follows after course B? 1. Q 2. P 3. S 4. T 37. Which course is taught in the month of January? 1. C 2. D 3. E 4. Data inadequate Directions (Questions 38-40): Six persons A, B, C, D, E and F sitting forming a circle and one is facing other front to front B is between A and C, E is between F and D. F is sitting straight opposite to A and right to E. 38. D is between which of the following pairs? 1. EF 2. AE 3. AB 4. CF 39. If the position of B and E are interchanged and also that of C and D, A will be in between which of the following pairs? 1. CB 2. ED 3. FD 4. CE 40. Who is at the immediate left of D? 1. E 2. F 3. B 4. A 41. Six friends A, B, C, D, E and F are sitting in a closed circle facing the center. E is to the left of D. C is between A and B. F is between E and A. Who is to the left of B? 1. D 2. C 3. A 4. F 42. In a row of children, Shibu is fifth from the left and Lakhya is sixth from the right. When they exchange position, Shibu will be thirteenth from the left. What will be Lakhya‟s position from the right? 1. 14 th 2. 7 th 3. 11 th 4. 18 th 43. In a march past seven persons are standing in a row. Q is standing in a row. Q is standing left to R but right to P. O is standing right to N and left to P. Similarly, S is standing right to R and left to T. Find out who is standing in the middle? 1. P 2. R 3. Q 4. O 44. Five boys took part in a race. Ram finished before Mohan but behind Gopal. Abbas finished before sailesh but behind Mohan. Who won the race? 1. Ram 2. Gopal 3. Mohan 4. Abbas 45. Six persons playing a game sitting in a circle facing the center. Vijay was to the left to Sudhir. Amar was between Rakesh and Saurav. Neerav was second to the left of Amar. Who is second to the right of Vijay? 1. Neerav 2. Rakesh 3. Saurav 4. Data Insufficient 46. In a row of girls, if Seeta who is 10 th from the left and Lalitha who is 7 th from the right, interchange their seats, Seeta becomes 15 th from the left. How many girls are there in the row? 1. 17 2. 20 3. 22 4. 21 47. In a row of boys, Anand is eleventh from the left and Deepak is fifteenth from the right. When Anand and Deepak interchange their positions, Anand will be fifth from the left. Which of the following will be Deepak‟s position from the right? 1. 7 th 2. 17 th 3. 11 th 4. 9 th 48. In a photograph Shyam is to the left of Madan. Mary is to the right of George, Karim is in between Shyam and Mary. Who is at the corner? 1. Shyam 2. Mary 3. George 4. Karim 49. Six students A, B, C, D, E and F are standing in a row. B is between F and D, E is between A and C. A does not stand next to either F or D. C does not stand next to D. F is between which of the following pairs of students? 1. B and D 2. B and A 3. B and E 4. B and C 50. Madhav ranks seventeenth in a class of thirty one. What is his rank from the last? 1. 13 2. 14 3. 15 4. 16 51. In a row of children, shibu is fifth from the left and Lakhya is sixth from the right. When they exchange positions, shibu will be thirteenth from the left. What will be Lakhya‟s position from the right? 1. 4 th 2. 5 th 3. 13 th 4. 14 th 52. Four girls A, B, C and D are sitting in a circle. B and C are facing each other. Which of the following is definitely true? 1. A is to the left of C 2. D is to the left of C 3. A & D are facing each other 4. A is not between B & C 53. Raju and Manoj are ranked 14 and 15 respectively from the top in a class of 30 students. What will be their respective ranks from the bottom. 1. 15 th & 16 th 2. 16 th & 15 th 3. 17 th & 16 th 4. 18 th & 17 th 54. Mahesh ranked 13 th from the top and 26 th from the bottom among those who have passed the annual examination in a class. If six students have failed in the annual examination, what was the total number of students in that class? 1. 44 2. 20 3. 21 4. 38 55. There are five books A, B, C, D, E. C lies above D, E is below A. D is above A, B is below E. Which is the bottom most book? 1. A 2. B 3. E 4. C 56. If (A) Suresh is taller than Ashutosh (B) Raju is taller than Charu but shorter than Bala (C) Ashutosh is shorter than Charu (D) Charu is taller than Suresh, then who is the tallest? 1. Suresh 2. Ashutosh 3. Raju 4. Bala 57. If (A) Mahesh is taller than suresh (B) Anil is taller than Mahesh (C) Ramesh is taller than Anil (D) Puneet is tallest of all. If they stand according to their height, who will be exactly in the middle? 1. Mahesh 2. Suresh 3. Ramesh 4. Anil 58. Sunita is standing on a stairs below Sulekha, Rani is below Sulekha and Madhu is between Rani and Sulekha who is second from bottom? 1. Rani 2. Sulekha 3. Madhu 4. Sunita 59. Five boys are up on the ladder. A) A is further up the ladder than B B) B is between A and C C) D is further up than A. Who is the third from the bottom. 1. B 2. C 3. A 4. D 60. Five books are lying in a pile. E is lying on A and D is under B. A is lying above B and C is lying under D. Which book is lying at the bottom? 1. A 2. B 3. C 4. D 61. Four boys are sitting in a row. Bipin is sitting just on one side to Gopal, but not just on any side to Raju. If raju is not just on any side of Farukh then who are sitting just both side of Farukh? 1. Only gopal 2. Only bipin 3. nobody 4. Bipin and Gopal 62. Five students are sitting in a row. Tapesh is on the right of Zahir. Manoj is on the left of Zahir but is on the right of Love. Tapesh is on the left of Qeer. Who is sitting 1 st from the left? 1. Zahir 2. Tapesh 3. Qeer 4. Love 63. Five bags are lying in a pile one above the other. If A is above B, C is above D but below E and D is above A, which bag is in the middle? 1. A 2. D 3. C 4. B 64. Prakash is taller than Geetha. Amar is taller than Prabhat but not as tall as Geetha. Prabodh is taller than Prakash. Who among them is the shortest? 1. Prabhat 2. Geetha 3. Amar 4. Prabodh 65. Of the six towns, Dhulia is bigger than Amalner, Shrirampur is bigger than Nasik, Jalgaon is not as big as Shrirampur but bigger than Amalner, Amalner is smaller than Nasik but bigger than Manmad. Which is the smallest? 1. Amalner 2. Nasik 3. Jalgaon 4. Manmad 66. Ashok is taller than Kavitha but not as tall as Jayesh. Jayesh is shorter than Subodh who is not as tall as Prabodh. Who is tallest in the group? 1. Prabodh 2. Subodh 3. Kavitha 4. Ashok 67. Ravi is taller than Jyoti who is shorter than Raju. Mohan is taller than Ravi but shorter than Suresh. Raju is shorter than Ravi. Who is the tallest? 1. Ravi 2. Raju 3. Suresh 4. Data Insufficient 68. Amar is taller than Samir, Pravath is taller than Umesh but not as tall as Samir; Ashok is shorter than Umesh. Who is shortest? 1. Amar 2. Samir 3. Pravath 4. Ashok 69. Shyam is older than Pradeep. Praveen is as old as Anjan. Amrut is younger than Suresh who is as old as Anjan. Pradeep is older than Praveen. Which boy is oldest of all? 1. Pradeep 2. Praveen 3. Suresh 4. Shyam 70. Roshan is taller than Hardik who is shorter than Susheel, Mirza is taller than Harry but shorter than Hardik, Susheel is shorter than Roshan. Who is the tallest? 1. Roshan 2. Susheel 3. Hardik 4. Harry Directions Read the following statements and answer the questions given below. a) Six friends A, B, C, D, E and F are sitting in a closed circle facing the center, b) E is to the left of D, c) C is between A and B, d) F is between E and A. 71. Who is to the left of E? 1. A 2. C 3. D 4. F 72. Who is to the right of C? 1. A 2. B 3. D 4. E Directions Read the following information to answer questions below. Six persons were playing game sitting in a circle facing the center. Vijay was to the left of Sudhir, Amar was between Rakesh and Saurav. Neeru was second to the left of Amar. 73. Who is second to the right of Vijay? 1. Neeru 2. Rakesh 3. Saurav 4. Can‟t be determined 74. Who is/are between Amar and Vijay? 1. Saurav and Sudhir 2. Rakesh & Saurav 3. Sudhir & Rakesh 4. Data Insufficient 75. Which of the following is the position of Vijay from Neeru? 1. 2 nd from the left 2. 3 rd from left 3. 3 rd from right 4. Can‟t be determined Directions: Read the following information carefully and answer the questions given below: i. Seven members of World Forest Conservation Committee – A, B, C, D, E, F and G planted seven saplings on seven days of the week which was celebrated as “Plantation Week”. ii. A planted the sapling on Monday, the first day of the Plantation Week iii. B planted the sapling a day before when C planted the sapling and the very next day of E. iv. D planted the sapling on some day after that of B but that day was not the middle day of the week. v. F planted the sapling on the last day of the plantation week and it was the third day after C planted the sapling. 76. Which of the following pairs of members planted the saplings on Wednesday and Thursday respectively? 1. D and G 2. B and G 3. B and C 4. Can‟t be determined 77. On which day did B plant the sapling? 1. Tuesday 2. Wednesday 3. Thursday 4. Can‟t be determined 78. Who among the following planted sapling on Saturday? 1. Either B or C 2. Either D or G 3. Only C 4. Only E 79. Who planted the sapling on the middle day of the plantation week? 1. B 2. D 3. E 4. C 80. On which day did D plant the sapling? 1. Monday 2. Wednesday 3. Tuesday 4. Can‟t be determined Problem Solving: Directions (Questions 1-5): Read the following information and answer the questions given below it. 1. Seven students P, Q, R, S, T, U and V take a series of tests. 2. No two students get similar marks. 3. V always scores more than P. 4. P always scores more than Q. 5. Each time either R scores the highest and T gets the least, or alternatively S scores the highest and U or Q scores the least. 1. If S is ranked sixth and Q is ranked fifth, which of the following can be true? 1. V is ranked first of fourth 2. R is ranked second and third 3. P is ranked second or fifth 4. U is ranked third or fourth 2. If R gets most, V should be ranked not lower than ___________ 1. Second 2. Third 3. Fourth 4. Fifth 3. If R is ranked second and Q is ranked fifth which of the following must be true? 1. S is ranked third 2. T is ranked sixth 3. P is ranked sixth 4. V is ranked fourth 4. If S is ranked second, which of the following can be true? 1. U gets more than V 2. V gets more than S 3. P gets more than R 4. P gets more than V 5. If V is ranked fifth, which of the following must be true? 1. S scores the highest 2. R is ranked second 3. T is ranked third 4. Q is ranked fourth” Directions (Questions 6-10): Study the following information carefully and answer the questions given below it: Five friends A, B, C, D and E are sitting on a bench. 1. A is sitting next to B 2. C is sitting next to D 3. D is not sitting with E 4. E is on the left end of the bench 5. C is on second position from the right 6. A is on the right side of B and to the right side of E 7. A and C are sitting together 6. Where is A sitting? 1. Between B and C 2. Between D and C 3. Between E and D 4. Between C and E 7. Who is sitting in the centre? 1. A 2. B 3. C 4. D 8. C is sitting between ________ 1. B and D 2. A and E 3. D and E 4. A and D 9. What is the position of D? 1. Extreme left 2. Extreme right 3. Third from left 4. Second from left 10. What is the position of B? 1. Second from right 2. Centre 3. Extreme left 4. Second from left Directions (Questions 11-15): Study the following information carefully and answer the questions given below it. A sales representative plans to visit each of six companies K, N, P, Q, R and S exactly once during the course of one day. She is setting up her schedule for the day according to the following conditions. She must visit M before N and R. She must visit N before Q The third company she visits must be P 11. Which of the following must be true of the sales representative‟s schedule? 1. She visits M before Q 2. She visits N before R 3. She visits P before M 4. She visits P before S 12. If the sales representatives visits S first, which company must she visit second? 1. M 2. N 3. P 3. Q 13. The sales representative could visit any of the following companies immediately after P except ____ 1. S 2. R 3. Q 4. M 14. If the sales representative visits Q immediately before r and immediately after S, she must visit Q. 1. First 2. Second 3. Fourth 4. Fifth 15. Which of the following could be the order in which the sales representative visit the six companies? 1. M, S, P, N, R, Q 2. Q, N, P, R, S, M 3. M, R, N, Q, P, S 4. P, S, M, R, Q, N Directions (Questions 16-20): Read the following information carefully and answer the questions given below it. On a shelf are placed six volumes side by side labeled A, B, C, D, E and F. Three volumes B, C and E have green covers while the other volumes have yellow covers. A, D and B are new volumes while the rest are old volumes. A, C and B are law reports, while the rest are Gazetteers. 16. Which volume is new, yellow covered and a Gazetteer? 1. B 2. D 3. E 4. F 17. Which two volumes are old Gazetteers and have green covers? 1. B, C 2. B, E 3. B, F 4. Only E 18. Which is green covered, old and a law report volume? 1. A 2. B 3. C 4. D 19. Which is the yellow covered new law report volume? 1. A 2. D 3. B 4. C 20. Which of the following is the old volume of a Gazetteer? 1. C 2. D 3. E 4. B Directions (Questions 21-25): Study the following information carefully and answer the questions given below it: From amongst six boys A, B, C, D, E and F and five girls P, Q, R, S and T, a term of six is to be selected under the following conditions: A and D have to be together. C cannot go with S. S and T have to be together. B cannot be teamed with E. D cannot go with P. B and R have to be together. C and Q have to be together. 21. If there be five boys in the team, the long girls member is _____________ 1. P 2. Q 3. R 4. S 22. If including P, the team has three girls, the members other than P are ___________ 1. BCFQR 2. ADEST 3. ADBST 4. BFRST 23. If the team including C consist of four boys, the members of the team other than C are _________ 1. ADEPQ 2. ABDQR 3. DEFAQ 4. BEFRQ 24. If four members including E have to be boys, the members other than E are ___________ 1. ABCQR 2. ADFST 3. BCFQR 4. ACDFQ 25. If four members have to be girls, the members of the team are ____________ 1. BCPQRS 2. BFPRST 3. BCQRST 4. BCPQRT Directions (Questions 26-30): Study the following information carefully and answer the questions given below it: There are six teachers A, B, C, D, E and F in a school. Each of the teachers teaches two subjects, one compulsory subject and other optional subject. D‟s optional subject was History while three others have it as compulsory subject. E and F have Physics as one of their subjects. F‟s compulsory subject is Mathematics which is an optional subject of both C and E. History and English are A‟s subjects but in terms of compulsory and optional subjects, they are just reverse of those of D‟s. Chemistry is an optional subject of only one of them. The only female teacher in the school has English as her compulsory subject. 26. What is C‟s compulsory subject? 1. History 2. Physics 3. Chemistry 4. English 27. Who is a female member in the group? 1. A 2. B 3. D 4. None 28. Which of the following has same compulsory and optional subjects as those of F‟s? 1. D 2. B 3. A 4. None 29. Disregarding which is the compulsory which is the optional subject who has same two subject combination as F? 1. A 2. B 3. E 4. D 30. Which of the following groups has History the compulsory subject? 1. A, C and D 2. B, C and D 3. C and D 4. A, B and C Directions (31 – 36) : A family has 6 children viz., Savitha, Sadguna, Swathi, Srinivas, Suvidha and Susheel not born in the same order. Any two consecutive children has 2 years age difference. (i) Swathi is older than Srinivas and Susheel. (ii) Suvidha born as 2 nd child in the family and she is 4 years elder than Sadguna. (iii) Susheel born last and he is 6 years younger to Srinivas. 31. Who had born first? 1. Swathi 2. Suvidha 3. Srinivas 4. Sadguna 32. Who had born as a 5 th child in the family? 1. Srinivas 2. Swathi 3. Sadguna 4. Savitha 33. What is the age difference between Suvidha and Susheel? 1. 10 years 2. 8 years 3. 6 years 4. 2 years 34. If Swathi‟s age is 23 years then what is the age of Savitha? 1. 11 years 2. 13 years 3. 15 years 4. 17 years 35. Who is the eldest child of the family? 1. Swathi 2. Suvidha 3. Srinivas 4. Susheel 36. Who is the eldest child of the family? 1. Swathi 2. Suvidha 3. Srinivas 4. Susheel Directions (37 –40) : Four friends are playing cards game. Anil is facing North and Sunil sat to his left. Vikrant is opposite to Sunil and Vikranth‟s right is Vinod. 37. Who is opposite to Vinod? 1. Anil 2. Sunil 3. Vikranth 4. Can‟t be determined 38. Who is facing west? 1. Anil 2. Sunil 3. Vikranth 4. Vinod 39. Who is to the right of Vinod? 1. Vikranth 2. Anil 3. Sunil 4. Can‟t be determined 40. Who is facing South? 1. Anil 2. Sunil 3. Vikranth 4. Vinod Directions Study the following information carefully and answer the questions given below it: There are five persons P, Q, R, S and T. One is football player, one is chess player and one is hockey player. P and S are unmarried ladies and do not participate in any game. None of the ladies plays chess or football. There is a married couple in which T is the husband. Q is the brother of R and is neither a chess player nor a hockey player. 41. Who is the football player? 1. P 2. Q 3. R 4. S 42. Who is the hockey player? 1. T 2. S 3. R 4. Q 43. Who is the chess player? 1. S 2. P 3. T 4. R 44. Who is the wife of T? 1. P 2. Q 3. R 4. S 45. The three ladies are _____________ 1. P, Q and R 2. Q, R and S 3. P, Q and S 4. P, R and S Directions Study the following information carefully and answer the questions given below it: P, Q, R, S, T and X are members of a family. There are two married couple. Q is an Engineer and is father of T. X is grandfather of R and is a lawyer. S is grandmother of T and is a housewife. There is one Engineer, one Lawyer, one Teacher, one Housewife and two students in the family. 46. Who is the husband of P? 1. R 2. X 3. Q 4. S 47. Which of the following are two married couples? 1. XS, QP 2. XS, QT 3. XS, RP 4. TS, RX 48. Which of the following is definitely a group of male members? 1. Q, X, T 2. X, T 3. Q, X, P 4. Q, X 49. Who is the sister of T? 1. R 2. S 3. P 4. Data inadequate 50. Which of the following can be P‟s profession? 1. Housewife 2. Engineer 3. Teacher 4. Engineer or Teacher Directions Study the following information carefully and answer the questions given below it: Prashant Arora has three children – Sangeeta, Vimal and Ashish. Ashish married Monika, the eldest daughter of Mr. and Mrs. Roy. The Roys married their youngest daughter to the eldest son of Mr. and Mrs. Sharma, and they had two children name Amit and Shashi. The Roys have two more children, Roshan and Vandana, both elder to Veena. Sameer and Ajay are sons of Ashish and Monika. Rashmi is the daughter of Amit. 51. What is the surname of Rashmi? 1. Sharma 2. Roy 3. Arora 4. Can‟t be determined 52. How is Sameer related to the father of Monika? 1. Grandson 2. Son 3. Cousin 4. Son-in-law 53. What is the surname of Sameer? 1. Roy 2. Sharma 3. Arora 4. Can‟t be determined 54. How is Mrs. Roy related to Ashish? 1. Aunt 2. Mother-in-law 3. Mother 4. Sister-in-law Directions Study the following information carefully and answer the questions given below it: A training college has to conduct a refresher course for teaches of seven different subjects Mechanics, Psychology, Philosophy, Sociology, Economics, Science and Engineering from 22 nd July to 29 th July. Course should start with Psychology. 23 rd July, being Sunday, should be holiday. Science subject should be on the previous day of the Engineering subject. Course should end with Mechanics subject. Philosophy should be immediately after the holiday. There should be a gap of one day between Economics and Engineering. 55. The refresher course will start with which one of the following subjects? 1. Psychology 2. Mechanics 3. Philosophy 4. Economics 56. Which subject will be on Tuesday? 1. Mechanics 2. Engineering 3. Economics 4. Psychology 57. Which subject precedes Mechanics? 1. Sociology 2. Engineering 3. Philosophy 4. Psychology 58. How many day‟s gap is there between Science and Philosophy? 1. One 2. Two 3. Three 4. Four 59. Which subject is following by Science? 1. Engineering 2. Psychology 3. Philosophy 4. Economics 60. Which subject will be on Saturday? 1. Engineering 2. Mechanics 3. Philosophy 4. Data Inadequate Directions There are six students in a class A, B, C, D, E and F. D is taller than E and F. There is only one person between B and C. A is between E and F. There are four persons between C and F. 61. Who is the tallest in the group? 1. D 2. A 3. C 4. E 62. Who is between D and E? 1. B 2. A 3. F 4. C 63. Who is shortest in that group? 1. C 2. F 3. E 4. A 64. Who are shorter than E? 1. F and E 2. F and B 3. A and F 4. C and E 65. Who are taller than A but shorter than D? 1. F and E 2. E and B 3. F and B 4. C and E Directions Five persons P, Q, R, S and T belongs to five different cities Chennai, Bangalore, Hyderabad, Pune and Delhi. They are invited to deliver a seminar on different subject Viz., Chemistry, Physics, Mathematics, History and Economics but not necessarily in the same order. (i) P who belongs to Bangalore gives seminar on Economics. (ii) The person who gives seminar on Physics belongs to Chennai. (iii) T does not give seminar on Chemistry or History but belongs to Hyderabad. (iv) S does not belongs to Pune but gives seminar on Chemistry and History is the option of R. 66. Who belongs to Pune? 1. R 2. Q 3. S 4. T 67. Physics seminar will be given by? 1. Q 2. R 3. S 4. T 68. T gives seminar on? 1. Physics 2. Chemistry 3. History 4. Mathematics 69. S belongs to which city? 1. Chennai 2. Hyderabad 3. Pune 4. Delhi 70. Who belongs to Chennai? 1. R 2. S 3. Q 4. T Directions In a family of six persons P, Q, R, S, T and U, there are 3 males and 3 females. There are 2 married couples and 2 persons who are unmarried. Each one of them reads different News Papers Viz., Eenadu, Vaartha, Vijetha, AndhraJyothi, AndhraBhumi and Saakshi. T, who reads Vaartha is mother-in-law of P, who is the wife of R. S is the father of R and he does not read Eenadu or Saakshi. Q reads AndhraBhumi and is the sister of U who reads Vijetha. R does not read Saakshi. 71. Who among the following reads Eenadu? 1. R 2. S 3. P 4. Data inadequate 72. How is U related to T? 1. Brother 2. Son 3. Grandson 4. Can‟t say 73. Which of the following is one of the married couples? 1. P – S 2. T – R 3. T – P 4. R – P 74. Who reads Saakshi? 1. T 2. S 3. Q 4. P 75. How is T related to R? 1. Son 2. Father 3. Mother 4. Mother-in-law Directions 6 persons L, M, N, O, P and Q are standing in a row. They wear 6 different coloured dresses viz., Red, Green, Blue, Black, Violet and White. (i) M is 4 th from the right end and wears Blue colour dress. And Q is second left to him. (ii) Person wears Black dress stands 4 th from the left end and N is immediate right to him. (iii) P is at one end and wears Red dress. (iv) O does not wear violet or white and person stands immediate left to P wears violet dress. 76. Who wears green dress? 1. L 2. M 3. N 4. O 77. Who stands in the middle? 1. L and N 2. O and M 3. M and L 4. O and N 78. Who stands at the both ends? 1. M and L 2. P and Q 3. N and O 4. Q and N 79. If white dressed person is called Manager who is the Manager? 1. P 2. N 3. O 4. Q 80. O wears which colour dress? 1. Red 2. Green 3. Black 4. Violet Critical Reasoning Exercise 1: 1. Recent studies have highlighted the harmful effects of additives in food (colors, preservatives, flavor enhancers etc.). There are no synthetic substances in the foods we produce at Munchon Foods – we use only natural ingredients. Hence you can be sure you are safeguarding your family‟s health when you buy our products. Which of the following, if true, would most weaken the contention of Munchon Foods? A. Some synthetic substances are not harmful B. Some natural substances found in foods can be harmful C. Food without additives is unlikely to taste good D. Munchon Foods produces only breakfast cereals E. Without preservatives some foods could cause harm 2. A fruit known as amla in certain parts of Asia is an excellent source of vitamin C. A small quantity of the fruit grated and added to salads provides almost all the daily requirement of this vitamin. However, the fruit is very sour. A new process designed to remove most of the sour taste will make the fruit acceptable to American tastes. We are therefore starting to grow this fruit for sale in the United States. The argument above assumes all of the following except A. Americans generally won‟t eat very sour foods B. The new process does not remove a significant part of the vitamin content C. That a market exists for a new source of vitamin C D. The fruit can be used only in salads E. Apart from being sour there are no other objections to eating this fruit 3. Most scientists agree that new lines of interdisciplinary research are the need of the hour. Even government committees on science have stressed the need for more interdisciplinary projects. Yet, of ten proposals for new interdisciplinary projects last year, only one was successfully funded. Some have suggested that this means that as yet researchers are not coming up with sufficiently persuasive projects, or that their proposals are not of high enough quality, or even that the reputations of these researchers is not high enough. However, the real reason probably lies in the way funding is organized. Funding is still allocated according to the old categories and there are no funds specifically for research that overlaps different subject areas. The two parts in bold-face are related to each other in which of the following ways? A. The first is a finding that the author finds unacceptable; the second is the author‟s own position B. The first is a finding that the author attempts to account for; the second is a finding that contradicts the author‟s main conclusion. C. The first is a fact that the author attempts to account for. The second is data that explicitly supports the author‟s main conclusion. D. The first is a position that the author opposes; the second is the author‟s main position. E. The first is a situation that the author finds paradoxical; the second is an assumption that the author uses to reinforce the paradox. 4. Anton: I sold my house on an internet site last year and was happy with the price. I got a speedy sale and the cost of advertising was insignificant. I would advise you to avoid real estate agents. Barbie: It is in the interest of the real estate agent to get me the best price for my property because he gets a commission based on the selling price. Therefore, when selling my house I will certainly use an agent rather than trying to sell the house by word of mouth, or by advertising in newspapers or on the internet. Barbie‟s could strengthen her position by pointing out all of the following except A. Houses of comparable value often obtain a lower price when sold on the internet B. Very few houses are sold on the internet at the moment an so a valid comparison is difficult C. The agent‟s service includes many add-on benefits in terms of legal fees, surveyor‟s reports and advice that are not available on internet sites D. Some buyers pay the agent to find them a cheap house E. The agent‟s commission is usually less than the difference between the internet price and the higher price the agent obtains for you 5. Early data on seat-belt use showed that seat-belt wearers were less likely to be killed in road accidents. Hence, it was initially believed that wearing a seat-belt increased survival chances in an accident. But what the early analysts had failed to see was that cautious drivers were more likely to wear the belts and were also less likely to cause „big accidents‟, while reckless drivers were more likely to be involved in „big‟ accidents and were less likely to wear the belts. Which of the following, if true, could an opponent of the view presented above best cite as a reason for recommending continued use of seat-belts? A. Careful drivers who are involved in accidents caused by reckless drivers, would be more likely to survive if wearing a belt B. All drivers should be required by law to wear a belt C. The ratio of „big‟ to „small‟ road accidents is very small D. In fatal accidents seat-belt wearers in the front seat are less likely to survive than those wearing seat belts in the back seat E. On average, careful drivers pay lower insurance premiums than do drivers who have been involved in accidents. 6. French cuisine is highly regarded all over the world. Yet in Paris there are more American restaurants selling burgers and fries (which many people now class as „junk food‟) than there are in any other European capital city. Obviously the French are very fond of „junk food‟, and are not too proud to eat it. Which of the following, if true, would most weaken the author‟s contention? A. There are also a larger number of Lebanese restaurants in Paris than there are in other European capital cities B. French Cordon Bleu cuisine is very expensive C. The number of French tourists eating in New York burger restaurants is very low D. Junk food is actually has high nutritional value when eaten in moderation E. There are an unusually large number of American tourists in Paris who eat at burger joints 7. Scientists investigating a rare metabolic disorder hypothesized that obesity was a predisposing factor in the development of the disease. A study of twenty patients found that, on average, the patients were close to the normal weight for their height. Before concluding that obesity is not a predisposing factor, the researchers would find the answer to which of the following questions most useful? A. Are the patients above or below normal height? B. Were any of the patients underweight when the disorder was diagnosed? C. Does weight loss reduce the severity of the symptoms? D. Have the patients always been close to the normal weight for their heights? E. How many of the patients had obese parents? 8. In research designed to investigate the possibility of animals developing friendship with other, unrelated, members of their species, a group of 29 chimpanzees were reared together for 15 years. At the end of that time the chimps were presented with two options for obtaining food: press a lever and feed themselves, or press another identical lever and feed themselves, and at the same time deliver food to the chimp next door. (The chimps were able to see each other). The researchers found that the chimps were no more likely to choose the lever that fed a neighbor. The researchers concluded that the chimps had no concept of friendship. However, one critic has suggested that the animals were in an artificial environment from which little can be concluded, and that, at the least, the test ought to have involved the animals being able to touch. What role do the parts in boldface play in the argument above? A. The first is a position that the critic opposes. The second is a position that the critic supports. B. The first is an observation that supports the researchers‟ position. The second is an observation that opposes the researchers‟ position. C. The first is a finding on which the researchers base their conclusion. The second is a suggestion that might cast doubt on that finding. D. The first is an observation that supports the critic‟s conclusion. The second is the critic‟s conclusion. E. The first is part of the evidence that the critic disputes. The second is a suggestion that the researchers do not accept. 9. Questions 9-10 refer to the following: Jay: We have too many people working on each of our computers in the office. The high frequency of breakdowns is due to too many people handling the same hardware. Ada: We have just as many people working in our office, yet we hardly need any repairs to our systems. Our systems must be more robust than yours. Ada‟s argument would be most strengthened by providing data on the A. actual number of people in the two offices B. type of computers that are in both offices C. ratio of computers to users in her office D. number of visits by computer engineers to service the computers in Jay‟s office E. number of computers in Jay‟s office 10. Refer to the extract in the previous question Jay apparently believes that A. he has the best available hardware B. the frequency of breakdowns in his office is above average C. software specifications are not important in his office D. no other office has a similar ratio of computers to users E. he does not need more people working in his office 11. A rare disease, malicitis, is being diagnosed with increasing frequency. The number of cases reported this year is more than double the number reported four years ago. The government should now allocate more funds for treatment and prevention of malicitis. All of the following, if true, would weaken the conclusion except A. funds already available for research in malicitis are currently under-utilized B. a new test employed for the first time this year detects malicitis at a considerably earlier stage in the development of the disease C. the number of cases reported this year represents the same fraction of the population as reported in all of the last five years D. a committee of experts reviewed the funding four years ago E. a private foundation has committed sufficient funds to cover treatment and prevention needs as well as research for the next five years 12. Thousands of people have tonsillectomies every year and all live normal lives after the operation. We can conclude, from this observation, that the tonsils have no function in the body. The argument would be most weakened by which of the following, if it were true? A. People live normal lives after appendectomies but the appendix is known to be part of the digestive system. B. Another part of the body can take over the function of the tonsils if they are removed. C. The tonsils have been shown to have a vital role to play in the physiology of laboratory rabbits and guinea pigs. D. The human tonsil develops as part of the immune system, a system of vital importance in defense against disease. E. Tonsillectomies are performed only when the tonsils become seriously infected. 13. Photography is no longer an art form. Nowadays everyone has access to digital cameras that only need to be pointed at the subject in order to generate a perfect image. The writer of the argument apparently assumes that A. the selection of the subject is not an important artistic factor in photography B. digital cameras will continue to improve in quality C. digital cameras can never go wrong D. photography with all other types of camera is an art form E. art is not perfect 14. The enormous distances between stars are not spaces entirely devoid of matter. The interstellar spaces are filled with ‘dust’: very low density matter. This miniscule amount of matter, spread over almost infinite distances, acts like a curtain obscuring the stars that lie behind. If it were not for this material we would see no dark patches in the sky at night: the sky would be entirely covered with stars. The two parts in boldface play what roles in the argument above? A. The first is a suggestion that the author wishes to dispute. The second is hypothesis that the author wishes to explain. B. The first is the main point the author wishes to make. The second is a hypothetical result of accepting that point. C. The first is a fact that the author thinks is important in explaining a certain phenomenon. The second is a result that the author would expect if that fact were not true. D. The first is a speculation that the author wishes to justify. The second is a consequence that would result if that speculation is not true. E. The first is an established fact that the author wishes to explain. The second is a consequence of accepting this fact. 15. The number of people diagnosed with dengue fever (which is contracted from the bite of an infected mosquito) in North India this year is twice the number diagnosed last year. The authorities have concluded that measures to control the mosquito population have failed in this region. All of the following, if true, would cast doubt on the authorities‟ conclusion except A. more cases are now reported because of increases in administrative efficiency B. a very high proportion of the cases were in people who had recently returned from neighboring countries C. an effective diagnostic test was introduced about nine months ago D. the disease is prevalent only in some industrialized areas which have shown a dramatic increase in population due to migration E. the incidence (number of cases per thousand) of malaria, also contracted from mosquito bites, has increased 16. Questions 16-17 refer to the following: In a recent study of responses to visual images, researchers found that women most frequently gave the rating „most attractive‟ to images of male faces that were more feminine in contour, and rated more masculine faces, on average, „less attractive‟. The researchers concluded that modern women prefer men who are less obviously masculine in their facial features. The conclusion would be most severely weakened if which of the following were true? A. Facial features are not the criterion that most women use to decide whether a man is attractive. B. The visual images were computer generated composites of photographs and not pictures of actual men. C. The rating scale was a ten point scale with most attractive scoring 1-2 and least attractive scoring 8-10. D. Most popular male actors have the features that the study allocated to the more masculine category. E. The faces with the more masculine features were all significantly older than those with the feminine features. 17. Refer to the extract in the previous question Which is the following is an assumption that the researchers apparently made in this study? A. The women who participated in the study were sufficiently representative of modern women in general. B. Male faces are, in general, attractive to women. C. Visual images are important to women. D. It is impossible to predict what features an ideal face would have. E. Women in previous ages would have preferred more masculine men. 18. Red is a color which has powerful effects on human beings as well as animals. A group of psychologists carried out an experiment which confirms the subconscious effects of this color on human behavior. They provided selected sports teams at school and college level with either red or blue shorts and recorded the outcome of the games. The teams wearing red won in a disproportionate number of matches. The psychologists suggested that either the teams wearing red subconsciously felt themselves more powerful, or that the non-red teams were subconsciously intimidated by the red color. Which of the following, if true, would most weaken the psychologists‟ suggestion? A. Each team wore red in some matches and blue in others. B. The color blue has the subconscious effect of making human beings less competitive. C. The effect was only observed if all the team members wore white shirts. D. Red signifies danger in some cultures whereas it signifies happiness in others. E. In a subsequent study, teams with all-red outfits were more likely to report that they thought they would win no matter what color the opponents wore. 19. It is often thought that our own modern age is unique in having a large number of people who live into old age. It has frequently been assumed that plagues, wars, and harsh working conditions killed off most people in previous ages before they could reach old age. However, recent research shows that in 17th century Europe, for example, people over sixty comprised 10 percent of the population. The studies also revealed that although infant mortality remained high until the 20th century in Europe, people who survived to adulthood could expect to live to be old. The portions in boldface play which of the following roles in the argument above? A. The first is a conclusion that the author supports. The second is data that contradicts that conclusion. B. The first is a finding that the author contests. The second is a finding that the author accepts. C. The first is an assumption that the author thinks is invalid. The second is data that validates that assumption. D. The first is a position that the author opposes. The second is a finding that supports the author‟s position. E. The first is a position that the author opposes. The second is an assumption which, if valid, negates the author‟s view. 20. A marriage counselor noted that couples who have occasional violent arguments are less likely to divorce within the next six months than those who have frequent but less violent arguments. He concluded that frequent arguing is a major factor in the causation of severe marital disharmony. The counselor‟s conclusion is most weakened by which of the following observations? A. Couples who have already come to the point of divorce argue continuously over small matters. B. People who have recently divorced are more likely to argue violently when they meet. C. Many people in happy marriages have occasional violent arguments. D. Recently divorced people rarely cite frequent arguments as a cause of marital disharmony E. A significant fraction of couples close to divorce do not talk to each other. 21. The Dean claimed that, as a result of continued cutbacks in the budget for pure science research, fewer students are choosing a career in physics, and therefore the number of postgraduate students studying physics is likely to decline. Which of the following, if true, casts most doubt on the Dean‟s conclusion? A. The number of students majoring in physics at the undergraduate level has been increasing steadily over the years, a trend that is expected to continue. B. The number of students studying chemistry declined even before cutbacks in research funding were noted. C. Most postgraduate students of physics move to careers in computer science and engineering. D. The Dean‟s own university has recently increased the number of staff members teaching physics. E. The budget cutbacks are less severe for the pure sciences than for applied sciences. 22. A nature conservancy expert found little support for his campaign to protect toads. He suggested that, even thought the campaign highlighted the vital role the toads played in the ecology of the region, people were unenthusiastic about saving toads as these animals are perceived as unpleasant creatures, and people seldom feel passionate about animals with which they have no positive feelings. The expert‟s opinion would be most strengthened by which of the following observations? A. Ecological conservation is an increasingly important concern in the region. B. A recent campaign to save bats achieved a measure of success only after a cartoon bat was adopted as the mascot of the local football team. C. Snakes and lizards also need protection in this region as a result of human activity. D. The campaign to protect toads has been in existence for over five years and yet the toad population continues to decline. E. The children in the local schools were found to have a greater aversion to toads than to snakes. 23. Many people report that exposure to certain foods such as cheese, red wine, and chocolate, are associated with the onset of migraine headaches. Other people report that exposure to certain smells (especially strong perfumes) seems to trigger a migraine headache, and some note that exposure to bright and flickering lights can be followed by a migraine. It would seem that a person with a tendency to get migraines should try to find which of these situations is associated with the onset of the headache and then avoid this stimulus. All of the following, if true, would indicate potential problems with the recommendation above except A. the time delay between the trigger and the onset of the headache can make it exceptionally difficult to identify the trigger B. the presence of a known trigger doesn‟t always cause a migraine C. in many cases an internal hormonal change triggers a migraine D. in a high proportion of cases the patients report multiple triggers for their headaches E. most of the known triggers are common and almost unavoidable features of modern life 24. It is strange that in Sentacity there are so many corner shops selling food items. After all there are many supermarkets in the city which sell food at cheaper prices, and many of these supermarkets are open 24-hours. Which of the following, if true, would be of least help in explaining the paradoxical observation? A. The corner shops are selling specialist food items not available in the supermarkets. B. The supermarkets are mostly located on the outskirts of the city and require residents to use cars or public transport to reach them. C. The main business of the local shops is newspaper distribution and food items represent a small part of their turnover. D. The corner shops are mainly family-owned businesses and have been there for much longer than the supermarkets and are perceived as an important feature of the community. E. The corner shops are willing to make home deliveries. Exercise 2: 1. Fact 1: Television advertising is becoming less effective: the promotion of brand names promoted on television that viewers of the advertising can recall is slowly decreasing. Fact 2: Television viewers recall commercials aired first or last in a cluster of consecutive commercials far better than they recall commercials aired somewhere in the middle. Fact 2 would be most likely to contribute to an explanation of fact 1 if which of the following were also true? a. The total time allotted to the average cluster of consecutive television commercials is decreasing. b. The average number of clusters of consecutive commercials per hour of television is increasing. c. The average number of hours per day that people spend watching television is decreasing. d. The average number of television commercials in a cluster of consecutive commercials is increasing. e. The average television viewer currently recalls fewer than half the brand names promoted in commercials he or she saw. 2. The average normal infant born in the United States weighs between twelve and fourteen pounds at the age of three months. Therefore, if a three-month-old child weighs only ten pounds, its weight gain has been below the United States average. Which of the following indicates a flaw in the reasoning above? a. The phrase "below average" does not necessarily mean insufficient. b. Average weight gain is not the same as average weight. c. Some three-month old children weigh as much as seventeen pounds. d. It is possible for a normal child to weigh ten pounds at birth. e. Weight is only one measure of normal infant development. 3. Which of the following best completes the passage below? People buy prestige when they buy a premium product. They want to be associated with something special. Mass-marketing techniques and price-reduction strategies should not be used because ___________ . a. continued sales depend directly on the maintenance of an aura of exclusivity b. expansion of the market niche to include a broader spectrum of consumers will increase profits c. manufacturing a premium brand is not necessarily more costly than manufacturing a standard brand of the same product d. affluent purchasers currently represent a shrinking portion of the population of all purchasers e. purchasers of premium products are concerned with the quality as well as with the price of the products 4. Which of the following best completes the passage below? In a survey of job applicants, two-fifths admitted to being at least a little dishonest. However, the survey may underestimate the proportion of job applicants who are dishonest, because _____. a. some generally honest people taking the survey might have claimed on the survey to be dishonest b. some people who claimed on the survey to be dishonest may have been answering honestly c. some people who claimed on the survey to be at least a little dishonest may be very dishonest d. some dishonest people taking the survey might have claimed on the survey to be honest e. some people who are not job applicants are probably at least a little dishonest 5. A program instituted in a particular state allows parents to prepay their children's future college tuition at current rates. The program then pays the tuition annually for the child at any of the state's public colleges in which the child enrolls. Parents should participate in the program as a means of decreasing the cost of their children's college education. Which of the following, if true, is the most appropriate reason for parents not to participate in the program? a. The prepayment plan would not cover the cost of room and board at any of the state's public colleges. b. The amount of money accumulated by putting the prepayment funds in an interest-bearing account today will be greater than the total cost of tuition for any of the public colleges when the child enrolls. c. Some of the state's public colleges are contemplating large increases in tuition next year. d. The annual cost of tuition at the state's public colleges is expected to increase at a faster rate than the annual increase in the cost of living. e. The parents are unsure about which public college in the state the child will attend. 6. Most consumers do not get much use out of the sports equipment they purchase. For example, seventeen percent of adults in the United States own jogging shoes, but only forty-five percent of the owners jog more than once a year, and only seventeen percent jog more than once a week. Which of the following, if true casts most doubt on the claim that most consumers get little use out of the sports equipment they purchase? a. Many consumers purchase jogging shoes for use in activities other than jogging. b. Joggers who jog more than once a week are often active participants in other sports as well. c. Consumers who take up jogging often purchase an athletic shoe that can be used in other sports. d. Joggers are most susceptible to sports injuries during the first six months in which they jog. e. Joggers often exaggerate the frequency with which they jog in surveys designed to elicit such information. 7. It is true that it is against international law to sell plutonium to countries that do not yet have nuclear weapons. But if United States companies do not do so, companies in other countries will. Which of the following is most like the argument above in its logical structure? a. It is true that it is illegal for a government official to participate in a transaction in which there is an apparent conflict of interest. But if the facts are examined carefully, it will clearly be seen that there was no actual conflict of interest in the defendant's case. b. It is true that it is against the police department's policy to negotiate with kidnappers. But if the police want to prevent loss of life, they must negotiate in some cases. c. It is true that it is against the law to burglarize people's homes. But someone else certainly would have burglarized the house if the defendant had not done so first. d. It is true that company policy forbids supervisors to fire employees without two written warnings. But there have been many supervisors who have disobeyed this policy. e. It is true that it is illegal to refuse to register for military service. But there is a long tradition in the United States of conscientious objection to serving in the armed forces. 8. Neither a rising standard of living nor balanced trade, by itself, establishes a country's ability to compete in the international marketplace. Both are required simultaneously since standards of living can rise because of growing trade deficits and trade can be balanced by means of a decline in a country's standard of living. If the facts stated in the passage above are true, a proper test of a country's ability to be competitive is its ability to a. keep its standard of living constant while trade deficits rise. b. balance its trade while its standard of living rises. c. balance its trade while its standard of living falls. d. increase trade deficits while its standard of living rises. e. decrease trade deficits while its standard of living falls. 9. The program to control the entry of illegal drugs into the country was failure in 1987. If the program had been successful, the wholesale price of most illegal drugs would not have dropped substantially in 1987. The argument in the passage depends on which of the following assumptions? a. The price paid for most illegal drugs by the average consumer did not drop substantially in 1987. b. The supply of illegal drugs dropped substantially in 1987. c. The wholesale price of a few illegal drugs increased substantially in 1987. d. Domestic production of illegal drugs increased at a higher rate than did the entry of such drugs into the country. e. A drop in demand for most illegal drugs in 1987 was not the sole cause of the drop in their wholesale price. 10. The program to control the entry of illegal drugs into the country was failure in 1987. If the program had been successful, the wholesale price of most illegal drugs would not have dropped substantially in 1987. The argument in the passage would be most seriously weakened if it were true that a. in 1987 smugglers of illegal drugs, as a group, had significantly more funds at their disposal than did the country's customs agents. b.domestic production of illegal drugs increased substantially in 1987. c. in 1987 illegal drugs entered the country by a different set of routes than they did in 1986. d. the author's statements were made in order to embarrass the officials responsible for the drug-control program. e. the country's citizens spent substantially more money on illegal drugs in 1987 than they did in 1986. 11. Hardin argued that grazing land held in common (that is, open to any user) would always be used less carefully than private grazing land. Each rancher would be tempted to overuse common land because the benefits would accrue to the individual, while the costs of reduced land quality that results from overuse would be spread among all users. But a study comparing 217 million acres of common grazing land with 433 million acres of private grazing land showed that the common land was in better condition. The answer to which of the following questions would be most useful in evaluating the significance, in relation to Hardin's claim, of the study described above? a. Was the private land that was studied of comparable quality to the common land before either was used for grazing? b. Did any of the ranchers whose land was studied use both common and private land? c. Were the users of the common land that was studied at least as prosperous as the users of the private land? d. Did the ranchers whose land was studied tend to prefer using common land before either was used for grazing? e. Were there any owners of herds who used only common land, and no private land for grazing. 12. Hardin argued that grazing land held in common (that is, open to any user) would always be used less carefully than private grazing land. Each rancher would be tempted to overuse common land because the benefits would accrue to the individual, while the costs of reduced land quality that results from overuse would be spread among all users. But a study comparing 217 million acres of common grazing land with 433 million acres of private grazing land showed that the common land was in better condition. Which of the following, if true and known by the ranchers, would best help explain the results of the study? a. With private grazing land, both the costs and the benefits of overuse fall to the individual user. b. An individual who overuses common grazing land might be able to achieve higher returns than other users can, with the result that he or she would obtain a competitive advantage. c. The cost in reduced land quality that is attributable to any individual user is less easily measured with common land than it is with private land. d. If one user of common land overuses it even sightly, the other users are likely to do so even more, with the consequence that the costs to each user outweigh the benefits. e. there are more acres of grazing held privately than there are held in common. 13. In Los Angeles, a political candidate who buys saturation radio advertising will get maximum name recognition. The statement above logically conveys which of the following? A. Radio advertising is the most important factor in political campaigns in Los Angeles. B. Maximum name recognition in Los Angeles will help a candidate to win a higher percentage of votes cast in the city. C. Saturation radio advertising reaches every demographically distinct sector of the voting population of Los Angeles. D. For maximum name recognition a candidate need not spend on media channels other than radio advertising. E. A candidate's record of achievement in the Los Angeles area will do little to affect his or her name recognition there. 14. The rate of violent crime in this state is up 30 percent from last year. The fault lies entirely in our court system: Recently our judges' sentences have been so lenient that criminals can now do almost anything without fear of a long prison term. The argument above would be weakened if it were true that a. 85 percent of the other states in the nation have lower crime rates than does this state. b. white collar crime in this state has also increased by over 25 percent in the last year. c. 35 percent of the police in this state have been laid off in the last year due to budget cuts. d. polls show that 65 percent of the population in this state oppose capital punishment. e. the state has hired 25 new judges in the last year to compensate for deaths and retirements. 15. The increase in the number of newspaper articles exposed as fabrications serves to bolster the contention that publishers are more interested in boosting circulation than in printing the truth. Even minor publications have staffs to check such obvious fraud. The argument above assumes that a. newspaper stories exposed as fabrications are a recent phenomenon. b. everything a newspaper prints must be factually verifiable. c. fact checking is more comprehensive for minor publications than for major ones. d. only recently have newspapers admitted to publishing intentionally fraudulent stories. e. the publishers of newspapers are the people who decide what to print in their newspapers. 16. Bill earns more commission than does Sandra. But since Andrew earns more commission than does Lisa, it follows that Bill earns more commission than does Lisa. Any of the following, if introduced into the argument as an additional premise, makes the argument above logically correct EXCEPT: a. Andrew earns more commission than Bill b. Sandra earns more commission than Lisa c. Sandra earns more commission than Andrew d. Sandra and Andrew earn the same amount of commission e. Bill and Andrew earn the same amount of commission 17. During the SARS days, about 23,500 doctors who had treated SARS sufferers died and about 23,670 doctors who had not engaged in treatment for SARS sufferers died. On the basis of those figures, it can be concluded that it was not much more dangerous to participate in SARS treatment during the SARS day than it was not to participate in SARS treatment. Which of the following would reveal most clearly the absurdity of the conclusion drawn above? a. Counting deaths among doctors who had participated in SARS treatment in addition to deaths among doctors who had not participated in SARS treatment b. Expressing the difference between the numbers of deaths among doctors who had treated SARS sufferers and doctors who had not treated SARS suffers as a percentage of the total number of deaths c. Separating deaths caused by accidents during the treatment to SARS suffers from deaths caused by infect of SARS suffers. d. Comparing death rates per thousand members of each group rather than comparing total numbers of deaths e. Comparing deaths caused by accidents in the United States to deaths caused by infect in treating SARS suffers. 18. In 2003 an airline in United State lost more than half, on average, of the foreign passengers they had previously served each year. Researchers have alleged that this extreme drop resulted from a rise in price of tickets for international lines from $60 to $90 per 1,000 miles. Which of the following, if feasible, offers the best prospects for alleviating the problem of the drop in passengers as the researchers assessed it? a. Cooperating with other airlines to provide more international lines. b. Allowing foreign passengers to pay the same as the previous international line c. Reemphasizing the goals and mission of the airline as serving both domestic passengers and foreign passengers d. Increasing the financial resources of the airline by raising the ticket price for domestic passengers e. Offering superior VIP service for foreign passengers. Answers: Exercise 1: 1. B 2. D 3. C 4. D 5. A 6. E 7. D 8. C 9. C 10. B 11. D 12. B 13. A 14. C 15. E 16. E 17. A 18. B 19. D 20. A 21. C 22. B 23. B 24. E Exercise 2: 1. d 2. b 3. a 4. d 5. b 6. a 7. c 8. b 9. e 10. b 11. a 12. d 13. d 14. c 15. e 16. a 17. d 18. b Cubes Examples Directions: A cube is coloured red on all faces. It is cut into 64 smaller cubes of equal size. Now, answer the following questions based on this statement. Example 1. How many cubes have no face coloured? (a) 24 (b) 8 (c) 0 (d) 16 Example 2. How many cubes are there which have only one face coloured? (a) 4 (b) 16 (c) 24 (d) 8 Example 3. How many cubes have two red opposite face? (a) 8 (b) 16 (c) 24 (d) 0 Example 4. How many cubes have three faces coloured (a) 16 (b) 24 (c) 4 (d) 8 Solution. The given figure shows the cube coloured real on all faces, and divide into 64 smaller cubes. Here n = Side of big cube/Side of small cube = 4/1 = 4 1. Number of smaller cubes with no surface painted = (n – 2) 3 = (4 – 2) 3 = 2 3 = 8 2. Number of smaller cubes with one surface painted (n – 2) 2 × 6 = (4 – 2) 2 × 6 = 2 2 × 6 = 24 3. Number of smaller cubes with two surface painted = (n – 2) × 12 = (4 – 2) × 12 2 × 12 = 24 4. Number of smaller cubes with three surfaces painted = 8 Exercise 20 Directions: A wooden cube is painted blue on all the four adjoining sides and green on two opposite sides, i.e., top and bottom. It is then cut at equal distances at right angles four times vertically (top to bottom) and two times horizontally (along the sides) as shown in the figure, where the dotted lines represents the cuts made. Study diagram and answer the following questions: 1. How many cubes will have one face painted only in Blue? (a) 2 (b) 1 (c) 4 (d) 3 2. How many cubes will have one face painted only in Green? (a) 1 (b) 2 (c) 3 (d) 4 3. How many cubes arte formed in all ? (a) 24 (b) 27 (c) 32 (d) 16 4. How many cubes will have at least three sides painted. (a) 6 (b) 2 (c) 3 (d) 8 5. How many cubes will have no face painted at all ? (a) 5 (b) 4 (c) 3 (d) 2 Directions: A cube is coloured red on two opposite faces. Blue on two adjacent faces and yellow on the two remaining faces. It is then cut into two halves along the plane parallel to the red faces. One piece is then cut into four equal cubes and the other one into 32 equal cubes. 6. How man cubes do not have any coloured face? (a) 2 (b) 4 (c) 8 (d) 0 7. How many cubes do not have any red face? (a) 16 (b) 8 (c) 24 (d) 20 8. How many cubes have at least two coloured faces? (a) 20 (b) 24 (c) 28 (d) 32 9. How many cubes have each a yellow face with other faces blank? (a) 16 (b) 14 (c) 17 (d) 4 10. How many cubes have at least one blue face? (a) 14 (b) 16 (c) 20 (d) 4 Directions: A cube is painted red on two adjacent faces and black on the faces opposite to the red faces and green on the remaining faces is cut into sixty-four smaller cubes of equal size. 11. How many cubes are there which have no face painted? (a) 0 (b) 4 (c) 8 (d) 16 12. How many cubes have only one face painted? (a) 8 (b) 16 (c) 24 (d) 32 13. How many cubes have less then three faces painted? (a) 8 (b) 24 (c) 28 (d) 48 14. How many cubes are there with three faces painted ? (a) 8 (b) 16 (c) 4 (d) 24 15. How many cubes have one face green and one of the adjacent faces black or red ? (a) 8 (b) 16 (c) 24 (d) 28 Direction: A cube is painted red on two adjacent faces and on one opposite face, yellow on two opposite faces and green on the remaining face. It is then cut into 64 equal cubes. 16. How many cubes have only one red coloured face? (a) 8 (b) 4 (c) 16 (d) 12 Directions: A solid cube has been painted yellow, blue and black on pairs of opposite face. The cube is the cut into 36 smaller cubes such that 32 cubes are of the same size while 4 others are of bigger size. Also no face of any of the bigger cubes is painted blue. 17. How many cubes have at least one face painted blue. (a) 0 (b) 8 (c) 16 (d) 32 18. How many cubes have only one face painted. (a) 12 (b) 8 (c) 4 (d) 0 19. How many cubes have at least two faces painted. (a) 8 (b) 16 (c) 20 (d) 24 20. How many cubes have two or more faces painted. (a) 36 (b) 34 (c) 28 (d) 24 21. How many cubes only three faces painted? (a) 8 (b) 4 (c) 2 (d) 0 22. How many cubes do not have any of their faces painted yellow? (a) 0 (b) 8 (c) 16 (d) 20 23. How many cubes have at least one of their faces painted black ? (a) 0 (b) 8 (c) 16 (d) 20 24. How many cubes have at least one of their faces painted yellow or blue? (a) 36 (b) 32 (c) 16 (d) 0 25. How many cubes have no face painted? (a) 0 (b) 8 (c) 12 (d) 16 26. How many cubes have two faces painted yellow and black respectively? (a) 0 (b) 8 (c) 12 (d) 16 Directions: A cube is painted blue on all faces is cut into 125 cubes of equal size. Now, answer the following questions 27. How many cubes are not painted on any face? (a) 8 (b) 16 (c) 18 (d) 27 28. How many cubes are painted on one face only? (a) 8 (b) 16 (c) 36 (d) 54 Directions :A cuboid of dimensions (4 cm x 3 cm x 3 cm). The block is painted yellow on the pair of opposite surfaces of dimensions (4 cm x 3 cm). Remaining two opposite surfaces of dimensions (4 cm x 3 cm) are painted red. And two surfaces of dimensions (3 cm x 3 cm) are painted with green colours. Now the block is divided among cubes of dimensions (1 cm x 1 cm 1 cm)? 29. How many smaller cubes will have one surface painted? (a) 16 (b) 12 (c) 14 (d) 18 30. How many cubes will have no surfaces painted? (a) 1 (b) 4 (c) 2 (d) 8 31. In how many cubes all the three colours appear? (a) 24 (b) 20 (c) 8 (d) 16 32. How many cubes will have only two surfaces painted ? (a) 12 (b) 16 (c) 20 (d) 32 33. How many cubes will have at least one surface painted? (a) 32 (b) 18 (c) 24 (d) None of these Directions: A solid cube each side 8 cm has been painted red, blue and black on pairs of opposite faces. It is then cut into cubical block of each side 2 cm. 34. How many cubes have no face painted? (a) 0 (b) 4 (c) 8 (d) 12 35. How many cubes have only one face painted? (a) 8 (b) 16 (c) 24 (d) 28 36. How many cubes have only two faces? (a) 8 (b) 16 (c) 20 (d) 24 37. How many cubes have three faces painted? (a) 0 (b) 4 (c) 6 (d) 8 38. How many cubes have three faces painted with different colours? (a) 0 (b) 4 (c) 8 (d) 12 39. How many cubes have two faces painted red and black and all other faces unpainted? (a) 4 (b) 8 (c) 16 (d) 32 40. How many cubes have only one face painted red and all other faces unpainted ? (a) 4 (b) 8 (c) 12 (d) 16 41. How many cubes have two faces painted black? (a) 2 (b) 4 (c) 8 (d) None 42. How many cubes have one face painted blue and one face painted red? (the other faces may be painted or unpainted): (a) 16 (b) 12 (c) 8 (d) 0 43. How many cubes are there in all? (a) 64 (b) 56 (c) 40 (d) 32 Directions: The six faces of a cube are coloured black brown, green, red ,white and blue, such that: (i) Red is opposite black (ii) Green is between red and black (iii) Blue is adjacent to White (iv) Brown is adjacent to blue (v) Red is at the bottom. Answer the following questions based on this information. 44. Which colour is opposite brown? (a) White (b) Red (c) Green (d) Blue 45. The four adjacent colours are (a) Black, Blue, Brown, Red (b) Black, Blue, Brown, White (c) Black, Blue, Red, White (d) Black, Brown, Red, White 46. Which of the following can be deduced from (i) and (iv) (a) Black in on the top (b) Blue is on the top (c) Brown is on the top (d) Brown is opposite Black Logical Deductions Types of statements: The statements can be divided into four categories depending on their sense. They are 1. General 2. Particular 3. Negative and 4. Particular Negative A general statement starts with a word “all” or “every” or “each” Eg: All x are y. Every x is y. A particular statement focuses on a particular group or sector. It normally starts with “some”, “many”, “most” or a name. Eg: Some x are y. Many x are y. Sachin is good. A negative statement contains a negative word like “no” or “not”. Eg: No x is y. All y are not x. A particular negative statement combine both the features of particular and negative statement. Eg: Some x are not y. Many y are not z. Sachin is not good. Distribution: When “All x are y” is given we can say that all the points of set x belong to y but we cant define such a property common to all the points of y. In other words we can say a property common to all points of x but not y. Then it is said that “x” is distributed but “y” is not. In “All x are y”, x becomes the subject and y becomes the object. So, a general statement distributes only the subject but not the object. Similarly, a particular statement distributes neither subject nor the object. A negative statement distributes both the subject and the object. A particular statement distributes the object but not the subject. In short, the distribution can be said as follows: General statement: Subject – Yes Object – No Particular Statement: Subject – No Object – No Negative Statement: Subject – Yes Object – Yes Particular Negative: Subject – No Object – Yes Deriving a deduction: When two statements are given to you, your duty is to derive a deduction that logically follows both the statements logically. For this we will make use of the distribution. The process of deriving a conclusion is as follows: Step 1: Identify the common term for both the statements. If no common term is present the no deduction can be derived. Step 2: Apply the distribution properties to subjects and objects depending on the type of the statement. Rule: If and only if the common term is having the distribution only once, then the deduction can be derived. Else there can be no deduction. Eg: All x are y. All x are z. Soln: Common term : x In first statement and the second statement, x is distributed (since x is subject in both). So the common term has 2 distributions => no deduction follows. Step 3: When you decide that there is a deduction possible then read out all the words present in the two statements excluding the common term and repeated words, from left to right. Eg: All x are y. All y are z. Soln: Common term: y. It is distributed only once (in second statement). So a deduction can follow. It is All x are z. (Excluding y and repeated words). Rule: Particularity and negation are called special properties and if any statement contains a special property the same should be followed by the conclusion also. Eg: Some x are y. All y are z. Soln: Common term: y. It is distributed only once (in second statement). So a deduction follows. It is Some x are z. (Here some is a special property and so conclusion also follows the same. Common term is excluded.) Rule: For two particular or negative statements there can be no conclusion. Examples: 1. All x are y. All z are y. Soln: No conclusion follows. (since common term y is not distributed at all) 2. All x are y. Some y are z. Soln: No conclusion since common term y is not distributed at all. 3. All x are y. No y is z. Soln: No x is z (or) No z is x. (Since No is a special property) 4. Some x are y. No y is z. Soln: Some x are not z. (Since some and not are special properties and so should be present in conclusion). Exercise: 1. All books are hooks. All hooks are crooks. a) All hooks are books. b) All crooks are hooks. c) All crooks are books. d) All books are crooks. 2. Some crooks are hooks. No hook is a book. a) Some hooks are not books. b) Some hooks are crooks. c) Some crooks are books. d) Some crooks are not books. 3. Some goods are expensive. Some expensive things are qualitative. a) Some goods are qualitative. b) Some goods are not qualitative. c) Some qualitative are goods. d) No conclusion 4. All posters are good looking. Some posters are expensive. a) Some good looking are not expensive. b) Some good looking are expensive. c) Some expensive are not good looking. d) Some expensive are good looking. 5. All expensive are posters. Some good looking are posters. a) Some posters are good looking. b) Some good looking are expensive. c) Some expensive are good looking. d) None of these 6. All boxes are dolls. No baskets are boxes. a) Some dolls are baskets. b) Some dolls are not baskets. c) Some baskets are not dolls. d) None of these 7. All dolls are boxes. No baskets are boxes. a) Some dolls are not baskets. b) Some dolls are baskets. c) No dolls are baskets. d) None of these 8. No tables are watches. Some watches are lamps. a) Some lamps are tables. b) No lamp is a table. c) Some lamps are not tables. d) None of these 9. All my girl friends are beautiful. Sudha is very beautiful. a) Sudha is my friend. b) Sudha is not my friend. c) (a) or (b) d) None of these 10. No cow is a cat. All cats are rats. a) Some rats are cats. b) Some rats are not cats. c) Some rats are not cows. d) None of these 11. All women are men. All men are crazy. a) All men are women. b) No men is crazy. c) All women are crazy. d) All crazy are women. 12. Some shirts are benches. No bench is a table. a) Some shirts are tables. b) Some shirts are not tables. c) No table is a shirt. d) None of these 13. All roads are poles. No pole is a house. a) Some roads are houses. b) Some roads are not houses. c) No road is house. d) None of these 14. No man is monkey. John is a man. a) John is not a monkey. b) John may or may not be a monkey. c) (a) or (b) d) None of these 15. All businessmen except Ramji are dishonest. All dishonest people smoke. a) All businessmen except Ramji smoke. b) Ramji does not smoke. c) (a) or (b) d) None of these 16. Few takers are givers. No givers are almighty. a) Some givers are not takers. b) Some takers are not almighty. c) Some almighty are takers. d) None of these 17. Some crows are jackals. No fox is a crow. a) Some jackals are not foxes. b) Some jackals are foxes. c) No jackal is a fox. d) No fox is a jackal. 18. Only cats are animals. No historian is an animal. a) Some cats are historians. b) Some historians are cats. c) Some cats are not historians. d) Some historians are not cats. 19. Some girls are cute. Some Americans are cute. a) Some Americans are not cute. b) Some girls are Americans. c) Some girls are not Americans. d) None of these 20. No kindhearted is bandit. All bandits are blackmailers. a) Some blackmailers are kindhearted. b) Some kindhearted are blackmailers. c) Some kindhearted are not blackmailers. d) Some blackmailers are not kindhearted. 21. No fruit is a flower. No flower is a stem. a) No fruit is a stem. b) Some fruits are not stems. c) No stem is a fruit. d) None of these 22. Some bowls are dishes. No dish is a glass. a) Some bowls are not glasses. b) Some glasses are not bowls. c) No bowl is a glass. d) No glass is a bowl. 23. Some bowls are plates. All plates are glasses. a) Some bowls are not glasses. b) Some glasses are bowls. c) Some bowls are glasses. d) None of these 24. Some huts are not buildings. No building is a hotel. a) Some huts are not hotels. b) No hotel is a hut. c) Some hotels are not huts. d) None of these 25. All cups are pens. Some pens are tables. a) Some cups are tables. b) Some tables are cups. c) Some cups are not tables. d) None of these 26. All colleges are schools. No theatre is a school. a) No school is a theatre. b) Some colleges are not schools. c) Some colleges are not theatres. d) No college is a theatre. 27. Some computers are CPUs. All CPUs are mouses. a) Some computers are not mouses. b) Some mouses are computers. c) Some computers are mouses. d) None of these 28. Some horses are dogs. No rabbit is a dog. a) Some horses are not rabbits. b) Some horses are rabbits. c) No horse is a rabbit. d) None of these 29. Some pearls are beads. All rings are beads. a) Some pearls are rings. b) All rings are pearls. c) Some rings are pearls. d) None of these 30. Some biscuits are chocolates. No brinks are biscuits. a) No biscuits are fruits. b) Some chocolates are drinks. c) Some drinks are not chocolates. d) None of these Data Interpretation - It deals with careful reading, understanding, organizing and interpreting the data provided so as to derive meaningful conclusions. - Mostly used tools for interpretation of a data are o Ratio o Percentage o Rate o Average Types of Data Interpretation: The numerical data pertaining to any event can be presented by any one or more of the following methods. 1. Tables 2. Line Graphs 3. Bar Graphs or Bar Charts 4. Pie Charts or Circle Graphs 1. Tables: It is the systematic presentation of data in tabular form to understand the given information and to make clear the problem in a certain field of study. It has six elements namely: o Title: It is the heading of the table. o Stule: It is the section of the table containing row headings o Column Captions: It is the heading of each column o Body: It consists the numerical figures o Footnotes: It is for further explanation of the table o Source: It is the authority of the data Eg: Study the following table and answer the questions given below it. Annual Income of Five Schools Figures in ‟00 rupees Sources of Income School A School B School C School D School E Tuition Fee 120 60 210 90 120 Term Fee 24 12 45 24 30 Donations 54 21 60 51 60 Funds 60 54 120 42 55 Miscellaneous 12 3 15 3 15 Total 270 150 450 210 280 1. The income by way of donation to school D is what per-cent of its miscellaneous? Sol: Required percentage = % 27 300 5100 = 2. Line Graph: A line graph indicates the variation of a quantity w.r.t two parameters calibrated on X and Y-axis respectively. Note: 1. Any part of the line graph parallel to X-axis represents no change in the value of Y parameter w.r.t the value of X parameter. 2. The steepest or maximum part of the line graph indicates maximum percentage change of the value during the two consecutive period in which the related part lies. 3. If the steepest part is a rise slope, then it is the highest percentage growth. 4. If the steepest part is a decline slope, it will represent a maximum percentage fall of the value calibrated in the other axis. 3. Bar Graph: Bar graphs are diagrammatic representation of a discrete data. Types of Bar Graphs: o Simple Bar Graphs: A simple bar graph relates to only one variable. The values of the variables may relate to different years or different terms. o Sub-divided Bar Graph: It is used to represent various parts of sub-classes of total magnitude of the given variable. o Multiple Bar Graphs: In this type, two or more bars are constructed adjoining each other, to represent either different components of a total or to show multiple variables. 4. Pie Chart: In this method of representation, the total quantity is distributed over a total angle of o 360 which is one complete circle or pie. Note: Here, the data can be plotted w.r.t only one parameter. Exercise Directions (Questions 1 to 5): In the graph given below, the sales in Rs. Thousand are shown. Answer the questions based on it. 1. By how much the amount of sales in 1991 was less than those in 1993? a) Rs.100 b) Rs.1 lakh c) Rs. One thousand d) None of these 2. What were the approximate average sales (in thousands) for period 1990 to 1995? a) 300 b) 400 c) 450 d) None of these 3. The sales in 1991 are what percent of those in 1992? a) 80 b) 70 c) 15 d) 45 S a l e s i n t h o u s a n d s 4. In which year the sales showed the least percentage increase to those in preceding year? a) 1990 b) 1992 c) 1993 d) 1994 5. The sales in 1994 are how many times to those in 1992? a) 1.4 b) 1.1 c) 0.60 d) 0.75 Directions (Questions 6 to 10): Study the table carefully and answer the questions given below it. Factories 1990 1991 1992 1993 1994 A 15 18 25 15 18 B 12 23 40 20 15 C 20 20 50 25 20 D 25 18 38 14 18 E 30 32 32 30 30 6. In which year, the production of cars of all factories was the closest to the average no. of cars produced during 1990-1994? a) 1990 b) 1991 c) 1994 d) None of these 7. Which factory showed a decrease of 20% in the production of cars in 1994 as compared to 1993? a) A & C b) B c) C d) D & E 8. In which of the given years was there maximum production of cars? a) 1994 b) 1993 c) 1990 d) None of these 9. What is the ratio of production of cars of factory A to that of factory E in 1994? a) 5 : 3 b) 3 : 5 c) 2 : 7 d) None of these 10. In which year was the total production of cars of factories about 30% of the total production of cars during 1990-1994? a) 1991 b) 1993 c) 1994 d) 1992 Production of Cars in different factories during the period 1990-1994 Directions (Questions 11 to 15): India‟s total trade with foreign countries for a year is given in the pie charts as shown below. Analyze the charts carefully and answer the questions based on them. 11. India‟s exports to which of the following countries are more than the imports from that country? a) U.S.A. b) U.S.S.R. c) JAPAN d) Both U.S.A. & U.S.S.R. 12. The ratio of the angle subtended by the arcs corresponding to U.S.A. for the exports to imports is nearly? a) 165 9 113 15 x x b) 113 9 165 15 x x c) 1.67 d) 1.33 13. The ratio of the total imports from France and U.K. to the total exports to these countries is nearly? a) 1.25 b) 1.33 c) 1.22 d) 1.46 14. Which of the following statement is not true? a) The exports to Japan are less than the imports from Japan. b) The imports from U.K. are more than the exports to U.K. by 6% of Rs.51,959 million. c) The total exports of U.S.A., U.S.S.R., Japan, U.K., West Germany and France are more than the total imports from these countries. d) Two of the above statements are true. 15. If the area of the sector corresponding to U.S.S.R. in exports pie chart is A, the area of the sector corresponding to Japan in the imports pie chart is? (the radii of both the circles being same) a) 2 A b) 8 3A c) 8 5A d) 8 7A Directions (Questions 16 to 20): Study the following table carefully & answer the questions given below. Sugar cane production in million tons by six major states during 1986 to 1990. Year/States P Q R S T X TOTAL 1986 140 65 48 38 39 22 352 1987 132 63 62 56 40 23 376 1988 150 55 72 49 36 27 389 1989 168 60 45 65 43 25 406 1990 170 45 70 62 42 23 412 16. In the year 1990, how many of the given states have a share of 15% or more in the total sugarcane production? a) 3 b) 4 c) 5 d) All 17. Which of the following states shows constant fall in sugarcane production every year? a) P b) Q c) R d) None 18. What was the approximate % increase in sugarcane production in S from 1987 to 1990? a) 5 b) 7 c) 20 d) 11 19. In which year does P has a share about 35% in the total sugarcane production? a)1986 b) 1987 c) 1988 d) 1989 20. In which year during the given period was the % of Q‟s share the highest in the total production? a) 1986 b) 1987 c)1988 d) 1989 Directions (Questions 21 to 25): The questions given below are based on the following table. Railway Time Table Geetanjali Express City Arrival Time (hrs) Departure Time (hrs) Cumulative Mileage BOMBAY --- 0900 0 IGATPURI 1100 1102 80 NASIK 1450 1455 281 BHUSAWAL 1710 1712 391 AKOLA 2240 2245 730 NAGPUR 0005 0015 800 DURG 0100 0102 845 JAMSHEDPUR 0415 0428 995 CALCUTTA 0625 --- 1100 21. The largest run for the train between two successive halts is? a) Jamshedpur-Calcutta b) Bombay-Calcutta c) Bhusawal-Akola d) Akola-Nagpur 22. The average speed the train maintained between two successive stations was the highest between? a) Bhusawal-Akola b) Jamshedpur-Calcutta c) Nagpur-Durg d) Bombay-Igatpuri 23. The average speed that the train maintained between Bombay and Calcutta was nearly equal to? a) 42 miles/hr b) 52 miles/hr c) 61 miles/hr d) 74 miles/hr 24. If we consider the journey that begins at Bombay and ends at Calcutta, the train has the longest halt at? a) Bombay b) Calcutta c) Jamshedpur d) Nagpur 25. The train begins its journey from Calcutta to Bombay eight hours after it has arrived Calcutta. If the train left Bombay on Monday, on what day will it have returned to Bombay? (Assume that on the return journey the train maintains the same average speed as on onward journey) a) Monday b) Tuesday c) Wednesday d) None of these Directions (Questions 26 to 30): Study the following graph and answer the questions given below it. 26. In which of the following year was it likely that the quantity of rubber imported to bridge the gap between demand and supply was maximum? a) 1991 b) 1993 c) 1995 d) None 27. In 1991, the production of rubber was what percent of the requirement? a) 150 b) 67 c) 45 d) 300 28. During which year was the percentage drop in the requirement of rubber over the previous year, the maximum? a) 1994 b) 1993 c) 1991 d) None of these Requirement and production of Rubber over the years Production Requirement 29. For which of the two years was the average yearly production of rubber equal to the average yearly requirement? a) 1992 & 1995 b) 1992 & 1993 c) 1994 & 1995 d) 1993 & 1995 30. In 1992, the quantity of requirement of rubber was what percent of the quantity of production? a) 25 b) 72 c) 65 d) 70 Data Sufficiency Data sufficiency questions appear in the ANALYTICAL section of the exam.. These questions require knowledge of the following topics: - Arithmetic - Elementary algebra - Commonly know concepts of geometry Data sufficiency questions are designed to measure your ability to analyze a quantities problem, recognize which given information is relevant, and determine at what point there is sufficient information to solve a problem. In these questions, you are to classify each problem according to the five or four fixed answer choice, rather than find a solution to the problem. Each Data sufficiency question consists of a question, often accompanied by some initial information, and two statements, labeled (1) and (2), which contain additional information. You must decide whether the information in each statement is sufficient to answer the question or- if neither statement provides enough information –whether the information in the two statements together is sufficient. It is also possible that the statements in combination do not give enough information answer the question. Begin by reading the initial information and the question carefully. Next, consider the first statement. Does the information provided by the first statement is sufficient to answer the question? Go on the statement. Try to ignore the information given in the first statement when you consider the second statement. Now you should be able to say, for each statement, whether it is sufficient to determine the answer. Next, consider the two statements in tandem. Do they, together, enable you to answer the question? Give our answers as per the following statements A statement (1) alone is sufficient but statement (2) alone is not sufficient B statement (2) alone is sufficient but statement (1) alone is not sufficient C Both statements together are sufficient but neither statement alone is sufficient D Each statement alone is sufficient E Both statement together are still not sufficient EXERCISE-1 1. How much is 20 percent of a certain number? 1) 10 percent of the number is 5. 2) 40 percent of twice the number is 40. 2. A thoroughly blended biscuit mix includes only flour and baking powder. What is the ratio of the number of grams of baking powder to the number of grams of flour in the mix? 1) Exactly 9.9 grams of flour is contained in 10 grams of the mix. 2) Exactly 0.3 gram of baking powder is continued in 30 grams of the mix. 3. What is the value of ׀ x ׀ ? 1) x = - ׀x ׀ 2) x 2 = 4 4. Is r greater than 0.27? 1) r is grater than ¼. 2) r is equal to 3/10. 5. What is the value of the sum of a list of n odd integers? 1) n = 8 2) The square of the number of integers on the list is 64. 6. In the figure above, if lines k and m are parallel, what is value of x? 1) y = 120 2) z =60 7. What percent of a group of people are women with red hair? 1) Of the women in the group, 5 percent have red hair. 2) Of the men in the group, 10 percent have red hair. 8. If r and s are positive integers, r is what percent of s? 1) r =3/4 s 2) r ÷ s =75/100 9. Is it true that a > b? 1) 2a > 2b 2) a + c> b + c 10. In a certain class, one student is to be selected at random to read. What is the probability that a boy will read? 1) Two-third of the students in the class are boys. 2) Ten of the students in the class are girls. 11. If 5x + 3y = 17, what is the value of x? 1) x is a positive integer. 2) y = 4x 12. Does the product jkmn equal 1? 1) jk / mn =1 2) j = 1/k and m = 1/n 13. A certain expressway has exits J, K, L, and M, in that order. What is the road distance from exit k to exit L? 1) The road distance from exit J to exit L is 21 kilometers 2) The road distance from exit M is 26 kilometers. 14. Is the integer k a prime number? 1) 2k = 6 2) 1 < k < 6 15. If ab ≠ 0, in what quadrant of the coordinate system above does point (a, b) lie? 1) (b, a)lies in quadrant IV. 2) (a, -b) lies in quadrant III. EXERCISE- 2 1. Is x greater than 1.8? 1) x > 1. 7 2) x > 1. 9 2. If n is an integer, is n + 1 odd? 1) n + 2 is an even integer. 2) n -1 is an odd integer. 3. Is 1< x < 2? 1) 0 < x 2) x < 3 4. Water is pumped into a partially filled tank at a constant rate through an inlet pipe. At the same time, water is pumped out of the tank at a constant rate though an outlet pipe. At what rate, in gallons per minute, is the amount of water in the tank increasing? 1) The amount of water initially in the tank is 200gallons. 2) What is pumped into the tank at a rate of 10 gallons per minute and out of the tank at rate of 10 gallons every 2 ½ minutes. 5. Is x a negative number? 1) 9x > 10x 2) x + 3 is positive. 6. Does 2m – 3n = 0? 1) m ≠ 0 2) 6m = 9n 7. What is the value of the integer x 1) X is a prime number. 2) 31 ≤ x ≤ 37 8. If P, Q, and R are three distinct points, do line segments PQ and PR have the same length? 1) P is the midpoint of line segment QR. 2) Q and R lie on the same circle with center P 9. Is the number x between 0.2 and 0.7? 1) 560x < 280 2) 700x > 280 10. If i and j are integers, is i + j an even integer? 1) i < 10 2) i = j 11. If n + k = m, what is the value of k? 1) n = 10 2) m + 10 = n 12. Is the triangle above equilateral? 1) x = y 2) z = 60 13. Is x an integer? 1) x/2 is an integer. 2) 2x is an integer. 14. What is the value of x? 1) 2x + 1 = 0 2) (x +1) 2 = x 2 15. What is the value of 1/k + 1/r? 1) k + r = 20 2) kr = 64 EXERCISE-3 1. If x is equal to one of the numbers ¼, 3/8, or 2/5, what is the value of x? 1) ¼ < x < ½ 2) 1/3 < x < 3/5 2. In Δ PQR, if PQ = x, QR = x+2, and PR = y, which of the three angles of Δ PRQ has the greatest degree measure? 1) y = x + 3 2) x = 2 3. What distance did Jane travel? 1) Bill traveled 40 miles in 40 minutes. 2) Jane traveled at the same average rate as Bill. 4. What number is 15 percent of x? 1) 18 is 6 percent of x. 2) 2/3 of x is 200. 3.2☐ Δ 6 5. If ☐ and A each represent single digits in the decimal above, what digit does ☐ represent? 1) When the decimal does is rounded to the nearest tenth, 3.2 is the result. 2) When the decimal is rounded to the nearest hundredth, 3.24 is the result. 6. The profit from the sale of a certain appliance increases, though not proportionally, with number of units sold. Did the profit exceed $4 million on sales of 380,000units? 1) The profit exceeded $2 million on sales of 200, 000 units. 2) The profit exceeded $5 million on sales of 350, 000 units. 7. What is the value of xy – yz? 1) y = 2 2) x – z =5 8. Will the first 10 volumes of a 20- volume encyclopedia fit upright in the book rack shown above? 1) x= 50 centimeters 2) The height of the tub is 1 meter. 9. A circular tub has a band painted around its circumference, as shown above. What is the surface area of this painted band? 1) x = 0.5 2) The height of the tub is 1 meter. 10. What is the value of integer n? 1) n(n +1) = 6 2) 2 2n = 16 11. The inside of a rectangular carton is 48 centimeters long, 32 centimeters wide, and 15 centimeters high. The carton is filled to capacity with k identical cylindrical cans of fruit that stand upright in rows and columns, as indicated in the figure above. If the can are 15 centimeters high, what is the value of k? 1) Each of the cans has a radius of 4 centimeters. 2) Six of the cans fit exactly along the length of the carton x – 4 = z y – x = 8 8 – z =t 12. For the system of equation given, what is the value of z? 1) x = 7 2) t = 5 13. Is x equal to 5? 1) x≥ 5 2) x ≤ 5 14. The table above shows the distance, in kilometers, by the most direct route, between any two of the four cities, R, S, T, and U. For example, the distance between City R and City U is 62 kilometers. What is the value of x? 1) By the most direct route, the distance between S and T is twice the distance between S and R. 2) By the most direct route, the distance between T and U is 1.5 times the distance between R and T. 15. What is the value of the two-digit integer x ? 1) The sum of the two digits is 3. 2) x is divisible by 3 EXERCISE -4 1. What is the tenths digit in the decimal representation of a certain number? 1) The number is less than 1/3 2) The number is greater than1/4 2. If the two floors in a certain building are 9 feet apart, how many steps are there in a set of stairs that extends from the first floor to the second floor of the building? 1) Each step is ¾ foot high 2) Each step is 1 foot wide. 3. If xy ≠ 0, is x/y < 0? 1) x = - y 2) -x = -(-y) 4. How many people are directors of both Company k and Company R? 1) There were 17 directors present at a joint meeting of the directors of Company K and Company R, and no directors were absent. 2) Company K has 12 directors and Company R has 8 directors. 5. If x and y are positive, is x/y greater than 1? 1) xy > 1 2) x – y > 0 6. What is the value of z in the triangle above? 1) x + y = 139 2) y + z = 108 7. If x, y, and z are nonzero numbers, is xz = 12? 1) x 2 yz = 12 xy 2) z/4 = 3/x 8. A certain company currently has how many employees? 1) If 3 additional employees are hired by the company and all of the present employees remain, there will be at least 20 employees in the company. 2) If no additional employees are hired by the company and 3 of the present employees resign, there will be fewer than 15 employees in the company. 9. What is the value of n in the equation -25 + 19 +n = s? 1) s = 2 2) n/s = 4 10. At a certain picnic, each of the guests was served either a single scoop or a double scoop of ice cream. How many of the guests were served a double scoop of ice cream? 1) At the picnic, 60 percent of the guests were served a double scoop of ice cream. 2) A total of 120 scoops of ice cream were saved to all the guests at the picnic. 11. What is the value of xy? 1) y = x + 1 2) y = x 2 +1 12. What is the value of 1/x + 1/y? 1) x + y = 14 2) xy = 24 13. If d denotes a decimal, is d ≥ 0.5? 1) When d is rounded to the nearest tenth, the result is 0.5. 2) When d is rounded to the nearest integer, the result is 1. 14. If a real estate agent received a commission of 6 percent of the selling price of a certain house, what was the selling price of the house? 1) The selling price minus the real estate agent‟s commission was $84,600. 2) The selling price was 250 percent of the original purchase price of $36,000. 15. If √x = n, what is the value of x? y 1) yn =10 2) y = 40 and n = ¼ EXERCISE- 5 1. How many integers are there between, but not including, integers r and s? 1) s – r = 10 2) There are 9 integers between, but not including, r+1 and s+1. 2. What is the number of members of Club X who are at least 35 years of age? 1) Exactly ¾ of the members of Club X are under 35 years of age? 2) The 64 women in Club X constitute 40 percent of the club‟s membership. 3. Carlotta can drive from her home to her office by one of two possible roués. If she must also return by the longer route, what is the distance of the shorter route? 1) When she drive from her home to her office by the shorter route and returns by the longer route, she drives a total of 42 kilometers. 2) When she drive both ways, from her home to her office and back, by the longer route, she drives a total of 46 kilometers. 4. Is x > y? 1) x = y+2 2) x/2 = y -1 5. If m is an integer, is m odd? 1) m/2 is NOT an even integer. 2) m – 3 is an even integer. 6. What is the area of triangular region ABC above? 1) The product of BD and AC is 20. 2) x = 45 7. What is the value of b + c? 1) ab + cd + ac + cd = 6 2) a +d = 4 8. What is the average (arithmetic mean)of j and k ? 1) The average (arithmetic mean) of j +2 and k + 4 is 11. 2) The average (arithmetic mean) of j, k, and 14 is 10. 9. Paula and Sandy were among those people who sold raffle tickets to raise money for Club X. If Paula and Sandy sold a total of 100 if the tickets, how many of the tickets did Paula sell? 1) Sandy sold 2/3 as many of the raffle tickets as Paula did. 2) Sandy sold 8 percent of all the raffle tickets sold for Club X. 10. Is ax = 3 –bx? 1) x( a + b) =3 2) a =b = 1. 5 and x =1. 11. A number of people each wrote down one of the first 30 positive integers. Were any of the integers written down by more than one of the people? 1) The number of people who wrote down an integer was greater than 40 2) The number of people who wrote down an integer was less then 70. 12. In the figure above, is CD > BC? 1) AD = 20 2) AB = CD 13. How much did a certain telephone call cost? 1) The call lasted 53 minutes. 2) The cost for the first 3 minutes was 5 times the cost for each additional minute. 14. In a certain office, 50 percent of the employees are college graduates and 60 percent of the employees are over forty years old. If 30 percent of those over forty have master‟s degrees how many of the employees over forty have master‟s degrees? 1) Exactly 100 of the employees are college graduates. 2) Of the employees 40 years old or less, 25 percent have master‟s degrees. 15. Is rst = 1? 1) rs =1 2) st=1 EXERCISE- 6 1. The figure above represents a circle graph of Company H‟s total expenses broken down by the expenses for each of its five divisions. If O is the center of the circle and if Company H‟s total expenses are $5, 400, 000, what are the expenses for division R? 1) x= 94 2) The total expenses for division S and T are twice as much as the expenses for division R. 2. If Ms. Smith‟s income was 20 percent more for 1991 than it was for 1990, how much was her income for 1991? 1) Ms. Smith‟s income for the fist 6 months of 1990 was $17,500 and her income for the last 6 months of 1990 was $20,000. 2) Ms. Smith‟s income for 1991 was $7,500 great than her income for 1990. 3. In the figure above, segments PR and QR are each parallel to one of the rectangular coordinate axes. Is the ratio of the length of QR to the length of QR to the length of PR equal to 1? 1) c = 3 and d = 4. 2) a= -2 and b = -1 4. While on a straight road, car X and car Y are traveling at different rates. If car X is now 1 mile ahead of car Y, how many minutes from now will car X be 2 miles ahead of car Y? 1) Car X is traveling at 50 miles per hour and car Y is traveling at 40 miles per hour. 2) Three minutes age car X was ½ mile ahead of car Y. 5. If a, b and c are integers, is a – b + c greater than a + b – c? 1) b is negative. 2) c is positive. 6. If a certain animated cartoon consists of total of 17,280 frames on film, how many minutes will it take to run the cartoon? 1) The cartoon runs without interruption at the rate of 24 frames per second. 2) It takes 6 times as long to run the cartoon as it takes to rewind the film, and it takes a total of 14 minutes to do both. 7. A box contains only red chips, white chips, and blue chips. If a chip is randomly selected from the box, what is the probability that the chip will be either white or blue? 1) The probability that the chip will be blue is 1/5 2) The probability that the chip will be red is 1/3 8. If the successive tick marks shown on the number line above are equally spaced and if x and y are the numbers designating the end points of intervals as shown, what is the value of y? 1) x = ½ 2) y – x = 2/3 9. On a company- sponsored cruise, 2/3 of the passengers were company employees and the remaining passengers were their guests. If 3/4 of the company-employee passengers were managers, what was the number of company-employee passengers who were NOT mangers? 1) There were 690 passengers in the cruise. 2) There were 230 passengers who were guests of the company employees. 10. In the xy-plane, does the point (4, 12) lie on line k? 1) point (1, 7) lies on line k. 2) point (-2, 2) lies on line k. 11. The length of the edging that surrounds circular garden K is ½ the length of the edging that surrounds circular garden G. What is the area of garden K? ( Assume that the edging has negligible width.) 1) The area of G is 25π square meters 2) The edging around G is 10 π meters long. 12. An employee is paid 1.5 times the regular hourly rate for each hour worked in excess of 40 hours per week, excluding Sunday, and 2 times the regular hourly rate for each hour worked on Sunday. How much was the employee paid last week? 1) The employee‟s regular hourly rate is $10. 2) Last week the employee worked a total of 54 hours but did not work more than 8 hours on any day. 13. What was the revenue that a theater received from the sale of 400 tickets, some of which were sold at the full price and the remainder of which were sold at a reduced price? 1) The number of tickets sold at the full price was ¼ of the total number of tickets sold. 2) The full price of a ticket was $25 14. If o represents one of the operations +, -, and ×, is k o ( l +m) = (k o l) + (k o m)for all numbers k, l, and m ? 1) k o 1 is not equal to 1 o k for some numbers k. 2) 0 represents subtraction . 15. How many of the 60 cars sold last month by a certain dealer had neither power widows nor a stereo? 1) Of the 60 cars sold, 20 had a stereo but not power windows. 2) Of the 60 cars sold, 30 had both power windows and a stereo. EXERCISE-7 1. By what percent did the median household income in County Y decrease from 1970 to 1980? 1) In 1970 the median household income in Country Y was 2/3 of the median household income in Country X 2) In 1980 the median household income in Country Y was ½ of the median household income in Country X 2. A certain group of car dealerships agreed to donate x dollars to a Red Cross chapter for each car sold during a 30- day period. What was the total amount that was expected to be donated? 1) A total of 500 cars were expected to be sold. 2) Sixty more cars were sold than expected, so that the total amount actually donated was $28,000. 3. While driving on the expressway, did Robin ever exceed the 55-mile-per-hour speed limit? 1) Robin drove 100 miles on the expressway. 2) Robin drove for 2hours on the expressway. 4. In Jefferson School, 300 students study French or Spanish or both. If 100 of these students do not study French, how many of these students study both French and Spanish? 1) Of the 300 students, 60 do not study Spanish. 2) A total of 240 of the students study Spanish. 5. A certain salesperson‟s weekly salary is equal to a fixed base salary plus a commission that is directly proportional to the number of items sold during the week. If 50 items are sold this week, what will be the salesperson‟s salary for this week? 1) Last week 45 items were sold. 2) Last week‟s salary was $ 405. 6. If Juan had a doctor‟s appointment on a certain day, was the appointment on a Wednesday? 1) Exactly 60 hours before the appointment, it was Monday. 2) The appointment was between 1: 00 p.m and 9: 00 p.m 7. What is the value of 5x 2 + 4x -1? 1) x(x + 2) = 0 2) x = 0 8. At Larry‟s Auto supply Store, Brand X antifreeze is sold by the gallon and Brand Y motor oil is sold by the quart. Excluding sales tax, what is the total cost for 1 gallon of brand X antifreeze and 1 quart of Brand Y motor oil? 1) Excluding sales tax, the total cost for 6 gallons of Brand X antifreeze and 10 quarts of Brand Y motor oil is $58. (There is no quantity discount.) 2) Excluding sales tax, the total cost for 4 gallons of Brand X antifreeze and 12 quarts of Brand Y motor oil is $44. (There is not quantity discount.) 9. Is m = n ? 1) m + n < 0 2) mn < 0 10. When a player in a certain game tossed a coin a number of times, 4 more heads than tails resulted. Heads or tails resulted each time the player tossed the coin. How many times did heads result? 1) The player tossed the coin 24 time. 2) The player received 3 points each time heads resulted and 1 point each time tails resulted for a total of 52 points. 11. If S is the infinite sequence S1 = 9, S2 = 99, S3 = 999, …. Sk = 10 k – 1, ….is every term in S divisible by the prime number p ? 1) P is greater than 2. 2) At least one term in sequence S is divisible by p. 12. Quadrilateral RSTU shown above is a site plan for a parking lot in which side RU is parallel to side ST and RU is longer than ST. what is the area of the parking lot? 1) RU = 80 meters 2) TU = 20\10 meters 13. If n and k are greater than zero, is n/k an integer? 1) n and k are both integers. 2) n 2 and k 2 are both integers. 14. If the average (arithmetic mean) of six numbers is 75, how many of the numbers are equal to 75? 1) None of the six numbers is less than 75. 2) None of the six numbers is grater than 75. 15. Is x = y – z? 1) x + y =z 2) x < 0 EXERCISE -8 1. What was the total amount of revenue that a theater received from the sale of 400 tickets, some of which were sold at x percent of full price and the rest of which were sold at full price? 1) x = 50 2) Full-price tickets sold for $20 each. 2. Any decimal that has only a finite number of nonzero digits is terminating decimal. For example, 24, 0.82, and 5.096 are three terminating decimals. If r and s are positive integers and the ratio r/s is expressed as a decimal, is r/s a terminating decimal. 1) 90 < r < 100 2) s = 4 3. In the figure above, what is the value of x + y? 1) x = 70 2) AABC and AADC are both isosceles triangles. 4. Are positive integers p and q both greater than n? 1) p – q is greater than n. 2) q > p 5. Whenever Martin has a restaurant bill with an amount between $10 and $99, he calculates the dollar amount of the tip as 2 times the tens digit of the amount of his bill. If the amount of Martins most recent bill was between $10 and $99, was the tip calculated by Martin on this bill greater than 15 percent of the amount of the bill? 1) The amount of the bill was between $15 and $50. 2) The tip calculated by Martin was $8. 6. The price per share of stock X increased by 10 percent over the same period that the price per share of stock Y decreased by 10 percent. The reduced price per share of stock Y was what percent of the original price per share of stock X? 1) The increased price per share of stock X was equal to the original price per share of stock. 2) The increased price per share of stock X was 10/11 the decrease in the price per share of stock Y. 7. Is k greater than t? 1) kt = 24 2) k 2 > t 2 8. In the figure above, if the area of triangular region D is 4, what is the length of a side of square region A? 1) The area of square region B is 9. 2) The area of square region C is 64/9 9. If x is to be selected at random from set T, what is the probability that ¼ x -5 s 0? 1) T is a set of 8 integers 2) T is contained in the set of integers from 1 to 25, inclusive. 10. If Sara‟s age is exactly twice Bill‟s age, what is Sara‟s age? 1) Four years ago, Sara‟s age was exactly 3 times Bill‟s age. 2) Eight years now, Sara‟s age will be exactly 1.5 times Bill‟s age. 11. What is the value of ( a + b) 2 1) ab =0 2) (a – b) 2 = 36 12. In the figure above, what is the ratio KN / MN? 1) The perimeter of rectangle KLMN is 30 metes. 2) The three small rectangles have the same dimensions. 13. If n is a positive integer, is 150/n an intriguer? 1) n < 7 2) n is a prime number. 14. Is 2x – 3y < x 2 ? 1) 2x – 3y = -2 2) x > 2 and y > 0. 15. A report consisting of 2,600 words is divided into 23 paragraphs. A 2- paragraph preface is then added to the report. Is the average (arithmetic mean ) number of words per paragraph for all 25 paragraphs less than 120? 1) Each paragraph of the preface has more than 100 words. 2) Each paragraph of the preface has fewer than 150 words. EXERCISE-9 1. If x/2 = 3/y, is x less than y? 1) y > 3 2) y s 4 2. If v and w are different integers, does v = 0? 1) vw = v 2 2) w = 2 3. What is the value of 36,500(1.05) n ? 1) n 2 – 5n + 6 = 0 2) n – 2 =0 4. In the rectangular coordinate system above, if OP < PQ, is the area of region OPQ greater than 48? 1) The coordinates of point P are (6,8). 2) The coordinates of point Q are (13, 0). 5. If r and s are positive integers, is r/s an integer? 1) Every factor of s is also a factor of r. 2) Every prime factor of s is also a prime factor of r. 6. If z n = 1, what is the value of z? 1) n is a nonzero integer. 2) z > 0 7. In the expression above, if xn = 0, what is the value of S 1) x =2n 2) n = ½ 8. If x is an integer, is x x< 2 x ? 1) x < 0 2) x = -10 9. If n is a positive integer, is the value of b – a at least twice the value of 3 n – 2 n ? 1) a =2 n + 1 and b = 3 n + 1 2) n = 3 10. The inflation index for the year1989 relative to the year 1970 was 3.56, indicating that, on the average, for each dollar spent in 1970 for goods, $3.56 had to be spent for the same goods in 1989. If the price of a Model K mixer increased precisely according to the inflation index, what was the price of the of the mixer in 1970? 1) The price of the Model K mixer was $102. 40 more in 1989 than in 1970. 2) The price of the Model K mixer was $142. 40 in 1989. 11. Is 5 k less than 1,000? 1) 5 k +1 > 3,000 2) 5 k-1 = 5 k - 500 12. If the integer n is greater than 1, is n equal to 2? 1) n has exactly two positive factors. 2) The difference of any two distinct positive factors of n is odd. 13. Every member of a certain club volunteers to contribute equally to the purchase of a $60 gift certificate. How many members does the club have? 1) Each member‟s contribution is to be $4. 2) If 5 club members fail to contribute, the share of each contributing member will increase by $2. 14. If m and n are positive integers, is \n – m an integer? 1) n > m+ 15 2) n = m(m +1) 15. If x < 0, is y > 0? 1) x/y < 0 2) y – x> 0 EXERCISE-10 1. What is the circumference of the circle above with center O? 1) The perimeter of AOXZ is 20 + 10\2. 2) The length of arc XYZ is 5t. 2. What is the value of a 4 – b 4 ? 1) a 2 – b 2 = 16 2) a + b = 8 3. In a certain business, production index p is directly proportional to efficiency index e, which is in turn directly proportional to investment index i. What is p if I = 70? 1) e = 0 .5 whenever i = 60. 2) p = 2.0 whenever i = 50. 4. If x = -y, is x-y/ x + y > 1 1) x >0 2) y < 0 5. In the rectangular coordinate system, are the points (r, s) and (u, v) equidistant from the origin? 1) r + s =1 2) u = 1- r and v = 1 –s. 6. On Jane‟s credit card account, the average dally balance for a 30-day billing cycle is the average (arithmetic mean) of the daily balances at the end of each of the 30days. At the beginning of a certain 30-day billing cycle, Jane‟s credit card account had a balance of $600. Jane made a payment of $300 on the account during the billing cycle. If no other amounts were added to or subtracted from the account during billing cycle, what was the average daily balance on Jane‟s account for the billing cycle? 1) Jane‟s payment was credited on the 21 st day of the billing cycle. 2) The average daily balance through the 25 th day of the billing cycle was $540. 7. If x is an integer, is 9 x + 9 - x = b? 1) 3 x +3 - x = \b + 2 2) x > 0 8. If m > 0 and n >0, is m +x/ n + x > m/n? 1) m < n 2) x > 0 9. If n is a positive integer, is (1/10) n < 0.01? 1) n > 2 2) (1/10) n-1 <0.1 10. Is 1/p > r/ (r 2 +2)? 1) p = r 2) r > 0 11. Is n an integer? 1) n 2 is an integer. 2) \n is an integer. 12. If n is a positive integer, is n 3 – n divisible by 4? 1) n = 2k +1, where k is an integer. 2) n 2 + n is divisible by 6. 13. What is the tens digit of positive integer x? 1) x divided by 100 has a remainder of 30. 2) x divided by 110 has a remainder of 30. 14. If x, z and positive integers, is x-y odd? 1) x = z 2 2) y = (z -1) 2 15. Henry purchased 3 items during a sale. He received a 20 percent discount off the regular price of the most expensive items and a 10 percent discount off the regular price of each of the other 2 items. Was the total amount of the 3 discounts greater than 15 percent of the sum of the regular prices of the 3 items? 1) The regular price of the most expensive item was $50, and the regular price of the next most expensive item was $20. 2) The regular price of the least expensive item was $15. Venn Diagrams The term venn Diagram relates to the different type of figures drawn to represent relationship between two or more objects. These figures represent by a circle, triangle, square and rectangle. The concept of venn diagram originates from set theory. A basis concept of set, subset, disjoint set can help to understand the concept of venn diagram. To understand these terms, we are given following points with examples. Example 1. An object is said to have an intersection with the other object, when two objects share something in common. For Examples: (a) Dogs, Pets (b) Fathers, Brothers (c) Clerks, Government Employees Example 2. An object is said to be a subset of another object, if former is a part of latter. For examples: (a) Minutes, Hours (b) Females, Mothers (c) Engineers, Human Beings Example 3. An object is said to be disjoint with other, when two objects share nothing in common. For examples: (a) Table, Chair (b) Doctors, Engineers (c) Human Beings, Rates Directions (Qs. 1-4) : Each of the se questions below contains three group of things. You are to choose from the following fine numbered diagrams, a diagram that depicts the correct relationship among the three groups of things in each questions. 5. Tables, Chairs, Furniture 6. Tie, Shirts, Pantaloon 7. Dogs, Pets, Cats 8. Brinjal, Meat, Vegetables SOLUTIONS 1. (d) Tables and chairs are unrelated items, but both are the items of furniture. 2. (c) Tie, shirt and pantaloon are separated items. 3. (d) Dogs and cats are entirely different from each other. But both are pet animals. 4. (e) Brinjal is a vegetable. But meat is entirely different. Example 5. Which one of the following diagrams correctly represents the relationship among the classes: Judge, Thief, Criminal. Solution (b) All thieves are criminal. But judge is entirely different. Example 6. Which one of the following sets is best represented in the adjoining diagram? (a) Animals, Insects, Cockroaches (b) Country, States, Districts (c) Animals, Mates, Females and Hermaphrodities (d) States Districts, Union Territory Solution (d). Districts from the part of the state but, union territory is entirely different. Example 7. In the following diagram, the square represents girls, the circle represents tall persons, the triangle is for tennis players and the rectangle stands for the swimmers. On the basis of the above diagram, answer the following questions. 1. Which letter represents tall girl, who do not play tennis and are not swimmers? (a) E (b) G (c) D (d) C 2. Which letter represents girls who are swimmers, play tennis but are not tall? (a) F (b) B (c) E (d) None of these 3. Which letter represents tall persons who are gents and swimmers but do not play tennis? (a) J (b) K (c) L (d) I 4. Which letter represents tall girls who are swimmers but don‟t play tennis? (a) H (b) G (c) D (d) C SOLUTION 1. (c). Tall girls are represented by the region common to the square and the circle i.e., D, C, G, and H. But according to the given conditions, the girls are neither a part of rectangle nor the triangle. So, Answer is D. 2. (d). Girls, who are swimmers and play tennis are represented by the region i.e., H. But according to the given condition girls should not be tall. So, required region should not be a part of the circle. Since, it is a part of the circle, hence the answer is none of these. 3. (b). Tall persons are represented by regions inside the circle i.e., C, D, G, H, I, J and K. Since persons are not girls and do not play tennis, so the region should not be a part of either the square or the triangle. So, C, D, G, H should be excluded. Also according to the given conditions, the persons should be swimmers. So, the required region should be a part of the rectangle. Hence, the answer is K. 4. (b). Tall girls who are swimmers are represented by the region common to the square, circle and the rectangle i.e., G and H. But according to the given conditions, girls should not be tennis players. So, the required region should not be apart of the triangle, so H should be excluded. Hence, the answer is G. Example 8. Read the figure and find the region representing persons who are educated and employed but not confirmed. (a) b, d (b) a, b, c (c) a, c (d) a, d, c Solution (a). The required region is the one which is common to the circles but lies outside the triangle. So the answer is b and d. Exercise: Direction for Questions 1 to 3: In a class of 150 students 55 speak English; 85 speak Telugu and 30 speak neither English nor Telugu. 1. How many speak both English and Telugu? (a) 10 (b) 120 (c) 20 (d) 45 2. How many speak only Telugu? (a) 85 (b) 55 (c) 95 (d) 65 3. How many speak at least one of the two languages from English & Telugu? (a) 110 (b) 120 (c) 130 (d) 100 Directions for Questions 4 and 5: A class of 30 students comprises boys who can play Cricket, Hockey and Football. 3 boys play only cricket, 3 bys play only Hockey and 2 play only football. 4 boys could play all three games, while 11 could play Football and Cricket, and 10 boys could play Football and Hockey. 4. How may boys played Cricket and Hockey but not Football? (a) 1 (b) 2 (c) 3 (d) 5 5. How many boys can play atleast two games? (a) 16 (b) 18 (c) 10 (d) 22 Directions for Questions 6 to 9: In a class, 70 students passed in Mathematics, 50% of the students passed in English, 25% of the students passed in both and 5% of the students passed in neither Mathematics nor English. 6. How many students are there in the class? (a) 93 (b) 145 (c) 100 (d) 140 7. How many students passed in only one subject? (a) 75 (b) 53 (c) 80 (d) 70 8. How many students failed in atleast one subject? (a) 5 (b) 25 (c) 50 (d) 75 9. What is the ratio of the number of students who passed in English to that in Mathematics? (a) 1 : 1 (b) 2 : 3 (c) 5 : 7 (d) 10 : 9 Directions for Questions 10 to 13: In a survey of 150 readers it has been found that 75 read newspaper A, 90 read newspaper B ad 70 read newspaper C. 40 read A and B; 35 read B and C; 30 read A and C and 10 read all the three. 10. How many respondents read none of the newspapers? (a) 30 (b) 20 (c) 10 (d) 40 11. How many read exactly two newspapers? (a) 75 (b) 105 (c) 95 (d) 85 12. How many read exactly one newspaper? (a) 35 (b) 55 (c) 235 (d) 120 13. How many read neither A nor B? (a) 45 (b) 70 (c) 110 (d) 15 Directions for Questions 14 to 17: Scholars colony has a population of 2800 members. Number of members reading only English newspaper = 650 Number of members reading only Hindi newspaper = 550 Number of members reading only Marathi newspaper = 450 Number of members reading all three newspaper = 100 Number of members reading Hindi as well as English newspaper = 200 Number of members reading Hindi as well as Marathi newspaper = 400 Number of members reading English as well as Marathi newspaper = 300 14. Find number of members reading Hindi newspaper? (a) 950 (b) 1050 (c) 650 (d) 550 15. Find number of members reading none of the newspapers? (a) 450 (b) 550 (c) 2550 (d) 2650 16. Find number of members reading only one newspaper? (a) 450 (b) 1100 (c) 1600 (d) 1650 17. Find number of members reading atleast two newspapers? (a) 400 (b) 500 (c) 600 (d) 700 Directions for Questions 18 to 21: The following table gives the statistics of a class in which each student opted for Maths or Statistics or both. Unfortunately most of the figures have been erased but I remember some information. Mat hs Stati stics Bo th Tot al Male 50 Fem ale Total 70 15 0 The information is as follows: 1. 13 1/3% of the students took both Maths and Statistics 2. 40% of the students were females. 3. None of the females took both Mathematics and Statistics. Fill the table and answer the following Questions. 18. How many males took both Mathematics and Statistics? (a) 40 (b) 10 (c) 20 (d) 60 19. How many students took only Mathematics? (a) 50 (b) 80 (c) 60 (d) 10 20. How many males took only Statistics? (a) 0 (b) 40 (c) 20 (d) 30 21. How many females took only Mathematics? (a) 10 (b) 50 (c) 70 (d) 40 Directions for Questions 22 to 25: In a class of 160 students, it was found that 65 play Cricket 70 play Hockey and 90 play Football, 30 play Cricket and Hockey, 40 Cricket and Football, 35 play Hockey and Football and 15 play none of these three games. 22. How many play all three games? (a) 745 (b) 105 (c) 25 (d) 55 23. If 10 students who play only Hockey now start playing Cricket also; and 10 students who play only football stop playing Football and start playing Cricket how many will play both Cricket and Hockey? (a) 30 (b) 40 (c) 20 (d) 55 24. How many students play exactly one game? (a) 90 (b) 75 (c) 105 (d) 145 25. If 5 students stop playing Hockey and start playing Cricket, what is the least number of students playing only Football and Hockey but not Cricket? (a) 15 (b) 30 (c) 10 (d) 5 VERBAL Reading Comprehension Exercise 1: In the sixteenth century, an age of great marine and terrestrial exploration, Ferdinand Magellan led the first expedition to sail around the world. As a young Portuguese noble, he served the king of Portugal, but he became involved in the quagmire of political intrigue at court and lost the king's favor. After he was dismissed from service to the king of Portugal, he offered to serve the future Emperor Charles V of Spain. A papal decree of 1493 had assigned all land in the New World west of 50 degrees W longitude to Spain and all the land east of that line to Portugal. Magellan offered to prove that the East Indies fell under Spanish authority. On September 20, 1519, Magellan set sail from Spain with five ships. More than a year later, one of these ships was exploring the topography of South America in search of a water route across the continent. This ship sank, but the remaining four ships searched along the southern peninsula of South America. Finally they found the passage they sought near a latitude of 50 degrees S. Magellan named this passage the Strait of All Saints, but today we know it as the Strait of Magellan. One ship deserted while in this passage and returned to Spain, so fewer sailors were privileged to gaze at that first panorama of the Pacific Ocean. Those who remained crossed the meridian we now call the International Date Line in the early spring of 1521 after ninety-eight days on the Pacific Ocean. During those long days at sea, many of Magellan's men died of starvation and disease. Later Magellan became involved in an insular conflict in the Philippines and was killed in a tribal battle. Only one ship and seventeen sailors under the command of the Basque navigator Elcano survived to complete the westward journey to Spain and thus prove once and for all that the world is round, with no precipice at the edge. 1. The sixteenth century was an age of great ___exploration. A. cosmic B. land C. mental D. common man E. none of the above 2. Magellan lost the favor of the king of Portugal when he became involved in a political ___. A. entanglement B. discussion C. negotiation D. problems E. none of the above 3. The Pope divided New World lands between Spain and Portugal according to their location on one side or the other of an imaginary geographical line 50 degrees west of Greenwich that extends in a ___ direction. A. north and south B. crosswise C. easterly D. south east E. north and west 4. One of Magellan's ships explored the ___ of South America for a passage across the continent. A. coastline B. mountain range C. physical features D. islands E. none of the above 5. Four of the ships sought a passage along a southern ___. A. coast B. inland C. body of land with water on three sides D. border E. answer not available 6. The passage was found near 50 degrees S of ___. A. Greenwich B. The equator C. Spain D. Portugal E. Madrid 7. In the spring of 1521, the ships crossed the ___ now called the International Date Line. A. imaginary circle passing through the poles B. Imaginary line parallel to the equator C. area D. land mass E. answer not found in article Marie Curie was one of the most accomplished scientists in history. Together with her husband, Pierre, she discovered radium, an element widely used for treating cancer, and studied uranium and other radioactive substances. Pierre and Marie's amicable collaboration later helped to unlock the secrets of the atom. Marie was born in 1867 in Warsaw, Poland, where her father was a professor of physics. At the early age, she displayed a brilliant mind and a blithe personality. Her great exuberance for learning prompted her to continue with her studies after high school. She became disgruntled, however, when she learned that the university in Warsaw was closed to women. Determined to receive a higher education, she defiantly left Poland and in 1891 entered the Sorbonne, a French university, where she earned her master's degree and doctorate in physics. Marie was fortunate to have studied at the Sorbonne with some of the greatest scientists of her day, one of whom was Pierre Curie. Marie and Pierre were married in 1895 and spent many productive years working together in the physics laboratory. A short time after they discovered radium, Pierre was killed by a horse- drawn wagon in 1906. Marie was stunned by this horrible misfortune and endured heartbreaking anguish. Despondently she recalled their close relationship and the joy that they had shared in scientific research. The fact that she had two young daughters to raise by herself greatly increased her distress. Curie's feeling of desolation finally began to fade when she was asked to succeed her husband as a physics professor at the Sorbonne. She was the first woman to be given a professorship at the world-famous university. In 1911 she received the Nobel Prize in chemistry for isolating radium. Although Marie Curie eventually suffered a fatal illness from her long exposure to radium, she never became disillusioned about her work. Regardless of the consequences, she had dedicated herself to science and to revealing the mysteries of the physical world. 8. The Curies' ____ collaboration helped to unlock the secrets of the atom. A. friendly B. competitive C. courteous D. industrious E. chemistry 9. Marie had a bright mind and a __personality. A. strong B. lighthearted C. humorous D. strange E. envious 10. When she learned that she could not attend the university in Warsaw, she felt___. A. hopeless B. annoyed C. depressed D. worried E. none of the above 11. Marie ___ by leaving Poland and traveling to France to enter the Sorbonne. A. challenged authority B. showed intelligence C. behaved D. was distressed E. answer not available in article 12. _____she remembered their joy together. A. Dejectedly B. Worried C. Tearfully D. Happily E. Sorrowfully 13. Her ____ began to fade when she returned to the Sorbonne to succeed her husband. A. misfortune B. anger C. wretchedness D. disappointment E. ambition 14. Even though she became fatally ill from working with radium, Marie Curie was never ____. A. troubled B. worried C. disappointed D. sorrowful E. disturbed Mount Vesuvius, a volcano located between the ancient Italian cities of Pompeii and Herculaneum, has received much attention because of its frequent and destructive eruptions. The most famous of these eruptions occurred in A. D. 79. The volcano had been inactive for centuries. There was little warning of the coming eruption, although one account unearthed by archaeologists says that a hard rain and a strong wind had disturbed the celestial calm during the preceding night. Early the next morning, the volcano poured a huge river of molten rock down upon Herculaneum, completely burying the city and filling in the harbor with coagulated lava. Meanwhile, on the other side of the mountain, cinders, stone and ash rained down on Pompeii. Sparks from the burning ash ignited the combustible rooftops quickly. Large portions of the city were destroyed in the conflagration. Fire, however, was not the only cause of destruction. Poisonous sulphuric gases saturated the air. These heavy gases were not buoyant in the atmosphere and therefore sank toward the earth and suffocated people. Over the years, excavations of Pompeii and Herculaneum have revealed a great deal about the behavior of the volcano. By analyzing data, much as a zoologist dissects a specimen animal, scientist have concluded that the eruption changed large portions of the area's geography. For instance, it turned the Sarno River from its course and raised the level of the beach along the Bay of Naples. Meteorologists studying these events have also concluded that Vesuvius caused a huge tidal wave that affected the world's climate. In addition to making these investigations, archaeologists have been able to study the skeletons of victims by using distilled water to wash away the volcanic ash. By strengthening the brittle bones with acrylic paint, scientists have been able to examine the skeletons and draw conclusions about the diet and habits of the residents. Finally, the excavations at both Pompeii and Herculaneum have yielded many examples of classical art, such as jewelry made of bronze, which is an alloy of copper and tin. The eruption of Mount Vesuvius and its tragic consequences have provided us with a wealth of data about the effects that volcanoes can have on the surrounding area. Today volcanologists can locate and predict eruptions, saving lives and preventing the destruction of cities and cultures. 15. Herculaneum and its harbor were buried under ___lava. A. liquid B. solid C. flowing D. gas E. answer not available 16. The poisonous gases were not ___ in the air. A. able to float B. visible C. able to evaporate D. invisible E. able to condense 17. Scientists analyzed data about Vesuvius in the same way that a zoologist ___ a specimen. A. describes in detail B. studies by cutting apart C. photographs D. chart E. answer not available 18. ____have concluded that the volcanic eruption caused a tidal wave. A. Scientist who study oceans B. Scientist who study atmospheric conditions C. Scientist who study ash D. Scientist who study animal behavior E. Answer not available in article 19. Scientist have used ___water to wash away volcanic ash from the skeletons of victims. A. bottled B. volcanic C. purified D. sea E. fountain Conflict had existed between Spain and England since the 1570s. England wanted a share of the wealth that Spain had been taking from the lands it had claimed in the Americas. Elizabeth I, Queen of England, encouraged her staunch admiral of the navy, Sir Francis Drake, to raid Spanish ships and towns. Though these raids were on a small scale, Drake achieved dramatic success, adding gold and silver to England's treasury and diminishing Spain's omnipotence. Religious differences also caused conflict between the two countries. Whereas Spain was Roman Catholic, most of England had become Protestant. King Philip II of Spain wanted to claim the throne and make England a Catholic country again. To satisfy his ambition and also to retaliate against England's theft of his gold and silver, King Philip began to build his fleet of warships, the Armada, in January 1586. Philip intended his fleet to be indestructible. In addition to building new warships, he marshaled one hundred and thirty sailing vessels of all types and recruited more than nineteen thousand robust soldiers and eight thousand sailors. Although some of his ships lacked guns and others lacked ammunition, Philip was convinced that his Armada could withstand any battle with England. The martial Armada set sail from Lisbon, Portugal, on May 9,1588, but bad weather forced it back to port. The voyage resumed on July 22 after the weather became more stable. The Spanish fleet met the smaller, faster, and more maneuverable English ships in battle off the coast of Plymouth, England, first on July 31 and again on August 2. The two battles left Spain vulnerable, having lost several ships and with its ammunition depleted. On August 7, while the Armada lay at anchor on the French side of the Strait of Dover, England sent eight burning ships into the midst of the Spanish fleet to set it on fire. Blocked on one side, the Spanish ships could only drift away, their crews in panic and disorder. Before the Armada could regroup, the English attacked again on August 8. Although the Spaniards made a valiant effort to fight back, the fleet suffered extensive damage. During the eight hours of battle, the Armada drifted perilously close to the rocky coastline. At the moment when it seemed that the Spanish ships would be driven onto the English shore, the wind shifted, and the Armada drifted out into the North Sea. The Spaniards recognized the superiority of the English fleet and returned home, defeated. 20. Sir Francis Drake added wealth to the treasury and diminished Spain's ____. A. unlimited power B. unrestricted growth C. territory D. treaties E. answer not available in article 21. Philip recruited many ___soldiers and sailors. A. warlike B. strong C. accomplished D. timid E. non experienced 22. The ____ Armada set sail on May 9, 1588. A. complete B. warlike C. independent D. isolated E. answer not available 23. The two battles left the Spanish fleet ____. A. open to change B. triumphant C. open to attack D. defeated E. discouraged 24. The Armada was ___ on one side. A. closed off B. damaged C. alone D. circled E. answer not available in this article The victory of the small Greek democracy of Athens over the mighty Persian empire in 490 B. C. is one of the most famous events in history. Darius, king of the Persian empire, was furious because Athens had interceded for the other Greek city-states in revolt against Persian domination. In anger the king sent an enormous army to defeat Athens. He thought it would take drastic steps to pacify the rebellious part of the empire. Persia was ruled by one man. In Athens, however, all citizens helped to rule. Ennobled by this participation, Athenians were prepared to die for their city-state. Perhaps this was the secret of the remarkable victory at Marathon, which freed them from Persian rule. On their way to Marathon, the Persians tried to fool some Greek city-states by claiming to have come in peace. The frightened citizens of Delos refused to believe this. Not wanting to abet the conquest of Greece, they fled from their city and did not return until the Persians had left. They were wise, for the Persians next conquered the city of Etria and captured its people. Tiny Athens stood alone against Persia. The Athenian people went to their sanctuaries. There they prayed for deliverance. They asked their gods to expedite their victory. The Athenians refurbished their weapons and moved to the plain of Marathon, where their little band would meet the Persians. At the last moment, soldiers from Plataea reinforced the Athenian troops. The Athenian army attacked, and Greek citizens fought bravely. The power of the mighty Persians was offset by the love that the Athenians had for their city. Athenians defeated the Persians in archery and hand combat. Greek soldiers seized Persian ships and burned them, and the Persians fled in terror. Herodotus, a famous historian, reports that 6400 Persians died, compared with only 192 Athenians. 25. Athens had ____the other Greek city-states against the Persians. A. refused help to B. intervened on behalf of C. wanted to fight D. given orders for all to fight E. defeated 26. Darius took drastic steps to ___ the rebellious Athenians. A. weaken B. destroy C. calm D. placate E. answer not available 27. Their participation___to the Athenians. A. gave comfort B. gave honor C. gave strength D. gave fear E. gave hope 28. The people of Delos did not want to ___ the conquest of Greece. A. end B. encourage C. think about D. daydream about E. answer not available 29. The Athenians were ___by some soldiers who arrived from Plataea. A. welcomed B. strengthened C. held D. captured E. answer not available 30. Questions 30-32. The Trojan War is one of the most famous wars in history. It is well known for the ten-year duration, for the heroism of a number of legendary characters, and for the Trojan horse. What may not be familiar, however, is the story of how the war began. According to Greek myth, the strife between the Trojans and the Greeks started at the wedding of Peleus, King of Thessaly, and Thetis, a sea nymph. All of the gods and goddesses had been invited to the wedding celebration in Troy except Eris, goddesses of discord. She had been omitted from the guest list because her presence always embroiled mortals and immortals alike in conflict. To take revenge on those who had slighted her, Eris decided to cause a skirmish. Into the middle of the banquet hall, she threw a golden apple marked “for the most beautiful.” All of the goddesses began to haggle over who should possess it. The gods and goddesses reached a stalemate when the choice was narrowed to Hera, Athena, and Aphrodite. Someone was needed to settle the controversy by picking a winner. The job eventually fell to Paris, son of King Priam of Troy, who was said to be a good judge of beauty. Paris did not have an easy job. Each goddess, eager to win the golden apple, tried aggressively to bribe him. “I'll grant you vast kingdoms to rule, “ promised Hera. “Vast kingdoms are nothing in comparison with my gift,” contradicted Athena. “Choose me and I'll see that you win victory and fame in war.” Aphrodite outdid her adversaries, however. She won the golden apple by offering Helen, Zeus' daughter and the most beautiful mortal, to Paris. Paris, anxious to claim Helen, set off for Sparta in Greece. Although Paris learned that Helen was married, he accepted the hospitality of her husband, King Menelasu of Sparta, anyway. Therefore, Menelaus was outraged for a number of reasons when Paris departed, taking Helen and much of the king's wealth back to Troy. Menelaus collected his loyal forces and set sail for Troy to begin the war to reclaim Helen. 30. Eris was known for ___both mortals and immortals. A. scheming against B. involving in conflict C. feeling hostile toward D. ignoring E. comforting 31. Each goddess tried ___to bribe Paris. A. boldly B. effectively C. secretly D. carefully E. answer not stated 32. Athena ___ Hera, promising Paris victory and fame in war. A. denied the statement of B. defeated C. agreed with D. restated the statement E. questioned the statement One of the most intriguing stories of the Russian Revolution concerns the identity of Anastasia, the youngest daughter of Czar Nicholas II. During his reign over Russia, the Czar had planned to revoke many of the harsh laws established by previous czars. Some workers and peasants, however, clamored for more rapid social reform. In 1918 a group of these people, known as Bolsheviks, overthrew the government. On July 17 or 18, they murdered the Czar and what was thought to be his entire family. Although witnesses vouched that all the members of the Czar's family had been executed, there were rumors suggesting that Anastasia had survived. Over the years, a number of women claimed to be Grand Duchess Anastasia. Perhaps the best –known claimant was Anastasia Tschaikovsky, who was also known as Anna Anderson. In 1920, eighteen months after the Czar's execution, this terrified young woman was rescued from drowning in a Berlin river. She spent two years in a hospital, where she attempted to reclaim her health and shattered mind. The doctors and nurses thought that she resembled Anastasia and questioned heer about her background. She disclaimed any connection with the Czar's family. Eight years later, though, she claimed that she was Anastasia. She said that she had been rescued by two Russian soldiers after the Czar and the rest of her family had been killed. Two brothers named Tschaikovsky had carried her into Romania. She had married one of the brothers, who had taken her to Berlin and left her there, penniless and without a vocation. Unable to invoke the aid of her mother's family in Germany, she had tried to drown herself. During the next few years, scores of the Czar's relatives, ex-servants, and acquaintances interviewed her. Many of these people said that her looks and mannerisms were evocative of the Anastasia that they had known. Her grandmother and other relatives denied that she was the real Anastasia, however. Tried of being accused of fraud, Anastasia immigrated to the United States in 1928 and took the name Anna Anderson. She still wished to prove that she was Anastasia, though, and returned to Germany in 1933 to bring suit against her mother's family. There she declaimed to the court, asserting that she was indeed Anastasia and deserved her inheritance. In 1957, the court decided that it could neither confirm nor deny Anastasia's identity. Although we will probably never know whether this woman was the Grand Duchess Anastasia, her search to establish her identity has been the subject of numerous books, plays, and movies. 33. Some Russian peasants and workers___for social reform. A. longed B. cried out C. begged D. hoped E. thought much 34. Witnesses ___ that all members of the Czar's family had been executed. A. gave assurance B. thought C. hoped D. convinced some E. answer not stated 35. Tschaikovsky ____any connection with the Czar's family. A. denied B. stopped C. noted D. justified E. answer not stated 36. She was unable to ___the aid of her relative. A. locate B. speak about C. call upon D. identify E. know 37. In court she ___ maintaining that she was Anastasia and deserved her inheritance. A. finally appeared B. spoke forcefully C. testified D. gave evidence E. answer not stated King Louis XVI and Queen Marie Antoinette ruled France from 1774 to 1789, a time when the country was fighting bankruptcy. The royal couple did not let France's insecure financial situation limit their immoderate spending, however. Even though the minister of finance repeatedly warned the king and queen against wasting money, they continued to spend great fortunes on their personal pleasure. This lavish spending greatly enraged the people of France. They felt that the royal couple bought its luxurious lifestyle at the poor people's expense. Marie Antoinette, the beautiful but exceedingly impractical queen, seemed uncaring about her subjects; misery. While French citizens begged for lower taxes, the queen embellished her palace with extravagant works of art. She also surrounded herself with artists, writers, and musicians, who encouraged the queen to spend money even more profusely. While the queen's favorites glutted themselves on huge feasts at the royal table, many people in France were starving. The French government taxed the citizens outrageously. These high taxes paid for the entertainments the queen and her court so enjoyed. When the minister of finance tried to stop these royal spendthrifts, the queen replaced him. The intense hatred that the people felt for Louis XVI and Marie Antoinette kept building until it led to the French Revolution. During this time of struggle and violence (1789-1799), thousands of aristocrats, as well as the king and queen themselves, lost their lives at the guillotine. Perhaps if Louis XVI and Marie Antoinette had reined in their extravagant spending, the events that rocked France would not have occurred. 38. The people surrounding the queen encouraged her to spend money ____. A. wisely B. abundantly C. carefully D. foolishly E. joyfully 39. The minister of finance tried to curb these royal ___. A. aristocrats B. money wasters C. enemies D. individuals E. spenders Many great inventions are greeted with ridicule and disbelief. The invention of the airplane was no exception. Although many people who heard about the first powered flight on December 17,1903, were excited and impressed, others reacted with peals of laughter. The idea of flying an aircraft was repulsive to some people. Such people called Wilbur and Orville Wright, the inventors of the first flying machine, impulsive fools. Negative reactions, however, did not stop the Wrights. Impelled by their desire to succeed, they continued their experiments in aviation. Orville and Wilbur Wright had always had a compelling interest in aeronautics and mechanics. As young boys they earned money by making and selling kites and mechanical toys. Later, they designed a newspaper-folding machine, built a printing press, and operated a bicycle-repair shop. In 1896, when they read about the death of Otto Lilienthal, the brother's interest in flight grew into a compulsion. Lilienthal, a pioneer in hang-gliding, had controlled his gliders by shifting his body in the desired direction. This idea was repellent to the Wright brothers, however, and they searched for more efficient methods to control the balance of airborne vehicles. In 1900 and 1901, the Wrights tested numerous gliders and developed control techniques. The brothers' inability to obtain enough lift power for the gliders almost led them to abandon their efforts. After further study, the Wright brothers concluded that the published tables of air pressure on curved surfaces must be wrong. They set up a wind tunnel and began a series of experiments with model wings. Because of their efforts, the old tables were repealed in time and replaced by the first reliable figures for air pressure on curved surfaces. This work, in turn, made it possible for them to design a machine that would fly. In 1903 the Wrights built their first airplane, which cost less than one thousand dollars. They even designed and built their own source of propulsion- a lightweight gasoline engine. When they started the engine on December 17, the airplane pulsated wildly before taking off. The plane managed to stay aloft for twelve seconds, however, and it flew one hundred twenty feet. By 1905 the Wrights had perfected the first airplane that could turn, circle, and remain airborne for half an hour at a time. Others had flown in balloons or in hang gliders, but the Wright brothers were the first to build a full-size machine that could fly under its own power. As the contributors of one of the most outstanding engineering achievements in history, the Wright brothers are accurately called the fathers of aviation. 40. The idea of flying an aircraft was ___to some people. A. boring B. distasteful C. exciting D. needless E. answer not available 41. People thought that the Wright brothers had ____. A. acted without thinking B. been negatively influenced C. been too cautious D. had not given enough thought E. acted in a negative way 42. The Wright's interest in flight grew into a ____. A. financial empire B. plan C. need to act D. foolish thought E. answer not in article 43. Lilenthal's idea about controlling airborne vehicles was ___the Wrights. A. proven wrong by B. opposite to the ideas of C. disliked by D. accepted by E. opposed by 44. The old tables were __ and replaced by the first reliable figures for air pressure on curved surfaces. A. destroyed B. canceled C. multiplied D. discarded E. not used 45. The Wrights designed and built their own source of ____. A. force for moving forward B. force for turning around C. turning D. force to going backward E. none of the above Exercise 2: Americans have always been interested in their Presidents' wives. Many First Ladies have been remembered because of the ways they have influenced their husbands. Other First Ladies have made the history books on their own. At least two First Ladies, Bess Truman and Lady Bird Johnson, made it their business to send signals during their husbands' speeches. When Lady Bird Johnson thought her husband was talking too long, she wrote a note and sent it up to the platform. It read, “It's time to stop!” And he did. Once Bess Truman didn't like what her husband was saying on television, so she phoned him and said,” If you can't talk more politely than that in public, you come right home.” Abigail Fillmore and Eliza Johnson actually taught their husbands, Millard Fillmore and Andrew Johnson, the thirteenth and seventeenth Presidents. A schoolteacher, Abigail eventually married her pupil, Millard. When Eliza Johnson married Andrew, he could not read or write, so she taught him herself. It was First Lady Helen Taft's idea to plant the famous cherry trees in Washington, D. C. Each spring these blossoming trees attract thousands of visitors to the nation's capital. Mrs. Taft also influenced the male members of her family and the White House staff in a strange way: she convinced them to shave off their beards! Shortly after President Wilson suffered a stroke, Edith Wilson unofficially took over most of the duties of the Presidency until the end of her husband's term. Earlier, during World War I, Mrs. Wilson had had sheep brought onto the White House lawn to eat the grass. The sheep not only kept the lawn mowed but provided wool for an auction sponsored by the First Lady. Almost $100,000 was raised for the Red Cross. Dolly Madison saw to it that a magnificent painting of George Washington was not destroyed during the War of 1812. As the British marched toward Washington, D. C., she remained behind to rescue the painting, even after the guards had left. The painting is the only object from the original White House that was not burned. One of the most famous First Ladies was Eleanor Roosevelt, the wife of President Franklin D. Roosevelt. She was active in political and social causes throughout her husband's tenure in office. After his death, she became famous for her humanitarian work in the United Nations. She made life better for thousands of needy people around the world. 1. What is the main idea of this passage? A. The Humanitarian work of the First Ladies is critical in American government. B. Dolly Madison was the most influential president's wife. C. Eleanor Roosevelt transformed the First Lady image. D. The First Ladies are important in American culture. E. The First Ladies are key supporters of the Presidents. Of the many kinds of vegetables grown all over the world, which remains the favorite of young and old alike? Why, the potato, of course. Perhaps you know them as “taters,” “spuds,” or “Kennebees,” or as “chips,” “Idahoes,” or even “shoestrings.” No matter, a potato by any other name is still a potato- the world's most widely grown vegetable. As a matter of fact, if you are an average potato eater, you will put away at least a hundred pounds of them each year. That's only a tiny portion of the amount grown every year, however. Worldwide, the annual potato harvest is over six billion bags- each bag containing a hundred pounds of spuds, some of them as large as four pounds each. Here in the United States, farmers fill about four hundred million bags a year. That may seem like a lot of “taters,” but it leaves us a distant third among world potato growers. Polish farmers dig up just over 800 million bags a year, while the Russians lead the world with nearly 1.5 billion bags. The first potatoes were grown by the Incas of South America, more than four hundred years ago. Their descendants in Ecuador and Chile continue to grow the vegetable as high as fourteen thousand feet up in the Andes Mountains. ( That's higher than any other food will grow.) Early Spanish and English explorers shipped potatoes to Europe, and they found their way to North America in the early 1600s. People eat potatoes in many ways-baked, mashed, and roasted, to name just three. However, in the United States most potatoes are devoured in the form of French fries. One fast-food chain alone sells more than $1 billion worth of fries each year. No wonder, then, that the company pays particular attention to the way its fries are prepared. Before any fry makes it to the people who eat at these popular restaurants, it must pass many separate tests. Fail any one and the spud is rejected. To start with, only russet Burbank potatoes are used. These Idaho potatoes have less water content than other kinds, which can have as much as eighty percent water. Once cut into “shoestrings” shapes, the potatoes are partly fried in a secret blend of oils, sprayed with liquid sugar to brown them, steam dried at high heat, then flash frozen for shipment to individual restaurants. Before shipping, though, every shoestring is measured. Forty percent of a batch must be between two and three inches long. Another forty percent has to be over three inches. What about the twenty percent that are left in the batch? Well, a few short fries in a bag are okay, it seems. So, now that you realize the enormous size and value of the potato crop, you can understand why most people agree that this part of the food industry is no “small potatoes.” 2. What is the main idea of this passage? A. Potatoes from Ireland started the Potato Revolution. B. The average American eats 50 lbs of potatoes a year. C. French fries are made from potatoes. D. Potatoes are a key vegetable in America. E. The various terms for potatoes have a long history. What does the word patent mean to you? Does it strike you as being something rather remote from your interests? If it does, stop and think a moment about some of the commonplace things that you use every day, objects that you take for granted as part of the world around you. The telephone, radio, television, the automobile, and the thousand and one other things (even the humble safety pin) that enrich our lives today once existed only as ideas in the minds of men. If it had not been possible to patent their ideas and thus protect them against copying by others, these inventions might never have been fully developed to serve mankind. If there were no patent protection there would be little incentive to invent and innovate, for once the details of an invention became known, hordes of imitators who did not share the inventor's risks and expenses might well flood the market with their copies of his product and reap much of the benefit of his efforts. The technological progress that has made America great would wither rapidly under conditions such as these. The fundamental principles in the U. S. patent structure came from England. During the glorious reign of Queen Elizabeth I in England, the expanding technology was furthered by the granting of exclusive manufacturing and selling privileges to citizens who had invented new processes or tools- a step that did much to encourage creativity. Later, when critics argued that giving monopoly rights to one person infringed on the rights of others, an important principle was added to the patent structure: The Lord Chief Justice of England stated that society had everything to gain and nothing to lose by granting exclusive privileges to an inventor, because a patent for an invention was granted for something new that society never had before. Another basic principle was brought into law because certain influential people in England had managed to obtain monopoly control over such age-old products as salt, and had begun charging as much as the traffic would bear. The public outcry became so great that the government was forced to decree that monopoly rights could be awarded only to those who created or introduced something really unique. These principles are the mainstays of our modern patent system in the United States. In colonial times patent law was left up to the separate states. The inconsistency, confusion, and unfairness that resulted clearly indicated the need for a uniform patent law, and the men who drew up the Constitution incorporated one. George Washington signed the first patent law on April 10,1790, and less than four months later the first patent was issued to a man named Samuel Hopkins for a chemical process, an improved method of making potash for use in soapmaking. In 1936 the Patent Office was established as a separate bureau. From the staff of eight that it maintained during its first year of operation it has grown into an organization of over 2500 people handling more than 1600 patent applications and granting over 1000 every week. The Patent Office in Washington, D. C., is the world's largest library of scientific and technical data, and this treasure trove of information is open for public inspection. In addition to more than 3 million U. S. patents, it houses more than 7 million foreign patents and thousands of volumes of technical literature. Abraham Lincoln patented a device to lift steam vessels over river shoals, Mark Twain developed a self-pasting scrapbook, and millionaire Cornelius Vanderbilt invented a shoe-shine kit. A patent may be granted for any new and useful process, machine, article of manufacture, or composition of matter ( a chemical compound or combinations of chemical compounds), or any distinct and new variety; of plant, including certain mutants and hybrids. The patent system has also helped to boost the wages of the American worker to an unprecedented level; he can produce more and earn more with the computer, adding machines, drill press or lathe. Patented inventions also help keep prices down by increasing manufacturing efficiency and by stimulating the competition that is the foundation of our free enterprise system. The decades of history have disclosed little need for modification of the patent structure. Our patent laws, like the Constitution from which they grew, have stood the test of time well. They encouraged the creative processes, brought untold benefits to society as a whole, and enabled American technology to outstrip that of the rest of the civilized world. 3. What is the main idea of this passage? A. The patent system encourages free enterprise. B. The Constitution protects the patent system. C. The patent system in England has been influential in American patent development. D. Patents are important tools for inventors. E. Patented inventions protect the inventor, free enterprise, and the creative process. Most people think it's fine to be “busy as a beaver.” Little do they know. Beavers may work hard, but often they don't get much done. Beavers are supposed to be great tree cutters. It is true that a beaver can gnaw through a tree very quickly. (A six-inch birch takes about ten minutes.) But then what? Often the beaver does not make use of the tree. One expert says that beavers waste one out of every five trees they cut. For one thing, they do not choose their trees wisely. One bunch of beavers cut down a cottonwood tree more than one hundred feet tall. Then they found that they could not move it. In thick woods a tree sometimes won't fall down. It gets stuck in the other trees. Of course, doesn't think to cut down the trees that are in the way. So a good tree goes to waste. Some people think that beavers can make a tree fall the way they want it to. Not true. (In fact, a beaver sometimes gets pinned under a falling tree.) When beavers cut a tree near a stream, it usually falls into the water. But they do not plan it that way. The fact is that most trees lean toward the water to start with. Now what about dam building? Most beaver dams are wonders of engineering. The best ones are strongly built of trees, stones, and mud. They are wide at the bottom and narrow at the top. Beavers think nothing of building a dam more than two hundred feet long. One dam, in Montana, was more than two thousand feet long. The largest one ever seen was in New Hampshire. It stretched four thousand feet. It made a lake large enough to hold forty beaver homes. So beavers do build good dams. But they don't always build them in the right places. They just don't plan. They will build a dam across the widest part of the stream. They don't try to find a place where the stream is narrow. So a lot of their hard work is wasted. Beavers should learn that it's not enough to be busy. You have to know what you're doing, too. For example, there was one Oregon beaver that really was a worker. It decided to fix a leak in a man-made dam. After five days of work it gave up. The leak it was trying to block was the lock that boats go through. 4. What is the main idea of this passage? A. Beavers may be hard working animals, but they don't always choose the most efficient mechanisms. B. Beavers are excellent dam builders. C. New Hampshire was the site of the largest beaver dam. D. Beavers are well developed tree cutters. E. Beavers are poor surveyors of aquatic environments in some cases. The raisin business in America was born by accident. It happened in 1873 in the San Joaquin Valley of California. Many farmers raised grapes in this valley. That year, just before the grape harvest, there was a heat wave. It was one of the worst heat waves ever known. It was so hot the grapes dried on the vines. When they were picked, California had its first raisin crop. People were surprised to find how good raisins were. Everybody wanted more. So the San Joaquin farmers went into the raisin business. Today, of course, they do not let the grapes dry on the vines. They treat them with much more care. In late August the grapes start to ripen. They are tested often for sweetness. The growers wait until the sugar content is twenty-one percent. Then they know the grapes are ripe enough to be picked. Skilled workers come to the vineyards. They pick the bunches of grapes by hand. The workers fill their flat pans with grapes. They gently empty the pans onto squares of paper. These squares lie between the long rows of vines. They sit in the sun. Here the grapes stay while the sun does its work. It may take two weeks or longer. The grapes are first dried on one side. When they have reached the right color, they are turned to dry on the other side. The grapes are dried until only fifteen percent of the moisture is left. Then they have turned into raisins. The raisins are rolled up in the paper on which they have dried. Trucks take them from the fields. They are poured into big boxes called sweatboxes. Each box holds one hundred and sixty pounds of raisins. Here, any raisins that are a bit too dry take moisture from those that have a bit too much. After a while they are all just moist enough. The big boxes are trucked next to the packaging plant. They are emptied onto a conveyor belt that shakes the raisins gently. This knocks them from their stems. A blast of air whisks the stems away. The water bath is next. Then the plump brown raisins have a last inspection. They are again checked for moisture and sugar. Then they go on a belt to packing machines. Here they are poured into packages, which are automatically weighed and sealed. The raisins are now ready for market. 5. What is the main idea of this passage? A. The creation of raisins in America was an accident. B. The process of raisin development requires multiple steps. C. Raisins on the grocery store shelf undergo a brief fermentation process. D. Raisins are cleaned thoroughly at the packing plant. E. California has been the leader in American raisin development. In 1976, Sichan Siv was crawling through the jungle, trying to escape from Cambodia. By 1989, however, Siv was working in the White House, in Washington D. C., as an advisor to the President of the United States. How did this strange journey come about? Like millions of Cambodians, Siv was a victim of a bloody civil war. One of the sides in this war was the Cambodian government. The other was a group called the Khmer Rouge. When the Khmer Rouge won the war, the situation in Cambodia got worse. Many people were killed, while others were forced into hard labor. Sometimes entire families were wiped out. Siv came from a large family that lived in the capital of Cambodia. After finishing high school, Siv worked for a while with a Cambodian airline company. Later, he taught English. After that, he took a job with CARE, an American group that was helping victims of the war. Siv had hope to leave Cambodia before the Khmer Rouge took over the country. Unfortunately, he was delayed. As a result, he and his family were taken from their homes and forced to labor in rice fields. After a while, Siv managed to escape. He rode an old bicycle for miles, trying to reach Thailand where he would be free and safe. For three weeks he slept on the ground and tried to hide from the soldiers who were looking for him. Caught at last, he was afraid he would be killed. Instead, he was put into a labor camp, where he worked eighteen hours each day without rest. After several months, he escaped again; this time he made it. The journey, however, was a terrifying one. After three days of staggering on foot through mile after mile of thick bamboo, Siv finally made his way to Thailand. Because he had worked for an American charity group, Siv quickly found work in a refugee camp. Soon he was on his way to the states. He arrived in June of 1976 and got a job-first picking apples and then cooking in a fast-food restaurant. Siv, however, wanted more than this; he wanted to work with people who, like himself, had suffered the hardship of leaving their own countries behind. Siv decided that the best way to prepare for this kind of work was to go to college. He wrote letters to many colleges and universities. They were impressed with his school records from Cambodia, and they were impressed with his bravery. Finally, in 1980, he was able to study at Columbia University in New York City. After finishing his studies at Columbia, Siv took a job with the United Nations. He married an American woman and became a citizen. After several more years, he felt that he was very much a part of his new country. In 1988, Siv was offered a job in the White House working for President Reagan's closest advisors. It was a difficult job, and he often had to work long hours. However the long hard work was worth it, because Siv got the opportunity to help refugees in his work. 6. What is the main idea of this passage? A. Persistence and courage are global ideas. B. Siv covered a large area during his life. C. Siv persevered to become an American citizen D. Siv overcame numerous challenges to come to American and help others. E. Siv persevered to become an American citizen. When you want to hang the American flag over the middle of a street, suspend it vertically with the blue field, called the union, to the north and east-west street. When the flag is displayed with another banner from crossed staffs, the American flag is on the right. Place the staff of the American flag in front of the other staff. Raise the flag quickly and lower it slowly and respectfully. When flying the flag at half-mast, hoist it to the top of the pole for a moment before lowering it to mid-pole. When flying the American flag with banners from states or cities, raise the nation's banner first and lower it last. Never allow the flag to touch the ground. 7. What is the main idea of this passage? A. The American flag is the symbol of American freedom. B. The American flag has fifty stars. C. Placing the American flag inappropriately will draw government intervention. D. American flag should be flown differently in certain situations. ","The flag should be lowered quickly and respectfully. What if someone told you about a kind of grass that grows as tall as the tallest trees? A grass that can be made as strong as steel? A grass from which houses, furniture, boats, and hundreds of other useful things can be made? A grass that you would even enjoy eating? Would you believe that person? You should, for that grass is bamboo, the “wood” of 1,001 uses. Bamboo may look like wood, but it is part of the family of plants that includes wheat, oats, and barley. It is a kind of grass. This grass is not just a material for making useful products. Young bamboo is eaten, often mixed with other vegetables, in many Asian foods. Bamboo grows in many parts of the world. In the United States it grows in an area from Virginia west to Indiana and south to Florida, Louisiana, and Texas. Most bamboo, however, is found in warm, wet climates, especially in Asia and on the islands of the South Pacific Ocean. In most Asian countries, bamboo is nearly as important as rice. Many Asians live in bamboo houses. They sit on bamboo chairs and sleep on bamboo mats. They fence their land with bamboo and use the wood for cages for chickens and pigs. Bamboo is used to build large buildings as well as homes. When it is glued in layers, it becomes as strong as steel. On some islands in the South Pacific, bamboo is even used for water pipes. This extraordinary material has many other uses. It is used to make musical instruments, such as flutes and recorders. Paper made from bamboo has been highly prized by artists for thousands of years. Bamboo is light and strong, and it bends without breaking. It is cheap, floats on water, almost never wears out, and is easy to grow. Nothing else on earth grows quite so fast as bamboo. At times you can even see it grow! Botanists have recorded growths of more than three feet in just twenty-four hours! Bamboo is hollow and has a strong root system that almost never stops growing and spreading. In fact, only after it flowers, an event that may happen only once every thirty years, will bamboo die. There are more than a thousand kinds of bamboo. The smallest is only three inches tall and one-tenth of an inch across. The largest reaches more than two hundred feet in height and seven inches in diameter. No wonder, then, that the lives of nearly half the people on earth would change enormously if there were no longer any bamboo. No wonder, too, that to many people bamboo is a symbol of happiness and good fortune. 8. What is the main idea of this passage? A. Bamboo has at least 2,000 uses. B. Bamboo grows at an amazing rate and is found primarily in Asia. C. Bamboo is an amazing grass that can be used in multiple ways. D. There are at least a 1,000 types of bamboo. E. Bamboo could be considered a flower in some cases. Every year since 1986, some of the world's most daring runners have gathered in the desert of Morocco. They are there to take part in one of the most difficult races in the world. The Marathon of the Sands, as it is called, covers over 125 miles of desert and mountain wilderness. The runners complete the course in fewer than seven days, and they run with their food, clothing, and sleeping bags on their backs. The Marathon of the Sands was founded in 1986 by Patrick Bauer. His idea was to give the runners, who come from all over the world, a special kind of adventure. Most of the runners in this race have found that they form deep friendships with the other runners during their days and nights in the desert. Facing terrible heat and complete exhaustion, they learn much about themselves and each other. For most of the runners, though, the challenge of the race is the main reason for coming. On the first day, for example, they run fifteen miles across a desert of sand, rocks, and thorny bushes. Few runners finish the day without blistered and raw feet. They also suffer from a lack of water. (They are allowed less than nine quarts of water during each day of the race.) Most of all, they are exhausted when they arrive at the campsite for the night. The second day, the runners are up at 6:00 A. M. Within a few hours, it is 100 degrees F, but the runners do not hesitate. They must cover eighteen miles that day. That night, they rest. They must be ready for the next day's run. On the third day, the runners must climb giant sand dunes- the first they have faced. Dust and sand mix with the runners' sweat. Soon their faces are caked with mud. After fifteen miles of these conditions, the runners finally reach their next camp. The race continues like this for four more days. The fourth and fifth days are the worst. On the fourth day, the runners pass through a level stretch and a beautiful, tree-filled oasis, but then, on this and on the next day, they cross more than twenty- one miles of rocks and sand dunes. The temperature soars to 125 degrees F, and many runners cannot make it. Helicopters rush fallen runners to medical help. Runners who make it to the end of the fifth day know that the worst is over. On the sixth day, heat and rocks punish the racers terribly. In the Valley of Dra, the wind picks up and, as the desert heat is thrust against them with great force, they grow more and more exhausted. The seventh day is the last, with only twelve miles to be covered. The dusty, tired, blistered runners set out at daybreak. Near the finish line, children race along with the runners, for everybody has caught the excitement. The ones who have run the whole marathon know they have accomplished what most people could not even dream of. “During the hard moments,” says one contestant who has raced here twice, “I'd think, „Why am I here?' Then I'd realize I was there to find my limits.” 9. What is the main idea of this passage? A. The Marathon of the Sands race tests the limits of human endurance. B. The runners run at their own pace. C. The race causes the strong to stumble and the weak to not finish. D. The seventh day is the hardest day of the race. E. Every runner runs the race to find their human limits. High in the Andes Mountains in Peru stands the ancient city of Machu Picchu. No one knows why this great city was built, nor is it likely that we will ever know. Nevertheless, the deserted city of Machu Picchu is important for what it reveals about the ancient Inca people of South America. The Incas once ruled a great empire that covered a large part of the South American continent. The empire was more than five hundred years old when the first Spanish explorers, looking for gold, went to that continent in the sixteenth century. The Incas were an advanced people. They were skillful engineers who paved their roads and built sturdy bridges. They plowed the land in such a way that rains would not wash away valuable soil. They dug ditches to carry water into dry areas for farming. Even though they did not know about the wheel, the Incas were able to move huge stone blocks- some as heavy as ten tons- up the sides of mountains to build walls. The blocks were fitted so tightly, without cement of any kind, that it would be impossible to slip a knife blade between them! The walls have stood firm through great storms and earthquakes that have destroyed many modern buildings. The Incas were great artists, too. Today, Incan dishes and other kinds of pottery are prized for their wonderful designs. Since both gold and silver were in great supply, the Incas created splendid objects from these precious metals. While it is true that the Incas had no written language, they kept their accounts by using a system of knotted strings of various lengths and colors. The sizes of the knots and the distances between them represented numbers. At its height, the Incan empire included as many as thirty million people. The emperor ruled them with an iron hand. He told his subjects where to live, what to plant, how long they should work-even whom they could marry. Since he owned everything, the emperor gave what he wished when he wished- and in the amount he wished -to his people. In 1533 Spanish explorers led by Francisco Pizarro murdered the emperor of the Incas. Earlier, the heir to the Incan empire had also been killed. The Incas, who had always been entirely dependent on their emperor, now had no recognized leader. The Spaniards easily conquered the empire and plundered its riches. Have the Incas disappeared from South America? Not at all. In Peru alone, once the center of that great empire, eighty percent of the twenty million people are descendants of the Inca people. Evidence of the Incan empire can be found in many other places in South America as well. You can even visit Machu Picchu. The remains of this ancient city still stand high in the mountains of Peru, an awesome tribute to this once powerful empire. 10. What is the main idea of this passage? A. The Incas once inhabited the ancient city of Machu Picchu. B. Peru was the primary country of the Incas. C. The Incan empire can be found in ancient cities and was plundered by the Spanish. D. Spanish conquerors destroyed the Incan empire in the thirteenth century. E. Machu Picchu was the capital of the Incan empire. Exercise 3: In 1892 the Sierra Club was formed. In 1908 an area of coastal redwood trees north of San Francisco was established as Muir Woods National Monument. In the Sierra Nevada mountains, a walking trail from Yosemite Valley to Mount Whitney was dedicated in 1938. It is called John Muir Trail. John Muir was born in 1838 in Scotland. His family name means “moor,” which is a meadow full of flowers and animals. John loved nature from the time he was small. He also liked to climb rocky cliffs and walls. When John was eleven, his family moved to the United States and settled in Wisconsin. John was good with tools and soon became an inventor. He first invented a model of a sawmill. Later he invented an alarm clock that would cause the sleeping person to be tipped out of bed when the timer sounded. Muir left home at an early age. He took a thousand-mile walk south to the Gulf of Mexico in 1867and 1868. Then he sailed for San Francisco. The city was too noisy and crowded for Muir, so he headed inland for the Sierra Nevadas. When Muir discovered the Yosemite Valley in the Sierra Nevadas, it was as if he had come home. He loved the mountains, the wildlife, and the trees. He climbed the mountains and even climbed trees during thunderstorms in order to get closer to the wind. He put forth the theory in the late 1860's that the Yosemite Valley had been formed through the action of glaciers. People ridiculed him. Not until 1930 was Muir's theory proven correct. Muir began to write articles about the Yosemite Valley to tell readers about its beauty. His writing also warned people that Yosemite was in danger from timber mining and sheep ranching interests. In 1901 Theodore Roosevelt became president of the United States. He was interested in conservation. Muir took the president through Yosemite, and Roosevelt helped get legislation passed to create Yosemite National Park in 1906. Although Muir won many conservation battles, he lost a major one. He fought to save the Hetch Valley, which people wanted to dam in order to provide water for San Francisco. In the late 1913 a bill was signed to dam the valley. Muir died in 1914. Some people say losing the fight to protect the valley killed Muir. 1. What happened first? A. The Muir family moved to the United States. B. Muir Woods was created. C. John Muir learned to climb rocky cliffs. D. John Muir walked to the Gulf of Mexico E. Muir visited along the east coast. 2. When did Muir invent a unique form of alarm clock? A. while the family still lived in Scotland B. after he sailed to San Francisco C. after he traveled in Yosemite D. while the Muir family lived in Wisconsin E. after he took the long walk 3. What did John Muir do soon after he arrived in San Francisco? A. He ran outside during an earthquake. B. He put forth a theory about how Yosemite was formed. C. He headed inland for the Sierra Nevadas. D. He began to write articles about the Sierra Nevadas. E. He wrote short stories for the local newspaper. 4. When did John Muir meet Theodore Roosevelt? A. between 1901 and 1906 B. between 1838 and 1868 C. between 1906 and 1914 D. between 1868 and 1901 E. between 1906-1907 5. What happened last? A. John Muir died. B. John Muir Trail was dedicated. C. Muir's glacial theory was proven. D. The Sierra Club was formed. E. John's family visited him. When using a metal file, always remember to bear down on the forward stroke only. On the return stroke, lift the file clear of the surface to avoid dulling the instrument's teeth. Only when working on very soft metals is it advisable to drag the file's teeth slightly on the return stroke. This helps clear out metal pieces from between the teeth. It is best to bear down just hard enough to keep the file cutting at all times. Too little pressure uses only the tips of the teeth; too much pressure can chip the teeth. Move the file in straight lines across the surface. Use a vice to grip the work so that your hands are free to hold the file. Protect your hands by equipping the file with a handle. Buy a wooden handle and install it by inserting the pointed end of the file into the handle hole. 6. These directions show you how to- A. work with a hammer B. use a file C. polish a file D. oil a vise E. repair shop tools 7. When using a file- A. always bear down on the return stroke B. move it in a circle C. remove the handle D. press down on the forward stroke E. wear protective gloves 8. When working on soft metals, you can- A. remove the handle B. clear metal pieces from the teeth C. bear down very hard on the return stroke D. file in circles E. strengthen them with added wood 9. Protect your hands by- A. dulling the teeth B. dragging the teeth on the backstroke C. using a vise D. installing a handle E. wearing safety gloves “Old woman,” grumbled the burly white man who had just heard Sojourner Truth speak, “do you think your talk about slavery does any good? I don't care any more for your talk than I do for the bite of a flea.” The tall, imposing black woman turned her piercing eyes on him. “Perhaps not,” she answered, “but I'll keep you scratching.” The little incident of the 1840s sums up all that Sojourner Truth was: utterly dedicated to spreading her message, afraid of no one, forceful and witty in speech. Yet forty years earlier, who could have suspected that a spindly slave girl growing up in a damp cellar in upstate New York would become one of the most remarkable women in American history? Her name then was Isabella (many slaves had no last names), and by the time she was fourteen she had seen both parents die of cold and hunger. She herself had been sold several times. By 1827, when New York freed its slaves, she had married and borne five children. The first hint of Isabella's fighting spirit came soon afterwards, when her youngest son was illegally seized and sold. She marched to the courthouse and badgered officials until her son was returned to her. In 1843, inspired by religion, she changed her name to Sojourner(meaning “one who stays briefly”) Truth, and, with only pennies in her purse, set out to preach against slavery. From New England to Minnesota she trekked, gaining a reputation for her plain but powerful and moving words. Incredibly, despite being black and female (only white males were expected to be public speakers), she drew thousands to town halls, tents, and churches to hear her powerful, deep-voiced pleas on equality for blacks-and for women. Often she had to face threatening hoodlums. Once she stood before armed bullies and sang a hymn to them. Awed by her courage and her commanding presence, they sheepishly retreated. During the Civil War she cared for homeless ex-slaves in Washington. President Lincoln invited her to the White House to bestow praise on her. Later, she petitioned Congress to help former slaves get land in the West. Even in her old age, she forced the city of Washington to integrate its trolley cars so that black and white could ride together. Shortly before her death at eighty-six, she was asked what kept her going. “I think of the great things,” replied Sojourner. 10. The imposing black woman promised to keep the white man- A. searching B. crying C. hollering D. scratching E. fleeing 11. This incident occurred in the- A. 1760s B. 1900s C. 1840s D. 1920s E. 1700s 12. Sojourner Truth was raised in a damp cellar in- A. New York B. Georgia C. New Jersey D. Idaho E. Maryland 13. Isabella lost both parents by the time she was- A. twenty-seven B. two C. seven D. fourteen E. nineteen 14. When New York freed its slaves, Isabella had- A. problems B. no children C. five children D. an education E. three children 15. Her change in name was inspired by- A. a fighting spirit B. religion C. her freedom D. officials E. friends 16. She traveled from New England to- A. Canada B. California C. Minnesota D. Alaska E. Virginia 17. She forced the city of Washington to- A. integrate its trolleys B. give land grants C. care for ex-slaves D. provide food for ex-slaves E. clean its trolleys 18. She preached against- A. smoking B. slavery C. alcohol D. hoodlums E. women having no rights 19. Sojourner Truth died at- A. 48 B. 72 C. 63 D. 86 E. 88 The Galapagos Islands are in the Pacific Ocean, off the western coast of South America. They are a rocky, lonely spot, but they are also one of the most unusual places in the world. One reason is that they are the home of some of the last giant tortoises left on earth. Weighing hundreds of pounds, these tortoises, or land turtles, wander slowly around the rocks and sand of the islands. Strangely, each of these islands has its own particular kinds of tortoises. There are seven different kinds of tortoises on the eight islands, each kind being slightly different from the other. Hundreds of years ago, thousands of tortoises wandered around these islands. However, all that changed when people started landing there. When people first arrived in 1535, their ships had no refrigerators. This meant that fresh food was always a problem for the sailors on board. The giant tortoises provided a solution to this problem. Ships would anchor off the islands, and crews would row ashore and seize as many tortoises as they could. Once the animals were aboard the ship, the sailors would roll the tortoises onto their backs. The tortoises were completely helpless once on their backs, so they could only lie there until used for soups and stews. Almost 100,000 tortoises were carried off in this way. The tortoises faced other problems, too. Soon after the first ships, settlers arrived bringing pigs, goats, donkeys, dogs and cats. All of these animals ruined life for the tortoises. Donkey and goats ate all the plants that the tortoises usually fed on, while the pigs. Dogs and cats consumed thousands of baby tortoises each year. Within a few years, it was hard to find any tortoise eggs-or even any baby tortoises. By the early 1900s, people began to worry that the last of the tortoises would soon die out. No one, however, seemed to care enough to do anything about the problem. More and more tortoises disappeared, even though sailors no longer needed them for food. For another fifty years, this situation continued. Finally, in the 1950s, scientist decided that something must be done. The first part of their plan was to get rid of as many cats, dogs and other animals as they could. Next, they tried to make sure that more baby tortoises would be born. To do this, they started looking for wild tortoise eggs. They gathered the eggs and put them in safe containers. When the eggs hatched, the scientists raised the tortoises in special pens. Both the eggs and tortoises were numbered so that the scientists knew exactly which kinds of tortoises they had-and which island they came from. Once the tortoises were old enough and big enough to take care of themselves, the scientists took them back to their islands and set them loose. This slow, hard work continues today, and, thanks to it, the number of tortoises is now increasing every year. Perhaps these wonderful animals will not disappear after all. 20. What happened first? A. Sailors took tortoises aboard ships. B. The tortoise meat was used for soups and stews. C. Tortoises were put onto their backs. D. Settlers brought other animals to the islands. E. Pigs had been all the sailors had to eat. 21. What happened soon after people brought animals to the islands? A. Tortoise eggs were kept in safe containers. B. Scientists took away as many animals as they could. C. The animals ate the tortoises' food and eggs. D. The tortoises fought with the other animals. E. The tortoises continued to wander freely. 22. When did people start to do something to save the tortoises? A. in the 1500s B. in the 1950s C. in the early 1900s D. in the 1960s E. in the 1400s 23. What happens right after the tortoise eggs hatch? A. The scientists take the tortoises back to their islands. B. The scientists get rid of cats, dogs, and other animals. C. The sailors use the tortoises for food. D. The scientist raised the tortoises in special pens. E. The scientist encouraged the villagers to help. 24. What happened last? A. The tortoises began to disappear. B. The number of tortoises began to grow. C. Scientists took away other animals. D. Tortoises were taken back to their home islands. E. The number of tortoises began to decrease. The first person in the group starts off by naming anything that is geographical. It could be a city, state, country, river, lake, or any proper geographical term. For example, the person might say,”Boston.” The second person has ten seconds to think of how the word ends and come up with another geographical term starting with that letter. The second participant might say, “Norway,” since the geographical term has to start with “N.” The third person would have to choose a word beginning with “ Y.” If a player fails to think of a correct answer within the time limit, that player is out of the game. The last person to survive is the champion. 25. This game may help you with- A. history B. music C. geography D. sports E. current events 26. The person trying to answer needs- A. no time limit B. to know geography only C. to ignore the last letters of words D. to know something about spelling and geography E. to be a good speller 27. Before you choose your own word, think about how- A. the last word starts B. the last word ends C. smart you are D. long the last word is E. the spelling of the first word 28. The answer must be- A. in New York B. within the United States C. proper geographical terms D. in the same region E. along a coast line Charles A. Lindbergh is remembered as the first person to make a nonstop solo flight across the Atlantic, in 1927. This feat, when Lindbergh was only twenty-five years old, assured him a lifetime of fame and public attention. Charles Augustus Lindbergh was more interested in flying airplanes than he was in studying. He dropped out of the University of Wisconsin after two years to earn a living performing daredevil airplane stunts at country fairs. Two years later, he joined the United States Army so that he could go to the Army Air Service flight- training school. After completing his training, he was hired to fly mail between St. Louis and Chicago. Then came the historic flight across the Atlantic. In 1919, a New York City hotel owner offered a prize of $25,000 to the first pilot to fly nonstop from New York to Paris. Nine St. Louis business leaders helped pay for the plane Lindbergh designed especially for the flight. Lindbergh tested the plane by flying it from San Diego to New York, with an overnight stop in St. Louis. The flight took only 20 hours and 21 minutes, a transcontinental record. Nine days later, on May 20,1927, Lindbergh took off from Long Island, New York, at 7:52 A. M. He landed at Paris on May 21 at 10:21 P. M. He had flown more than 3,600 miles in less than thirty four hours. His flight made news around the world. He was given awards and parades everywhere he went. He was presented with the U. S. Congressional Medal of Honor and the first Distinguished Flying Cross. For a long time, Lindbergh toured the world as a U. S. goodwill ambassador. He met his future wife, Anne Morrow, in Mexico, where her father was the United States ambassador. During the 1930s, Charles and Anne Lindbergh worked for various airline companies, charting new commercial air routes. In 1931, for a major airline, they charted a new route from the east coast of the United States to the Orient. The shortest, most efficient route was a great curve across Canada, over Alaska, and down to China and Japan. Most pilots familiar with the Arctic did not believe that such a route was possible. The Lindberghs took on the task of proving that it was. They arranged for fuel and supplies to be set out along the route. On July 29, they took off from Long Island in a specially equipped small seaplane. They flew by day and each night landed on a lake or a river and camped. Near Nome, Alaska, they had their first serious emergency. Out of daylight and nearly out of fuel, they were forced down in a small ocean inlet. In the next morning's light, they discovered they had landed on barely three feet of water. On September 19, after two more emergency landings and numerous close calls, they landed in China with the maps for a safe airline passenger route. Even while actively engaged as a pioneering flier, Lindbergh was also working as an engineer. In 1935, he and Dr. Alexis Carrel were given a patent for an artificial heart. During World War I in the 1940s, Lindbergh served as a civilian technical advisor in aviation. Although he was a civilian, he flew over fifty combat missions in the Pacific. In the 1950s, Lindbergh helped design the famous 747 jet airliner. In the late 1960s, he spoke widely on conservation issues. He died August 1974, having lived through aviation history from the time of the first powered flight to the first steps on the moon and having influenced a big part of that history himself. 29. What did Lindbergh do before he crossed the Atlantic? A. He charted a route to China. B. He graduated from flight-training school. C. He married Anne Morrow. D. He acted as a technical advisor during World War II. E. He was responsible for the fuel supply for planes. 30. What happened immediately after Lindbergh crossed the Atlantic? A. He flew the mail between St. Louis and Chicago. B. He left college. C. He attended the Army flight-training school. D. He was given the Congressional Medal of Honor. E. He married Anne Morrow. 31. When did Charles meet Anne Morrow? A. before he took off from Long Island B. after he worked for an airline C. before he was forced down in an ocean inlet D. after he received the first Distinguished Flying Cross E. when visiting his parents 32. When did the Lindberghs map an air route to China? A. before they worked for an airline B. before Charles worked with Dr. Carrel C. after World War II D. while designing the 747 E. when he was thirty 33. What event happened last? A. Lindbergh patented an artificial heart. B. The Lindberghs mapped a route to the Orient. C. Lindbergh helped design the 747 airline. D. Lindbergh flew fifty combat missions. E. Charles finally was given an honorary degree from college. Always read the meter dials from the right to the left. This procedure is much easier, especially if any of the dial hands are near the zero mark. If the meter has two dials, and one is smaller than the other, it is not imperative to read the smaller dial since it only registers a small amount. Read the dial at the right first. As the dial turns clockwise, always record the figure the pointer has just passed. Read the next dial to the left and record the figure it has just passed. Continue recording the figures on the dials from right to left. When finished, mark off the number of units recorded. Dials on water and gas meters usually indicate the amount each dial records. 34. These instructions show you how to – A. read a meter B. turn the dials of a meter C. install a gas meter D. repair a water meter E. be prepared for outside employment 35. Always read the meter dials- A. from top to bottom B. from right to left C. from left to right D. from the small to the large dial E. from the large dial to the small dial 36. As you read the first dial, record the figures A. on the smaller dial B. the pointer is approaching C. the pointer has just passed D. at the top E. at the bottom 37. When you have finished reading the meter, mark off- A. the number of units recorded B. the figures on the small dial C. the total figures D. all the zero marks E. the last reading of the month The village of Vestmannaeyjar, in the far northern country of Iceland, is as bright and clean and up-to-date as any American or Canadian suburb. It is located on the island of Heimaey, just off the mainland. One January night in 1973, however, householders were shocked from their sleep. In some backyards red-hot liquid was spurting from the ground. Flaming “skyrockets” shot up and over the houses. The island's volcano, Helgafell, silent for seven thousand years, was violently erupting! Luckily, the island's fishing fleet was in port, and within twenty-four hours almost everyone was ferried to the mainland. But then the agony of the island began in earnest. As in a nightmare, fountains of burning lava spurted three hundred feet high. Black, baseball-size cinders rained down. An evil-smelling, eye-burning, throat-searing cloud of smoke and gas erupted into the air, and a river of lava flowed down the mountain. The constant shriek of escaping steam was punctuated by ear-splitting explosions. As time went on, the once pleasant village of Vestmannaeyjar took on a weird aspect. Its street lamps still burning against the long Arctic night, the town lay under a thick blanket of cinders. All that could be seen above the ten-foot black drifts were the tips of street signs. Some houses had collapsed under the weight of cinders; others had burst into flames as the heat ignited their oil storage tanks. Lighting the whole lurid scene, fire continued to shoot from the mouth of the looming volcano. The eruption continued for six months. Scientists and reporters arrived from around the world to observe the awesome natural event. But the town did not die that easily. In July, when the eruption ceased, the people of Heimaey Island returned to assess the chances of rebuilding their homes and lives. They found tons of ash covering the ground. The Icelanders are a tough people, however, accustomed to the strange and violent nature of their Arctic land. They dug out their homes. They even used the cinders to build new roads and airport runways. Now the new homes of Heimaey are warmed from water pipes heated by molten lava. 38. The village is located on the island of- A. Vestmannaeyjar B. Hebrides C. Heimaey D. Helgafell E. Heimma 39. The color of the hot liquid was- A. orange B. black C. yellow D. red E. gray 40. This liquid was coming from the – A. mountains B. ground C. sea D. sky E. ocean 41. The island's volcano had been inactive for- A. seventy years B. seven thousand years C. seven thousand months D. seven hundred years E. seventy decades 42. Black cinders fell that were the size of__ A. baseballs B. pebbles C. golf balls D. footballs E. hail-stones 43. Despite the eruption- A. buses kept running B. the radio kept broadcasting C. the police kept working D. street lamps kept burning E. the television kept broadcasting 44. This volcanic eruption lasted for six ___. A. weeks B. hours C. months D. days E. years Answer Key Exercise 1: 1. B 2. A 3. A 4. C 5. C 6. B 7. A 8. A 9. B 10. B 11. A 12. A 13. C 14. C 15. B 16. A 17. B 18. B 19. C 20. A 21. B 22. B 23. C 24. A 25. B 26. C 27. B 28. B 29. B 30. B 31. A 32. A 33. B 34. A 35. A 36. C 37. B 38. B 39. B 40. B 41. A 42. C 43. C 44. B 45. A Exercise 2: 1. D 2. D 3. E 4. A 5. B 6. D 7. D 8. C 9. A 10. C Exercise 3: 1. C 2. D 3. C 4. A 5. B 6. B 7. D 8. B 9. D 10. D 11. C 12. A 13. D 14. C 15. B 16. C 17. A 18. B 19. D 20. A 21. C 22. B 23. D 24. B 25. C 26. D 27. B 28. C 29. B 30. D 31. D 32. B 33. C 34. A 35. B 36. C 37. A 38. C 39. D 40. B 41. B 42. A 43. D 44. C Vocabulary Test Directions: Choose the word most opposite in meaning to the capitalized word. 1. GRATUITOUS: (A) voluntary (B) arduous (C) solicitous (D) righteous (E) befitting 2. FALLOW: (A) fatuous (B) productive (C) bountiful (D) pertinacious (E) opprobrious 3. METTLE: (A) ad hoc (B) perdition (C) woe (D) trepidation (E) apathy 4. SAVANT: (A) dolt (B) sage (C) attaché (D) apropos comment (E) state of confusion 5. RIFE: (A) multitudinous (B) blemished (C) sturdy (D) counterfeit (E) sparse 6. ABRIDGE: (A) distend (B) assail (C) unfetter (D) enfeeble (E) prove 7. PRODIGAL: (A) bountiful (B) dependent (C) provident (D) superfluous (E) profligate 8. REQUIEM: (A) humility (B) prerequisite (C) resolution (D) reign (E) hiatus 9. METE: (A) indict (B) convoke (C) hamper (D) disseminate (E) deviate 10. SEVERANCE: (A) continuation (B) dichotomy (C) astringency (D) disclosure (E) remonstrance Match each word in the first column with its definition in the second column. 1. ANATHEMA A. hard 2. ANNIHILATE B. curse 3. ANOMALOUS C. gully 4. APATHETIC D. suffocate 5. ARCHAIC E. antiquated 6. ARDUOUS F. destroy 7. ARROYO G. abnormal 8. ASPHYXIATE H. unconcerned 9. ASTRINGENT I. make amends 10. ATONE J. causing contraction Directions: Choose the word most opposite in meaning to the capitalized word. 1. HYPOCRITICAL: (A) forthright (B) judicious (C) circumspect (D) puritanical (E) unorthodox 2. VOLUMINOUS: (A) obscure (B) cantankerous (C) unsubstantial (D) tenacious (E) opprobrious 3. FANATICISM: (A) delusion (B) fascism (C) remorse (D) cynicism (E) indifference 4. INTERMINABLE: (A) finite (B) jejune (C) tranquil (D) incessant (E) imprudent 5. ORNATE: (A) Spartan (B) blemished (C) sturdy (D) counterfeit (E) temporary 6. MUTABILITY: (A) simplicity (B) apprehension (C) frailty (D) maverick (E) tenacity 7. VIRULENT: (A) benign (B) intrepid (C) malignant (D) hyperbolic (E) tentative 8. ABSTEMIOUS: (A) timely (B) immoderate (C) bellicose (D) servile (E) irreligious 9. VERBOSE: (A) subliminal (B) myopic (C) pithy (D) dauntless (E) ubiquitous 10. VISCID: (A) subtle (B) faint (C) slick (D) vicious (E) difficult Match each word in the first column with its definition in the second column. 1. BESMIRCH A. unheeded prophet 2. BICAMERAL B. peevish 3. BILATERAL C. pertaining to dogs 4. BOOTLESS D. plot 5. BRANDISH E. farce 6. BURLESQUE F. display menacingly 7. CABAL G. unavailing 8. CANINE H. two-sided 9. CANTANKEROUS I. having two legislative branches 10. CASSANDRA J. sully Directions: Choose the word most opposite in meaning to the capitalized word. 1. DERISION: (A) urgency (B) admonishment (C) uniqueness (D) diversity (E) acclaim 2. ANTIPATHY: (A) fondness (B) disagreement (C) boorishness (D) provocation (E) opprobrium 3. CAJOLE: (A) implore (B) glance at (C) belittle (D) ennoble (E) engender 4. CENSURE: (A) prevaricate (B) titillate (C) aggrandize (D) obscure (E) sanction 5. ADULATION: (A) immutability (B) reluctance (C) reflection (D) defamation (E) indifference 6. NOISOME: (A) salubrious (B) affable (C) multifarious (D) provident (E) officious 7. CONSECRATE: (A) curb (B) destroy (C) curse (D) inveigh (E) exculpate 8. ILLUSTRIOUS: (A) bellicose (B) ignoble (C) theoretical (D) esoteric (E) immaculate 9. DEIGN: (A) inveigh (B) gainsay (C) speculate (D) reject (E) laud 10. SUBTERFUGE: (A) bewilderment (B) artlessness (C) deceit (D) felicitation (E) jeopardy Match each word in the first column with its definition in the second column. 1. COMMANDEER A. seize for military use 2. COMMUNION B. apologetic 3. COMPATRIOT C. perfect 4. CONCERTED D. accord 5. CONCORD E. done together 6. CONFLUENCE F. pile 7. CONGERIES G. flowing together 8. CONSONANT H. harmonious 9. CONSUMMATE I. countryman 10. CONTRITE J. fellowship Directions: Choose the word most opposite in meaning to the capitalized word. 1. UPSHOT: (A) consequence (B) descent (C) annihilation (D) termination (E) inception 2. WHET: (A) Obscure (B) blunt (C) desiccate (D) imbibe (E) enervate 3. PRODIGY: (A) vacuous comment (B) hegemony (C) plane (D) common occurrence (E) capitulation 4. AMBULATORY: (A) immutable (B) obdurate (C) hospitalized (D) pedantic (E) stationary 5. PLATITUDE: (A) sincere comment (B) enigmatic comment (C) hostile comment (D) disingenuous comment (E) original comment 6. SEEMLY: (A) Redoubtable (B) flaccid (C) imperceptible (D) indigenous (E) unbecoming 7. CHAMPION: (A) relinquish (B) contest (C) oppress (D) modify (E) withhold 8. AIR: (A) release (B) differ (C) expose (D) betray (E) enshroud 9. PERTURBATION: (A) impotence (B) obstruction (C) prediction (D) equanimity (E) chivalry 10: TEMPESTUOUS: (A) prodigal (B) reticent (C) serene (D) phenomenal (E) accountable Match each word in the first column with its definition in the second column. 1. DEBUNK A. decode 2. DECIPHER B. refute 3. DEDUCE C. conclusive 4. DEFINITIVE D. conclude 5. DEFUNCT E. to draw a line around 6. DELINEATE F. extinct 7. DENOMINATION G. belittle 8. DEPRECATE H. sect 9. DESOLATE I. pertaining to debate 10. DIALECTIC J. forsaken Directions: Choose the word most opposite in meaning to the capitalized word. 1. CURB: (A) bridle (B) encourage (C) reproach (D) ameliorate (E) perjure 2. DOCUMENT: (A) copy (B) implement (C) gainsay (D) blanch (E) rant 3. FLUID: (A) radiant (B) smooth (C) solid (D) balky (E) craggy 4. BOLT: (A) linger (B) refrain from (C) subdue (D) strip (E) transgress 5. TABLE: (A) Palliate (B) acclimate (C) garner (D) propound (E) expedite 6. HARBOR: (A) provide shelter (B) banish (C) acquiesce (D) extol (E) capitulate 7. STEEP: (A) desiccate (B) intensify (C) pontificate (D) whet (E) hamper 8. RENT: (A) reserved (B) restored (C) razed (D) busy (E) kinetic 9. EXACT: (A) extract (B) starve (C) lecture (D) menace (E) condone Match each word in the first column with its definition in the second column. 1. DORMANT A. exuberant 2. DOUGHTY B. puzzling 3. DUET C. comprehensive 4. EBULLIENT D. asleep 5. EFFEMINATE E. omission of words 6. ELLIPSIS F. unmanly 7. EMANCIPATE G. charm 8. ENCHANT H. liberate 9. ENCYCLOPEDIC I. twosome 10. ENIGMATIC J. resolute Directions: Choose the word most opposite in meaning to the capitalized word. 1. DISCORD: (A) agreement (B) supposition (C) strife (D) scrutiny (E) antithesis 2. KEEN: (A) concentrated (B) languid (C) rash (D) caustic (E) voracious 3. IRRELEVANT: (A) moot (B) onerous (C) impertinent (D) germane (E) true 4. FACILITATE: (A) appease (B) expedite (C) extol (D) foil (E) precipitate 5. FEND: (A) absorb (B) disperse (C) intensify (D) reflect (E) halt 6. PORTLY: (A) ill (B) thin (C) dull (D) rotund (E) insipid 7. DEPLETE: (A) tax (B) annotate (C) replenish (D) lecture (E) vanquish 8. INCESSANT: (A) intermittent (B) continual (C) increasing (D) enclosing (E) expanding 9. PERJURE: (A) absolve (B) forswear (C) impeach (D) authenticate (E) mortify 10. PLETHORA: (A) dishonor (B) paucity (C) glut (D) resolve (E) deluge Match each word in the first column with its definition in the second column. 1. EXHORT A. free from blame 2. EXONERATE B. strongly urge 3. EXPOSTULATE C. agitator 4. EXTRADITE D. untamed 5. EXULT E. debacle 6. FACTITIOUS F. inane 7. FATUOUS G. artificial 8. FERAL H. deport 9. FIASCO I. rejoice 10. FIREBRAND J. protest Directions: Choose the word most opposite in meaning to the capitalized word. 1. ASSIMILATE: (A) strive (B) adapt (C) synchronize (D) estrange (E) officiate 2. INADVERTENT: (A) accidental (B) disingenuous (C) forthright (D) inconsiderate (E) calculated 3. ABSCOND: (A) pilfer (B) replace (C) glean (D) substitute (E) surrender 4. FOMENT: (A) exhort (B) dissuade (C) cower (D) abet (E) fixate 5. EXTENUATE: (A) alleviate (B) preclude (C) worsen (D) subdue (E) justify 6. NONPAREIL: (A) consummate (B) juvenile (C) dutiful (D) ordinary (E) choice 7. REPUDIATE: (A) denounce (B) deceive (C) embrace (D) fib (E) generalize 8. NOXIOUS: (A) diffuse (B) latent (C) beneficial (D) unique (E) unjust 9. SUFFRAGE: (A) absence of charity (B) absence of franchise (C) absence of pain (D) absence of success (E) absence of malice 10. GLEAN: (A) gaffe (B) furor (C) gather (D) frolic (E) foist Match each word in the first column with its definition in the second column. 1. GRANDIOSE A. drink 2. GRIEVOUS B. pertaining to marriage 3. HALCYON C. arrogance 4. HARLEQUIN D. prejudiced 5. HEDONISM E. teaching device, method 6. HEURISTIC F. the pursuit of pleasure in life 7. HIDEBOUND G. clown 8. HUBRIS H. serene 9. HYMENEAL I. heinous 10. IMBIBE J. impressive Match each word in the first column with its definition in the second column. 1. INCONGRUOUS A. harden 2. INCONSPICUOUS B. relentless 3. INDECOROUS C. hostile 4. INDIGNANT D. cannot be fully understood 5. INDURATE E. out of place, absurd 6. INEXORABLE F. not noticeable 7. INIMICAL G. unseemly 8. INSCRUTABLE H. resentment of injustice 9. INSOUCIANT I. nonchalant 10. INSUPERABLE J. insurmountable Match each word in the first column with its definition in the second column. . 1. LACHRYMOSE A. trickery 2. LAGGARD B. roué 3. LASCIVIOUS C. very small 4. LEGERDEMAIN D. tearful 5. LIBERTINE E. loafer 6. LILLIPUTIAN F. lustful 7. LOQUACIOUS G. talkative 8. MACHIAVELLIAN H. comical misuse of a word 9. MAGISTERIAL I. arbitrary, dictatorial 10. MALAPROPISM J. politically crafty, cunning Match each word in the first column with its definition in the second column. 1. MISCELLANY A. peerless 2. MISSIVE B. to gather one‟s forces 3. MOOT C. newly coined expression 4. MOUNTEBANK D. self-love 5. MULTIFARIOUS E. loyal followers 6. MUSTER F. letter 7. MYRMIDONS G. diverse 8. NARCISSISM H. charlatan 9. NEOLOGISM I. disputable 10. NONPAREIL J. mixture of items Match each word in the first column with its definition in the second column. 1. ORDNANCE A. a model 2. ORTHODOX B. local speech 3. OUTMODED C. convulsion 4. PALAVER D. stingy 5. PANEGYRIC E. agent causing disease 6. PARADIGM F. artillery 7. PARLANCE G. conventional 8. PAROXYSM H. out-of-date 9. PARSIMONIOUS I. babble 10. PATHOGEN J. praise Match each word in the first column with its definition in the second column. 1. PHOENIX A. cliff 2. PILLORY B. inclination 3. PITTANCE C. warning 4. PLAUDIT D. acclaim 5. PLETHORA E. overabundance 6. POGROM F. after death 7. POSTHUMOUS G. massacre 8. PRECIPICE H. rebirth 9. PREDILECTION I. punish by ridicule 10. PREMONITION J. trifle Match each word in the first column with its definition in the second column. 1. PROTEAN A. bulge 2. PROTUBERANCE B. changing readily 3. PROVISIONAL C. steal 4. PUNDIT D. majority 5. PURLOIN E. temporary 6. PURPORT F. a cessation of activity 7. QUAVER G. line 8. QUEUE H. tremble 9. QUIETUS I. claim to be 10. QUORUM J. politically astute person Match each word in the first column with its definition in the second column. 1. REGIME A. vulgar 2. REJOINDER B. quick reply 3. REMUNERATION C. uneasy 4. RENDEZVOUS D. necessary 5. RENT E. miscreant 6. REPROBATE F. rupture 7. REQUISITE G. a meeting 8. RESTIVE H. compensation 9. RETRIBUTION I. retort 10. RIBALD J. a government Match each word in the first column with its definition in the second column. 1. SCRUPLES A. figure of speech 2. SCYTHE B. proper, attractive 3. SEEMLY C. long, curved blade 4. SENTENTIOUS D. left-handed 5. SERENDIPITY E. pertaining to the stars 6. SHIBBOLETH F. signer 7. SIDEREAL G. making fortunate discoveries 8. SIGNATORY H. password 9. SIMILE I. misgivings 10. SINISTRAL J. concise Match each word in the first column with its definition in the second column. 1. STAVE A. distress 2. STEVEDORE B. diligent 3. STRAIT C. ward off 4. STUDIOUS D. longshoreman 5. SUBJUGATE E. various 6. SUBTERFUGE F. overabundant 7. SUNDRY G. suppress 8. SUPERFLUOUS H. cunning 9. SUPINE I. dreamlike 10. SURREAL J. lying on the back Match each word in the first column with its definition in the second column. 1. SWATCH A. to foil 2. SYNOD B. anguish 3. TACIT C. concise 4. TALON D. provisional 5. TAURINE E. agitated 6. TEMPESTUOUS F. bull-like 7. TENTATIVE G. claw 8. TERSE H. understood without being spoken Match each word in the first column with its definition in the second column. 1. TIDINGS A. incisive 2. TITER B. omnipresent 3. TITULAR C. lethargic 4. TORPID D. figurehead 5. TRADUCE E. unrestrained 6. TRENCHANT F. news 7. UBIQUITOUS G. laugh nervously 8. ULULATE H. ceaseless 9. UNABATED I. wail 10. UNBRIDLED J. slander Match each word in the first column with its definition in the second column. 1. UNCOUTH A. disheveled 2. UNDULY B. capable of surviving 3. UNFLAGGING C. awkward 4. UNKEMPT D. uncultured 5. UNSTINTING E. truthfulness 6. UNTENABLE F. whim 7. UNWIELDY G. unrelenting 8. VAGARY H. cannot be achieved 9. VERACITY I. generous 10. VIABLE J. excessive Sentence Completion Directions for questions 1 to 25: Fill in the blanks with appropriate verbs. 1. I _____ him to come to the market with me. 1) warned 2) wished 3) requested 4) liked 2. As the floor was dirty she _____ the room quickly 1) rode 2) dusted 3) shoved 4) swept 3. He is going to start _____ around for a new job 1) making 2) going 3) looking 4) talking 4. She _____ the tray down on a table next to the 1) slowed 2) kept 3) set 4) shock 5. We have _____ some good times together, she and I 1) looked 2) laughed 3) smiled 4) seen 6. That girl really _____ after her mother 1) takes 2) talks 3) goes 4) backs 7. The UN has called on the warring factions to _____ aside their differences 1) keep 2) put 3) talk 4) give 8. The pastry was so fluffy that it _____ in my mouth 1) broke 2) melted 3) disappeared 4) filled 9. I got a number of addresses _____ for the festival season 1) bought 2) brought 3) stitched 4) borrowed 10. It was a bitter pill to _____ 1) swallow 2) take 3) eat 4) make 11. We _____ the station in time but the train was an hour late 1) came 2) went 3) reached 4) returned 12. There was a sale going on; I _____ some clothes at throw away prices 1) bought on 2) picked up 3) stitched 4) caught 13. They always _____ fault with me 1) show 2) tell 3) say 4) find 14. The principal _____ to speak to you 1) wanting 2) is wanting 3) wants 4) want 15. When I get home, my pet _____ at the door waiting for me 1) sits 2) has been sitting 3) will sit 4) will be sitting 16. I _____ a new car last month 1) had bought 2) have bought 3) bought 4) would have bought 17. If the _____ your plans, he will be surprised 1) hears for 2) would hear 3) hears of 4) will hear 18. She _____ unconscious since four „0‟ clock 1) is 2) has been 3) was 4) had been 19. He had some work, so he _____ out five minutes ago 1) has gone 2) had gone 3) went 4) was going 20. We were _____ the radio all evening for news 1) listening 2) listening to 3) hearing 4) hearing to 21. Grandma was very, very _____ because the little boy broke the vase. 1) pleased 2) cross 3) hurt 4) hated 22. The bus was so _____ that there was no place even to stand 1) applied 2) needed 3) used 4) crowded 23. The Indian team won the toss and _____ to bat first 1) left 2) fought 3) thought 4) opted 24. I _____ my fingers to the one on that particular project 1) burnt 2) spent 3) worked 4) tired 25. She _____ my watch when I was not looking 1) protested 2) stole 3) knocked 4) gave Directions for questions 1 to 25: Fill in the blanks with appropriate adjectives. 1. Marijuna has few with drawl effects and this has given rise to the _____ belief that it is not an addictive. 1) mistake 2) mistaken 3) misunderstood 4) mitigating 2. The _____ diet has too little fibre in it. 1) modernistic 2) modal 3) modern-day 4) mock 3. An _____ crowd assembled at the gate on Monday. 1) ordinary 2) ornery 3) ornate 4) orderly 4. I have a _____ hunting knife 1) raw 2) rationalistic 3) raven 4) razor-sharp 5. Have a sandwich; you must be _____. 1) thirsty 2) realistic 3) accomplished 4) unguarded 6. Although he is bind he is an _____ singer. 1) accident prone 2) accessible 3) accomplished 4) unguarded 7. The disappearance of the letter made the situation all the more _____. 1) piquant 2) pious 3) pioneering 4) pitiful 8. The Afghani refugees are living in _____ conditions. 1) pitch-black 2) pivotal 3) pitiable 4) funny 9. America is conducting _____ raids on Afghanistan 1) reticent 2) metro-active 3) revealing 4) retaliatory 10. He is an _____ athlete who also paints very well. 1) all-rounder 2) all time 3) all-round 4) all-star 11. She writes equally well with both hands; she is _____. 1) ambivalent 2) ambiguous 3) ambidextrous 4) articulate 12. Mandela‟s release was a/an _____ event in South Africa‟s history 1) pithy 2) pivotal 3) funny 4) interesting 13. This is a _____ disease 1) water-born 2) born and bread 3) water-borne 4) born-again 14. I am sure they will be _____ to rational argument 1) ambivalent 2) ambitious 3) amenable 4) ambient 15. They put up a/an I am sure they will be _____ to rational argument performance of King Lear 1) ambient 2) altruistic 3) amicable 4) sensible 16. She was tall, blonde and I am sure they will be _____ to rational argument looking. 1) interesting 2) beautiful 3) athletic 4) atavistic 17. Most refugees live in _____ conditions 1) worst 2) worse 3) dirty 4) atrocious 18. His paintings are _____ 1) amateurish 2) anaerobic 3) analgesic 4) antistatic 19. I think he requires a _____ diet. 1) great 2) large 3) hot 4) nutritious 20. The _____ friends that I have are very helpful. 1) little 2) many 3) few 4) most 21. I pretended not to notice but I saw that he had given me a _____ look. 1) balding 2) baleful 3) balmy 4) bald 22. She came In wet and _____. 1) bedraggled 2) becoming 3) cheerful 4) bereft 23. I am fed up with being _____ all the time. 1) hungry 2) thirsty 3) broke 4) broken-hearted 24. He waged a _____ fight against crime but was unsuccessful 1) ceaseless 2) central 3) censorious 4) certain 25. I wrote a _____ note on his success 1) communicable 2) congratulatory 3) commiseratory 4) committed Directions for questions 1 to 25: Fill in the blanks with suitable adverbs. 1. The guests were welcomed _________ by the host 1) cordially 2) casually 3) keenly 4) voluntarily 2. The sky, which thundered _________, indicated a terrible storm. 1) radiantly 2) menacingly 3) vigorously 4) alluringly 3. The Minister _________ stated that stringent action would be taken against the erring officials. 1) ambiguously 2) impudently 3) sarcastically 4) categorically 4. The waiter was tipped _________ by the rich man. 1) beautifully 2) handsomely 3) gently 4) prompously 5. The man was so _________ dressed that he almost looked like a clown. 1) garishly 2) modestly 3) decently 4) suavely 6. The brave warrior _________ fought against the enemies. 1) haltingly 2) valiantly 3) indiscriminately 4) distinctly 7. He _________ imposed strict discipline 1) rigorously 2) caustically 3) casually 4) abundantly 8. The sluggard did nothing constructive, except rambling on the strets _________. 1) aimlessly 2) religiously 3) perversely 4) spuriously 9. A country can be termed truly secular when people of all religions lived _________. 1) surreptiously 2) comfortable 3) decently 4) harmoniously 10. The wealthy old man _________ bequealthed a huge portion of his property to the orphanage. 1) magnanimously 2) courteously 3) graciously 4) covetously 11. He glanced _________ at the document, which was supposed to be kept confidential. 1) Stealthily 2) threateningly 3) dejectedly 4) benevolently 12. As the matter is _________ clear there is no reason for ambiguity. 1) pragmatically 2) practically 3) explicitly 4) conveniently 13. As she was thoroughly satisfied with her preparation, she entered the examination hall _________. 1) competently 2) adeptly 3) skillfully 4) confidently 14. Although I am averse to watching movies, I _________ visit the theatre to watch plays. 1) rarely 2) occasionally 3) fervently 4) specifically 15. The rose is _________ the queen of flowers. 1) controversially 2) authentically 3) indisputably 4) speciously 16. The boys _________ flung stones at the limping dog. 1) dangerously 2) casually 3) mercilessly 4) fearlessly 17. I drove the car _________ while negotiating the curves on the ghat road. 1) cautiously 2) conveniently 3) fearfully 4) precariously 18. Many people wept _________ at the loss of their beloved leader. 1) exclusively 2) inconsolably 3) intensely 4) excruciatingly 19. The workers _________ demanded better wages. 1) industriously 2) resolutely 3) persistently 4) decisively 20. The polyglot spoke many foreign languages quite _________. 1) proficiently 2) fluently 3) enthusiastically 4) incredibly 21. The thieves entered the house _________. 1) Timidly 2) docilely 3) furtively 4) discursively 22. As the Minister did not want to divulge the information, he replied _________ to the journalists‟ queries. 1) mockingly 2) sarcastically 3) secretly 4) evasively 23. One cannot form an opinion about a person by _________ looking at his face. 1) trivially 2) merely 3) peculiarly 4) intently 24. The event was so _________ planned that there was no cause for complaint. 1) minutely 2) meticulously 3) intricately 4) nimbly 25. Although I was initially nervous to address a gathering, _________ I overcame my nervousness. 1) eventually 2) generally 3) casually 4) evidently Directions for questions 1 to 25: Fill in the blanks with appropriate prepositions. 1. The carpet ____ the table is threadbare. 1) on 2) in 3) through 4) under 2. He stands ____ the school gate everyday six 0‟ clock. 1) about 2) up 3) on 4) near 3. Alcohol is injurious ____ health. 1) for 2) to 3) of 4) with 4. Since she is my neighbour, I am acquainted ____ her. 1) of 2) with 3) by 4) at 5. Although he is not rich, he is contended ____ his lot. 1) about 2) around 3) with 4) of 6. I congratulate you ____ your success. 1) at 2) on 3) for 4) before 7. The food was shared ____ ten girls. 1) between 2) besides 3) beside 4) among 8. The beggar walked ____ his dog. 1) besides 2) between 3) beside 4) near 9. The deer was killed ____ a hunter in the forest. 1) with 2) by 3) for 4) from 10. He was accused ____ forgery by his boss. 1) about 2) after 3) of 4) to 11. The dog ran ____ the road. 1) about 2) in 3) across 4) upon 12. Sheena and her friends quarreled ____ themselves without rhyme of reason. 1) between 2) among 3) about 4) around 13. She was ____ death‟s door, when the man entered her life. 1) in 2) on 3) for 4) at 14. I sent the parcel to my friend ____ courier 1) through 2) with 3) by 4) into 15. I never use a credit card; I always settle bills ____ cash. 1) by 2) with 3) in 4) to 16. He has not yet recovered ____ is illness. 1) with 2) from 3) over 4) about 17. Mahatma Gandhi worked very hard ____ the welfare of the country 1) by 2) with 3) for 4) towards 18. ____ his father‟s death, lyotiraditya Sandia was crowned king. 1) Before 2) Within 3) Behind 4) After 19. He hanged himself ____ a piece of cloth. 1) by 2) to 3) with 4) around 20. We must reach our destination ____ sunset. 1) besides 2) by 3) at 4) on 21. ____ his children, his nephews and nieces were present. 1) Beside 2) About 3) Around 4) Besides 22. I have eaten nothing ____ morning 1) from 2) for 3) since 4) till 23. He is bright boy; he is always ____ the top of his class 1) in 2) at 3) on 4) over 24. The ICICI charges interest ____ twelve percent. 1) on 2) for 3) with 4) at 25. ____ what I know of him, I hesitate to trust him. 1) Of 2) About 3) From 4) Since Directions for questions 1 to 25: Fill in the blanks with appropriate prepositions. 1. This work is ___ my capacity. 1) after 2) beyond 3) beside 4) after 2. ___ this, I wash my hands off you. 1) Before 2) Beyond 3) After 4) For 3. The goods were sold ___ the auction. 1) in 2) behind 3) around 4) at 4. The programme lasted ___ the night. 1) through 2) around 3) about 4) into 5. As he was walking on the road, he was stunned ___ a blow on the head. 1) with 2) by 3) on 4) from 6. She said something ___ leaving town. 1) around 2) with 3) about 4) of 7. Do you think this shirt is too tight ___ the shoulders? 1) around 2) on 3) across 4) throughout 8. The party went on until ___ midnight. 1) by 2) through 3) beyond 4) about 9. it is ___ my principles to borrow money. 1) around 2) about 3) against 4) beyond 10. The child stood ___ the curtain with only his shoes peeping out. 1) beyond 2) besides 3) behind 4) beside 5) 11. There was a ladder behind my house propped up ___ the wall. 1) around 2) through 3) at 4) against 12. My brother was working for Telco ___ 1995, when he got a job at Siemens Nixdorf. 1) with 2) at 3) until 4) from 13. We spent the whole after noon walking ___ the town. 1) about 2) within 3) beyond 4) in 14. The fool has parked his scooter right ___ the entrance to the driveway 1) beyond 2) across 3) within 4) on 15. ___ the span of a year, three of the town‟s biggest factories have closed down. 1) Within 2) In 3) Behind 4) Beyond 16. He beamed ___ pleasure when he heard the news. 1) in 2) with 3) from 4) on 17. ___ all his faults, I still like him. 1) In 2) At 3) Until 4) With 18. I could see something glittering ___ the water. 1) below 2) beneath 3) under 4) beyond 19. They were suddenly plunged into darkness as the train went ___ the tunnel. 1) into 2) through 3) in 4) between 20. She has been ___ a lot of pressure at work 1) by 2) in 3) under 4) beneath 21. Wait until the lights change ___ green 1) into 2) to 3) from 4) for 22. He was standing with his back ___ me 1) at 2) behind 3) towards 4) to 23. These families are living ___ the official poverty line. 1) below 2) under 3) beneath 4) beyond 24. Theves is a large international organization with offices ___ the world. 1) through 2) in 3) across 4) throughout 25. ___ the mist she could just make out his silhouette 1) Over 2) Beyond 3) Through 4) Across Directions for questions 1 to 25: Fill in the blanks with appropriate conjunctions. 1. Elizabeth works hard, ____ Jane is lazy. 1) and 2) or 3) because 4) but 2. ____ he is poor, he is contented. 1) Unless 2) Until 3) Though 4) Yet 3. I trust her ____ she always speaks the truth. 1) hence 2) thus 3) because 4) but 4. Wait for me ____ I return. 1) if 2) so 3) till 4) as 5. I range the bell ____ no one answered 1) but 2) but 3) so 4) if 6. He failed in the examination ____ he did not work hard. 1) but 2) although 3) because 4) therefore 7. You must not tell lies ____ your mother will punish you. 1) or 2) but 3) and 4) unless 8. Don‟t go there ____ you are called 1) since 2) therefore 3) unless 4) because 9. Is Rita your sister ____ your cousin? 1) and 2) but 3) or 4) because 10. I am going to Kolkata ____ my brother is going to Chennai. 1) whereas 2) even 3) because 4) since 11. ____ he was an industrious worker, I encouraged him. 1) Unless 2) Though 3) Before 4) As 12. You will get late ____ you hurry to the meeting 1) because 2) unless 3) if 4) though 13. You must be tired ____ you have walked such a long distance. 1) though 2) than 3) but 4) since 14. Not ____ I loved Caesar less, but that I loved Rome more. 1) than 2) if 3) that 4) though 15. I am in the right ____ you are in the wrong 1) because 2) since 3) for 4) but 16. We judge ourselves by what we feel capable of doing ____ others judge us by what we have already done. 1) than 2) and 3) but 4) except 17. ____ I have no money to spend, you have no one to spend it on. 1) When 2) While 3) And 4) But 18. He does well, ____ that he is nervous at the beginning 1) simply 2) only 3) and 4) so 19. ____ she had given up smoking, she kept her lighter with her. 1) If 2) That 3) Although 4) Except 20. ____ we approached the house, We heard the sound of music. 1) where 2) that 3) if 4) when 21. I know you better ____ he does! 1) that 2) than 3) while 4) when 22. He bled so profusely ____ he died 1) that 2) than 3) while 4) when 23. She has already packed all her belongings ____ I just have to take them to her new flat. 1) but 2) that 3) except 4) and 24. My shoes were full of water ____ I took them off 1) and 2) because 3) so 4) that 25. It was difficult to understand people for a long time ____ eventually I got used to them. 1) and 2) but 3) except 4) because Fill in the blanks with appropriate prepositions. 1. She jumped ________ the river. 1. into 2. in 3. on 4. onto 2. The thief jumped ______ the wall. 1. on 2. at 3. over 4. across 3. The bird flew in ____ the window. 1. from 2. at 3.through 4. of 4. He is looking _________ a painting 1. to 2. at 3. with 4. for 5. They are digging the earth _______ an axe 1. from 2. of 3. with 4. across 6. He has been waiting ________ the results 1. with 2. of 3. off 4. for 7. Ravi put up _____ his friend in Mysore 1. at 2. of 3. along 4. with 8. I prefer Hindi songs ________ Telugu songs 1. to 2. for 3. with 4. from 9. This house consists ________ many rooms 1. with 2. for 3. of 4. between 10. There was a quarrel _______ all members 1. between 2. beside 3. with 4. among 11. Mrs. Radhika watches E Tv ________ Gemini Tv 1. besides 2. beside 3. with 4. from 12. She was tired ______ the work 1. with 2. of 3. from 4. in 13. The temperature varies _________ 20 and 25 degrees 1. from 2. in 3. with 4. between 14. Children impress their parents ________ their mumbling words 1. with 2. in 3. from 4. on 15. Can I have a holiday ________ Monday? 1. on 2. in 3. since 4. for 16. We are not accustomed ________ the new place 1. at 2. to 3. in 4. on 17. Owing _________ some problems he stopped his education 1. on 2. to 3. at 4. from 18. They came ________ the room slowly 1. into 2. onto 3. in 4. for 19. The girl was absorbed _________ her work 1. on 2. in 3. for 4. upon 20. The child climbed _________ the chair slowly 1. into 2. from 3. onto 4. in 21. I am sorry ________ being late 1. on 2. for 3. since 4. into 22. _________ his house there is a small shop 1. besides 2. by 3. beside 4. at 23. A good judge never jumps _______ the conclusion 1. to 2. at 3. on 4. for 5. with 24. Are not these slums a disgrace __________ the civic authorities 1. for 2. to 3. towards 4. on 25. Very often we do not get what we pine _______ 1. about 2. for 3. at 4. on 26. The customer smashed his fist down ____ the table 1. into 2. at 3. on 4. against 27. He thought that his father was not happy ______ him 1. with 2. about 3. for 4. at 5. over 28. Let this be an example _________ the trouble makers 1. for 2. about 2. against 4. to 4. with 29. What you say hardly any bearing ______ the lives of tribals 1. about 2. for 3. on 4. with 30. Men have made ships that can sail _________ the sea and fly. _______ the air 1. along; above 2. on; in 3. over; into 4. upon; through 31. I must hold discussions ___ you ____ that matter shortly 1. about; in 2. with; in 3. with; for 4. about; for 32. The Indian magpie indulges _____ a long flight 1. in 2. with 3. on 4. at 5. over 33. The thunder was accompanied _________ heavy rains 1. with 2. by 3. up 4. through 34. A steady mind triumphs _______ difficulties 1. in 2. over 3. at 4. with 35. He resembles ________ his mother 1. with 2. in 3. at 4. None of these 36. The teacher has no control _______ the students 1. on 2. over 3. in 4. at 37. Ram is confident _____ his success 1. of 2. for 3. about 4. toward 38. Your statement is very much similar mine 1. to 2. of 3. about 4. on 39. My relations _______ Preeti are good 1. to 2. on 3. with 4. against 40. I have a distaste _______ publicity 1. for 2. about 3. against 4. at 41. There is an old building ________ the rice fields. 42. The mad beggar threw stones _______ the children. 1. at 2. in 3. on 4. from 43. The car knocked against the sign post and ran _____ the road. 1. across 2. over 3. on 4. from 44. The old man walked _______ the park towards the road. 1. at 2. in 3. to 4. from 45. The car went slowly ________ the tunnel. 1. through 2. in 3. to 4. from 46. They went ______ the railway line looking for the missing child. 1. towards 2. to 3. at 4. from 47. The crowd pressed ________ the gate. 1. from 2. to 3. on 4. towards 48. The thief jumped ________ the wall. 1. across 2. over 3. on 4. at 49. The aero plane flew _______ the clouds. 1. to 2. in 3. through 4. from 50. We are leaving ________ the school in a few minutes. 1. at 2. in 3. on 4. for 51. We asked the thieves to come _________ their hiding place. 1. at 2. in 3. to 4. from 52. The meeting will be over ________about an hour. 53. The prize distribution function will be held ________17 th March _______ 4 p.m. 54. I shall wait for you ________ 5 p.m.______ 6 p.m.______ Sunday. I hope you will come. 55. Progress reports are sent to the parents _______ the end of the month. 56. I am always at home _______ a Sunday morning. 57. The examinations will begin ______ the first week of May and end ______ the 15 th . 58. He has been in the hospital _________ January. 59. He was in the hospital _______ January _________ March. 60. Our shop has announced a clearance sale __________ Durga Puja. 61. ______ the time the fire brigade arrived, the house had been reduced to ashes. 62. The next meeting will be held _______ my house _________ Model Town. 63. The train was passing ________ a bridge. 64. Two cars collided __________ the middle of the road. 65. A boy sitting _________ the back of the class tried to disturb me. 66. The members of his family are always quarrelling _______ themselves. 67. Our boat was exactly ________ the bridge. 68. She stood ___________ the window and waved to me. 69. There is a thick fog __________ the entire city. 70. There is an almirah _________ the window and the door. 71. She had a deep cut ______ her left eye. 72. I took off my shoes and put them _________ the table. 73. I could see only his head _______ water. 74. There was a fan exactly ___________ my head. 75. I stayed _______ my uncle‟s house last night. 76. He sat _____ the table to write a letter. (at, on) 76. We rested ________ a tree. (under, below) 77. They have troubled us _______ the beginning. (since, from) 78. Come and sit _______ me. (beside, besides) 79. Someone is knocking _______ the door. (at, on) 80. Distribute these books ________ the two sisters. (between, among) 81. The soldiers marched __________ battlefield. (in, into) 82. The traveller was struck ________ lightning. (with, by) 83. Father is not ________ home just now. (in, at) 84. Is the train _______ time? (in, on) 85. This book is quite different ________ that. (than, from) 86. She was born ________ Bombay. (at, in) 87. She peeled the vegetables _________ a knife. (by, with) 88. I have been suffering from fever ________ Monday. (since, from) 89. I shall return your money _______ a week. (in, at) 90. Come _________ the garden, please. (in, into) 91. The hunter killed the bird ________ a stone. (with, by) 92. The work should be finished __________ Sunday. (by, till) 93. We travelled to Bombay ________ train. (in, by) 94. We arrived _________ the station quite ________ time. (on, at; on, in) 95. He aimed ______ becoming a dentist. 96. The police wrongly charged him ________ murder. 97. You need not feel anxious _________ my welfare. 98. If you had availed yourself ________ that offer, you would have risen high in life. 99. Students complained __________ the poor food provided in the hostel. 100. She always dreamt ________ becoming an accomplished dancer. 101. The judge held him guilty ________ theft. 102. The doctor insisted ________ performing the operation immediately. 103. I take pride ____________ being an Indian. 104. Your complaint was referred ______ the higher authorities. 105. Our bus collided __________ a van. 106. Your essay is worthy ________ the first place. 107. The blind man knocked _________ a wall. 108. I requested my neighbour to send __________ a doctor. 109. He appealed ________ the High Court _______ decision of the city magistrate. 110. He might have been blind _______ an eye but he was not blind __________ his weakneses. 111. If you are dealing ________ jewellery, you may have to deal ________ different customers. 112. The whole class agreed _____ this point. 113. Do you trust ________ God? 114. We warned the driver _______ danger ahead. 115. I enquired ________ him about your address. 116. Maruti is superior _________ any other Indian car. 117. They were quarrelling ________ an ordinary matter. 118. Neha is always boasting __________ her intelligence. 119. King Humayun died _______ a fall. 120. One should always take care ________ one‟s health. 121. My father was very angry _______ me. 122. She was annoyed _______ her son ________ behaving so stupidly. 123. She was annoyed _____ her son‟s stupid behaviour. 124. Bindu apologized ______ her teacher _______ her rudeness. Choose the appropriate choice: 1. It rained heavily while they ________ home. 1. are returning 2. returning 3. were returning 4. returned 2. When the doctor touched the patient he _________ 1. had already died 2. already died 3. already dead 4. has already died 3. I bought a new house last year, but I __________ my old house yet 1. did not sell 2. have not sold 3. not sell 4. have sold 4. Mary _______ in Germany for years 1. has been 2. is been 3. is 4. was been 5. The government _______________ a lot of money on welfare schemes last year 1. spends 2. spending 3. spent 4. was spending 6. When we ______________ the station the train had already left 1. had reached 2. reached 3. was reaching 4. has reached 7. She never _______ in others affairs 1. interferes 2. is interfering 3. had interfered 4. interfere 8. The driver will not start the bus until all vacant seats ________ 1. filled 2. are filled 3. had filled 4. were filled 9. Mr. Gopal ________ on the ice for two hours when his friends arrived 1. has been skating 2. was skating 3. had been skating 4. is skating 10. They sold their old colour TV set two months ago. They ______ a new one yet. 1. have not bought 2. have bought 3. had not bought 4. did not buy 11. Ms. Revati ________ her mother 1. resembles 2. is resembling 3. has resembled 4. has been resembling 12. Children will not learn anything if they ________ 1. are discouraged 2. have been 3. had been 4. were 13. If he had answered all questions well, he _________ 1. will have selected 2. would have been selected 3. was selected 4. had selected 14. They asked me what __________ 1. is my name 2. was my name 3. has been my name 4. my name was 15. Shaker enquired the guard whether anyone _________ in his absence 1. had come 2. has come 3. was coming 4. is coming 16. He insisted on he was innocent. 1. insisted on that 2. insisted that 3. insists that 4. No correction 17. John, who studies medicine at present, hopes to go abroad after graduation. 1. is studying 2. will study 3. studies 4. No correction 18. Students are attending spoken English classes since 6 th February. 1. were attending 2. have been attending 3. have attended 4. No correction 19. Would you please tell me when the next train comes? 1. when the next train come 2. when comes the next train 3. when the next train does come 4. No correction 20. In this deteriorate condition, you should call in a good doctor. 1. deteriorating 2. deteriorating 3. to deteriorated 4. No correction 21. I went to see the film as it is being directed by Satyajit Ray. 1. had been directed by 2. was directed by 3. had directed by 4. No correction 22. To lock up a man and let him doing nothing is a cruel punishment. 1. let him do nothing 2. letting him do nothing 3. to let him do nothing 4. No correction 23. At last we realized what was truth. 1. what was the truth 2. what the truth was 3. the truth was 4. No correction 24. In summer, days are more warmer than night. 1. more warm 2. warmer 3. warmest 4. No correction 25. He has studied French since four years. 1. since four years ago 2. from four years 3. from four years 4. for four years 26. He had not ought to do it. 1. has not ought to do 2. ought not had done 3. ought not has done 4. ought not have done 27. It will depend now on they coming on time. 1. their coming 2. them coming 3. theirs coming 4. they come 28. I felt that the music was sweetly and soothingly. 1. sweetly but soothingly 2. sweet and soothing 3. sweetly and soothing 4. sweet but soothing 29. He did not know the answer and I did not neither. 1. and neither did I 2. and either did I 3. and neither have I 4. and either did have Use the appropriate form of the verbs:- 42. I had to leave early next morning. So I _______ to bed early. 1. go 2. went 3. am going 4. have gone 43. She wasn‟t feeling well. So she ______ much. 1. eats 2. don‟t eat 3. ate 4. didn‟t eat 44. We were getting late. We _____ time to wait for anybody. 1. have 2. don‟t have 3. didn‟t have 4. do have time 45. How did you learn to paint? My father ________ me. 1. teaches 2. teach 3. taught 4. has taught 46. The sound system wasn‟t good. We _____ the movie. 1. enjoyed 2. were not enjoying 3. did not enjoy 4. have enjoyed 47. I knew you were inside praying. So I _____ you. 1. disturbed 2. didn‟t disturb 3. don‟t disturb 4. have disturbed 48. It was a noisy place. So I _____ well. 1. did sleep 2. could sleep well 3. couldn‟t sleep 4. slept 49. Vicky wasted a lot of money yesterday. He _______ an imported camera, which ____ Out to be good. 1. purchased, turned 2. has purchased, turned 3. has purchased, didn‟t turn out 4.purchased, didn‟t turn out 50. As soon as Dick______ the message over his radio, he ____ off towards the site of the accident. 1. hears, shot 2. heard, is shooting 3. heard, shot 4. heard, is shooting 51. Your performance in most of the subjects is good. But why----- poor marks in science? 1. did you secure 2. didn‟t secure 3. have you secured 4. secured 52. She ______ for more than two hours. She must be quite tired by now. 1. sang 2. was singing 3. has been singing 4. is singing 53. It _____ so hard since yesterday that all the rooftops have turned totally white. 1. Snowed 2. is snowing 3. has been snowing 4. had been snowing 54. Since when _____ medicines from this chemist? 1. you are purchasing 2.you have purchased 3. have you been purchasing 4. you purchased 55. A: Any interesting news? B: Sorry. I ______ the newspaper yet. 1. did not read 2. have not read 3. have not been reading 4. don‟t read 56. When is Anil leaving for office? He _____ . 1. is already leaving 2. is already left 3. has already left 4. has been leaving 57. I ____ that you have resigned your job. 1. hear 2. am hearing 3. will hear 4. will have heard 58. I_______ he will come. 1. am doubting 2. doubt 3. will doubt 4. shall be doubting 59. The car you _______ at ________ to my father. 1. are looking, belonged 2. are looking, belongs 3. looked, is belonging 4. looks, belongs 60. The captain was the last man ______ the sinking ship. 1. left 2. to leave 3. to be leaving 4. has left 61. _______ her work, she went to sleep. 1. completing 2. having to complete 3. having completed 4. after completed Directions (Questions 62-92): Fill in the blanks with the correct form of the verbs given in brackets: 62. If it ____________ hot today, I‟ll stay at home. (be) 63. The police _________ you if you spread rumors. (arrest) 64. How much will he be fined if he ____________ the traffic rules? (break) 65. If the cake is spoiled, _________ me. (not blame) 66. You ________ a lot of time if you use a calculator. (save) 67. If you need the services of a nurse, please ____________ this button. (press) 68. ___________ this job if you get a better one? (you resign) 69. I would certainly see this movie if tickets ___________ available. (be) 70. Would he be granted leave if he ______ for it? (apply) 71. ___________ if I kept this book a little longer? (you mind) 72. If god granted you two boons, what _____________? (you ask) 73. If she dressed carefully, she __________ pretty. (look) 74. If someone hijacked the plane, what ___________? (you do) 75. If you pressed that knob, the machine ___________ working. (start). 76. He would have won the race if he __________. (not slip) 77. If the paper __________ easier, he would have got very good marks. (be) 78. The soup would have tasted better if you ___________ more salt in it. (put) 79. If I had found the samples satisfactory, I ________ a huge order. (place) 80. Had I seen the red signal, I _________ the car. (stop) 81. If the farmers had used good quality seeds, there __________ a rich crop. (be) 82. If the army ____________ a little longer, it might have won the battle. (persist) 83. If the voltage suddenly rises, the fuse ________ off. (blow) 84. If you ___________ that funny cartoon, you would have laughed heartily. (see) 85. You _________ if you repeat the mistake. (repent) 86. ___________ if I pressed this button? (the machine stop) 87. If the water level ___________ the danger mark, low-lying areas would have got flooded. (cross) 88. If you ____________ you lunch, let me ask for the bill. (finish) 89. If you are satisfied, __________ others. (tell) 90. If you were satisfied, ________ others? (you tell) 91. If you ____________ satisfied, you should have complained to us. (not feel) 92. If she had been less proud, she __________ happier. (be) Sentence Correction Exercise 1: Identify the underlined part that has an error 1. Many a man have succumbed to this temptation, inviting his own downfall and 1 2 3 4 destruction. 2. Neither the chairman nor the directors is present at the crucial meeting between 1 2 3 4 workers and the officers. 3. We have helped them not only with money and also with a body of workers, all 1 2 3 4 well-trained and experienced. 4. Euclid proved that the sum of the three angles of a triangle are equal to the two right 1 2 3 4 angles. 5. Loosing the favour of his master, Ramesh was dismissed from his high office. 1 2 3 4 6. Were an angel to tell me such a thing of you, I will not believe it. 1 2 3 4 7. Even though Miss India lost the beauty contest, she was still more prettier than the 1 2 3 4 other girls in the pageant. 8. Before the advent of television, the common man seldom never had an 1 2 opportunity to see as well as listen to his favourite singer‟s live performances. 3 4 9. In order for one to achieve the desired results in this examination, it is necessary 1 2 3 that he work as hardly as possible. 4 10. The purpose of the United Nations is to maintain peace and security and 1 2 3 encouraging respect for human rights. 4 11. The introduction of tea and coffee and such other beverages have not been without some effect. 12. Each of the scholars have done well in the seminar. 13. Anyone who wish to participate in our slogan competition may do so by filling the coupon supplied along with every bottle of our beverage purchased. 14. Either one of the three top rankers in the class is eligible for a scholarship only after going through an elimination process. 15. Chand will probably buy some more computer software when he will get paid his annual dues. 16. Every student needs an identification number so he can get a university library card made to gain access to valuable. 17. The Marwaries are not least enterprising than any other business community in India. 18. She is wonder and an example of what a human being in spite of infirm health is capable. 19. Laxmi, accompanied by her brother on the piano, were given a standing ovation at the talent search contest. 20. Professor Sarcar tol his class that the best way to achieve distinction in biochemistry is to practice the structures of the compounds. 21. In a survey conducted by the market research agency. DRISHTI, a sample of 4000 students who had just given their class X examination, were questioned about their future plans. Surprisingly it was found that more than 3400 students replied that they had not taken any decision, they are still thinking out. 1. they are still thinking out 2. they are still thinking. 3. they are still over thinking it. 4. they are still thinking it over. 22. Hurry up lest you should not miss the train. 1. not miss the train 2. miss the train 3. miss the train not 4. not miss train 23. Most of the members of management committee were in favour of Alternative B as this idea is definitely more preferable to Alternative A. 1. More preferable to Alternative A 2. preferable to Alternative A 3. highly preferable to Alternative A 4. to be preferable 24. When asked about the appearance of stranger, the Innkeeper replied, “He appeared to be a tall man with a slight limp.” 1. a tall man with a slight limp 2. tall and had a slight limp 3. tall and limping slightly 4. limping slightly but tall 25. The Principal, knowing about my interest in music, asked me that would like to perform during the public celebrations. 1. that I would like to perform 2. that I might like to perform 3. if I would like to perform 4. if I should like to perform 26. John Higginbotham is a man of many ideas and who knows how to express them appropriately. 1. of many ideas and who knows how to express them appropriately. 2. who has many ideas and who knows how to express them? 3. of many ideas and knows to express them appropriately. 4. who has many ideas and who knows how to express them appropriately? 27. Radha wishes that she took English at high school. 1. Radha wishes that she took English at high school. 2. Radha wishes that she had taken English at high school. 3. Radha wishes that she would have taken English at high school. 4. Radha wished that she take English that high school. 28. My son says that he almost has written twenty compositions this year. 1. he almost has written twenty competitions. 2. he almost has written twenty pieces of composition. 3. he almost has written twenty composition pieces. 4. he has written almost twenty compositions. 29. When only a baby, my father took me to the circus. 1. When only a baby, my father took me to the circus. 2. Being a baby, my father took me to the circus. 3. When only a baby, I was taken to the circus by my father. 4. Being a baby, my father, to the circus, took me. 30. The criminal was caught, convicted and hanged in a short period of time. 1. The criminal was caught, convicted and hanged in a short period of time. 2. The criminal was caught, convinced and hung in a short period of time. 3. The criminal was applauded, acquitted and hung in a short period of time. 4. The criminal was caught, convicted and hung in a short period of time. 31. I hate sitting along him as he always smells of garlic. 1. along 2. besides 3. beside 4. at 32. Although we are free for last forty-five years or so, yet we continue to be economically backward. 1. Although we are free 2. Even through we are free 3. Although we have been free 4. Though we are free 33. Neither the famine or the subsequent fire was able to destroy the spirit of the people. 1. Neither the famine or the subsequent fire was able to destroy the spirit of the people 2. The famine and the subsequent fire was able to destroy the spirit of the people. 3. Neither the famine or the subsequent fire was not able to destroy the spirit of the people. 4. Neither the famine nor the subsequent fire was able to destroy the spirit of the people. 34. He sent a word to me that he would be coming late. 1. He sent word to me that he will come late. 2. He had sent a word to me that he would be coming late. 3. He sent word to me that he would be coming late. 4. He passed on a word to me that he would be coming late. 35. The company does to great length to ensure that employee can be comfortable in their work environment. 1. The company goes to great length to ensure that employees can be comfortable in their work environment. 2. The company goes to great length to ensure that employees will be comfortable in their work environment. 3. The company goes to great length to ensure that employees are comfortable in their work environment. 4. The company goes to great length to ensure that employees should be comfortable in their work environment. 36. He sat until he was chilled with cold, dancing occasionally at the figure of the old woman peering into the window. 1. He sat until he was chilled with cold, glancing occasionally at the figure of the old woman peering into the window. 2. He sat until he was chilled with cold, glancing occasionally at the figure of the old woman peering up the window. 3. He sat until he was chilled with cold, glancing occasionally at the figure of the old woman peering at the window. 4. He sat until he was chilled with cold, glancing occasionally at the figure of the old woman peering in through the window. 37. The winter this year has been severe specially. 1. The winter this year has been severe specially 2. The winter this year has been specially severe. 3. The winter this year has been severe especially. 4. The winter this year has been especially severe. 38. We received an invitation to the palace; we are going to go there now. 1. we are going to go there now. 2. and therefore we are going to go there now. 3. we are going there now 4. and therefore we are going there now 39. My husband wanted to buy two floor carpets yesterday, but he forgot to take his money purse. 1. buy two floor-carpet yesterday, but he forgot to take his money-purse. 2. buy to carpet yesterday, but he forgot to take his money purse. 3. buy two floor-carpets yesterday, but he forgot to take his purse. 4. buy two carpets yesterday, but he forgot to take his purse. 40. Competition has taken a lot of his business; he is finding it difficult to make both his ends meet. 1. he is finding it difficult to make both his ends meet. 2. he is finding making both his ends meet difficult. 3. he is finding it difficult to make both ends meet. 4. he is finding the difficulty to making both ends meet. 41. Scarcely had he gone a few steps that he was told by someone on the way that his mother was no more. 42. If I was a despot, even though I knew my territory was crammed with fanatical revolutionaries, would not repress freedom of speech. No error 43. Napoleon dimly saw what Mahatma Gandhi demonstrated ……………. That the spirit was more strong than the sword. No error 44. Gandhiji was a social scientist who tried to analyze the ills of society and find a cure of them in the context of all the facts and personalities involved. No error 45. I listened attentively to his long rambling speech, but could not make out what he was driving. No error 46. These two young people were to be married, but the young woman changed her mind and now the engagement is broken up. No error 47. Efforts are being made by the government to create further employment opportunities in the wake of the growing abyss of employment in the country. No error. 48. If properly entrapped, the direct taxes of various types and income tax in particular can prove to be a source of substantial revenue. No error 49. Some remarks casually dropped by a woman put the police on the right scent and they soon discovered the whole gang of brigands. No error 50. If the city falls a prey before the enemy, it remains to be seen what flag will fly over the citadel. No error 51. This Youngman would not follow his father‟s occupation of wood-carving but insist on preparing himself for clerkship. No error 52. The Prime Minister sometimes makes an important statement in Parliament in order that through the comments made on it in the public press he may feel the pulse of the nation. No error 53. I was in the tunnel when the train came up before I was aware, but I squeezed myself close to the wall and escaped. Not till the last coach passed I breathed freely. No error 54. You have made a very important proposal to me. I will turn the thing up in my mind and give you an answer tomorrow. No error 55. Boling broke at first paid homage to King Richard, but when his cause grew stronger, he threw up the mask and claimed the crown. No erro 56. A fascinating feature of the Indian tradition is the interchange between classical art tradition and folk craft tradition. No error 57. The Bar councils, which are entrusted the responsibility of disciplining members in addition to enrolling and maintaining the roll of lawyers, must wake up to the need for reform at the bar. No error 58. He is one of the few younger painters of to day who practice their art with absolute sincerity and deep introspective concentration. No error 59. I thus made an intimate study of the hard condition of the Indian settlers, not only by reading and hearing of it, but by personal experience. No error 60. The D T C management took special care to see that there was no place for discourtesy at any level. No error 61. Tension ran high to-day in Upper Assam‟s Dibrugarh district following from a clash between two linguistic groups. No error 62. The University in a determined effort to restore its clean image of yester years, is all set out to mount a multi-pronged attack on unfair means at examinations. No error 63. Fidel Castro wrested power from Batista 26 years ago and set up the first and the only communist government in the western hemisphere. No error 64. We judge ourselves by what we feel capable of doing, when others judge us by what we have already done. No error 65. The present speech is mild contrasted to his past utterances on the same subject. No error 66. In case of his dying without an issue, his nephew would inherit the whole property. No error 67. It is said to Akbar that he rarely had slept more than three hours at a time, even during those three hours he was unconsciously awake and vigilant. No error 68. Nelson had done his duty; Captain Hardy congratulated him on him having gained a complete victory. No error 69. The enquiry revealed that the accident was due to the engine-driver disregarding the signals. No error 70. He is the representative of the king, and as therefore we are bound to honour him. No error 71. A few clothes they had were all tattered and torn, but they did not worry and went ahead with their preparation to stage a show with the improvised material. No error 72. Pope professed to have learned his poetry from Dryden, who whenever an opportunity was presented he praised throughout his life with unvaried liberality. No error 73. With whatever luxuries a bachelor may be surrounded he will always find his happiness incomplete until he has a wife and children. No error 74. Weather permitted, there will be a garden party at government House tomorrow. No error 75. There are many truths of which the full meaning can not be realized unless personal experience has bought it home. No error 76. The man who eats in a hurry loses both the pleasure of eating as well as the profit of digestion.No error 77. Neither life nor property were safe, and the poor and the weak were oppressed by the strong. No error 78. The Restoration crushed for a time the Puritan party besides placed supreme power in the hands of a libertine. No error 79. As long as he lived, he was the guiding-star of a brave nation; while he died, the little children cried in the streets. No error 80. There never can be prosperity in any country until all the numerous cultivators of the soil are permanently depressed and injured. No error 81. I instruct you to remain here and not to budge an inch so long as I return from my inspection of the other formation. No error 82. Sentinels were posted and every other precaution taken lest the camp may be taken by surprise. No error 83. I must refuse your request, in as much I believe it unreasonable. No error 84. This technological breakthrough, according to the scientists, would be highly beneficient in various areas including electric locomotion. No error 85. The formal agreement between India and Pakistan to set up a joint commission will undoubtly inject momentum into the ongoing efforts to establish peace and amity on the sub-continent. No error 86. New Delhi has disclosed last year its intention of borrowing from the A D B for the first time since it became a member of that institution. No error 87. The government announced a state of emergency in Lima on Wednesday and placed the capital‟s six million residents under limited martial law. No error 88. Huge land slides blocked the coming up convoy of vehicles including passenger buses on the Srinagar-Jammu national high way. No error 89. Five persons were killed and seven others injured when a lorry in which they were travelling fell in a ditch. No error 90. Four armed miscreants have looted Rs.1 lakh from the Nagri branch of Bank of India, under Ratu Police station yesterday. No error 91. With the lever of hiked oil price being exercised by the Arab countries, there is a scramble for alternate sources of energy. No error 92. Four dacoits were killed and three captured living by villagers and policemen. No error 93. The criminal investigational agency claims to have busted three inter-state gangs of automobile lifters. No error 94. Despite of an increase in postal rates in 1982-1983 the postal loss this year has substantially grown. No error 95. Before half a century, judges were reluctant to apply the principles of liability of the manufacturer towards the consumer. No error 96. The chairman of the Board accepted that they had received complaints and will take action on the basis of records submitted to them. No error 97. The African leader asked the countries in the region of the Indian Ocean not to help the super powers in their design for expanding their spheres of influence. No error 98. Prince Faisal said the unability of the non-aligned countries to find an amicable solution to the Iran-Iraq war had undermined the cohesiveness of the movement. No error 99. A secular state cannot be of much help to a community as far as the solution of these two problems is concerned. No error 100. External Affairs Minister of India and Pakistan Foreign Minister to-day signed an agreement setting up the Indo-Pakistan Joint Commission as had previously been agreed. No error Exercise 2: 1. Everyone in the bank-including the manager and the tellers, ran to the door when the fire alarm rang. A. tellers, ran B. tellers:ran C. tellers, had run D. tellers-ran E. tellers' ran” 2. To no ones surprise, Joe didn't have his homework ready. A. no ones surprise B. noones surprise C. no-ones surprise D. no ones' surprise E. no one's surprise 3. If he would have read “The White Birds,” he might have liked William Butler Yeats's poetry. A. would have read B. could have read C. would of read D. could of read E. had read 4. After the hurricane, uprooted trees were laying all over the ground. A. were laying B. lying C. were lying D. were laid E. was laid 5. Ralph Waldo Emerson (1803-1882), the great Transcendentalist philosopher, wrote in his essay “Self-Reliance” of the need for an individual to develop his capacities. A. essay “Self–Reliance” B. essay, “Self-Reliance” C. essay: Self-Reliance D. essay, Self-Reliance E. essay; “Self-Reliance” 6. The recently built children's amusement park has been called “ a boon to the community “ by its supporters and “an eyesore” by its harshest critics. A. and “an eyesore” by its harshest B. and, “ an eyesore,” by its harshest C. and, an eyesore; by its harshest D. and-an eyesore- by its' harshest E. and-“an eyesore”- by its' harshest 7. I always have trouble remembering the meaning of these two common verbs, affect (to change” or “to influence”) and effect (“to cause” or “ to accomplish ) . “ A. “ to accomplish ). “ B. “ to accomplish” ). C. “to accomplish). D. To accomplish. E. ( “ to accomplish. “ ) 8. My class just finished reading- “ The Fall of the House of Usher “, a short story by Edgar Allen Poe. A. reading- “ The Fall of the House of Usher”, B. reading, The Fall of the House of Usher, C. reading “The Fall of the House of Usher, “ D. reading, The Fall of the house of Usher, “ E. reading: The Fall of the House of Usher- 9. After it was repaired it ran perfect again. A. ran perfect B. ran perfectly C. could run perfect D. could of run perfect E. would run perfectly 10. "Are there two e's in beetle," asked Margo? A. there two e's in beetle," asked Margo? B. their two e's in beetle?" asked Margo. C. there two e's in beetle," asked Margo? D. there two e's in beetle?" asked Margo. E. there two e's in beetle, asked Margo? 11. The circus audience received a well-deserved round of applause for the perfectly timed acrobatic stunt. A. audience received a well-deserved B. audience gave a well deserved C. audience did receive a well deserved D. audience gave a well-deserved E. audience did get a well-deserved 12. Looking directly at me, my Mother said, “ These are your options: the choice is yours.” A. Mother said, “ These are your options: the choice is B. Mother said- these are your options, the choice is C. Mother had said, These are your options; the choice is D. Mother had said, “These are your options; the choice is E. Mother said, “These are your options; the choice is 13. Porcupine is from Latin porcus, “pig,” and spina, “spine.” A. porcus, “pig,” and spina, “spine.” B. Porcus-pig and spina, “spine.” C. Porcus-pig, and Spina, “spine.” D. Porcus-Pig-,Spina-spine. E. Porcus, “pig,” and spina “spine”. 14. Seeing the dolphins, some sharks, a killer whale, and a Moray eel made the visit to the marine park worthwhile. A. a killer whale, and a Moray eel made the visit B. a killer whale, and a moray eel made the visit C. a killer whale and a moray eel makes the visit D. a killer whale and a Moray eel makes the visit E. a killer whale and a moray eel made the visit 15. Still, the fact that a planet exists outside our solar system encourages hope that other solar systems exist, and in them, perhaps, a planet that does support life. A. that a planet exists outside our solar system encourages hope that other solar systems exist, and B. that a Planet exists out side our solar system encourages hope that other solar systems exist and C. could be that a planet exists outside our solar system encourages hope that other solar systems exist, and D. that a planet exist outside our solar systems encourage hope that other solar systems exist, and E. that a planet does exists out side our solar system encourages hope that other solar systems exist, and 16. Mail-order shopping can be convenient and timesaving with appropriate precautions, it is safe as well. A. can be convenient and timesaving B. can be convenient and timesaving; C. should be convenient and time saving; D. could be convenient and time saving; E. can be convenient and time-saving; 17. Among the many fields of science, no matter what turns you on, there are several fields of study. A. science, no matter what turns you on, B. Science, no matter what turns you on, C. Science, no matter which you chose, D. Science, no matter which of these you chose- E. science, no matter which you choose, 18. The fact that boxing is known to cause head injuries and brain damage should lead us to inform the public and push for a ban on boxing. A. should lead us to inform B. could lead us to inform C. should of led us to inform D. will lead us to inform E. should have led us to inform, 19. The first part of the test was on chemistry, the second on mathematics, and the third on english. A. on mathematics, and the third on english. B. on mathematics; and the third on English. C. on Mathematics; and the third on English. D. on mathematics, and the third on English. E. on mathematics: and the third on English. 20. The Diary of Anne Frank showed a young girl's courage during two years of hiding. A. showed a young girl's courage B. shows a young girl's courage C. did show a young girls courage D. has shown a young girl's courage E. showed a young girl's courage 21. In August my parents will be married for twenty-five years. A. will be married for twenty-five years. B. shall have been married for twenty-five years. C. will have been married for twenty-five years. D. will be married for twenty five years. E. will have married for twenty-five years. 22. Hours of driving laid ahead of us. A. laid B. have lain C. lay D. has lay E. lie 23. By the time we get to the picnic area, the rain will stop. A. will stop B. shall stop C. will has stopped D. shall have stopped E. will have stopped 24. If Judy would not have missed the deadline, the yearbook delivery would have been on time. A. would not have missed B. should have not missed C. wouldn't have missed D. had not missed E. would have not missed 25. We spent Sunday afternoon wandering aimless in the park. A. wandering aimless B. wandering aimlessly C. wandering without purpose D. wandering in an aimless manner E. wandering almost aimlessly 26. Only after I went home did I remember my dental appointment. A. went home B. had went home C. had gone home D. gone home E. should go home 27. By this time next year Johanna will begin classes at the University of Colorado. A. will begin classes B. will have begun classes C. has began classes D. should begin classes E. should have begun classes 28. After comparing my air conditioner with the one on sale, I decided that mine was the most efficient. A. was the most efficient. B. should be the most efficient. C. was the more efficient. D. was, by far the most efficient E. should be considered the most efficient. 29. I would have liked to have gone swimming yesterday. A. to have gone swimming B. to go swimming C. to had gone swimming D. to go to swim E. to of gone swimming 30. I wish I read the chapter before I tried to answer the questions. A. read the chapter B. would read the chapter C. should of read the chapter D. could have read the chapter E. had read the chapter 31. Nathanael West said that he'd never have written his satirical novel if he had not visited Hollywood. A. have written his B. would have written his C. could of written his D. could have written his E. should of written his 32. The smell from the paper mill laid over the town like a blanket. A. laid B. has lain C. will lie D. lay E. has laid 33. When I was halfway down the stairs, I suddenly knew what I had wanted to have said. A. to have said B. too say C. to have been said D. to had say E. to say 34. I would be more careful if I had been you. A. had been B. could have been C. was D. were E. could have been 35. They read where the governor has appointed a special committee to improve the school calendar. A. where B. how C. that of where D. of where E. where- 36. In study hall I sit besides Paul Smith, who is captain of the swim team and one of the best swimmers in the state. A. sit besides B. sat beside C. have set beside D. sit beside E. have sit beside 37. This classic has been read with enjoyment for nearly two hundred years. A. has been read B. will have been read C. shall have been read D. is being read E. was read 38. Many nineteenth-century biographers rely on their imagination, not on real facts. A. rely on their imagination, B. relied on their imagination, C. have relied on their imagination D. could have relied on their imagination, E. could rely on their imaginations: 39. The private lives of politicians, generals, and other notables fascinates the reading public. A. fascinates the reading B. have fascinated the reading C. will fascinate the reading D. fascinate the reading E. has fascinate the reading 40. That small man chose a seat near the door and carefully sat down. A. sat B. will sit C. could of sat D. have sit down E. set down Time and Distance Speed: We have the relation between speed, time and distance as follows: Speed = distance / time. So the distance covered in unit time is called speed. This forms the basis for Time and Distance. It can be re-written as Distance = Speed X Time or Time = Distance / Speed. Units of Speed: The units of speed are kmph (km per hour) or m / s. 1 kmph = 5 / 18 m / s 1 m / s = 18 / 5 kmph Average Speed: When the travel comprises of various speeds then the concept of average speed is to be applied. Average Speed = Total distance covered / Total time of travel Note: In the total time above, the time of rest is not considered. Example 1: If a car travels along four sides of a square at 100 kmph, 200 kmph, 300 kmph and 400 kmph find its average speed. Soln: Average Speed = Total distance / Total time. Let each side of square be x km. Then the total distance = 4x km. The total time is sum of individual times taken to cover each side. To cover x km at 100 kmph, time = x / 100. For the second side time = x / 200. Using this we can write average speed = 4x / (x/100 + x/200 + x/300 + x/400) = 192 kmph. Example 2: A man if travels at 5/6 th of his actual speed takes 10 min more to travel a distance. Find his usual time. Soln: Let s be the actual speed and t be the actual time of the man. Now the speed is (5/6)s and time is (t+10) min. But the distance remains the same. So distance 1 = distance 2 => s X t = (5/6)s X (t+10) => t = 50 min. Example 3: If a person walks at 30 kmph he is 10 min late to his office. If he travels at 40 kmph then he reaches to his office 5 min early. Find the distance to his office. Soln: Let the distance to his office be d. The difference between the two timings is given as 15 min = 1 / 4 hr. Now if d km are covered at 30 kmph then time = d/30. Similarly second time = d/40. So, d/30 – d/40 = 1 / 4 => d = 30 km. Note: When two objects move with speeds s1 and s2 a. In opposite directions their combined speed = s1 + s2 b. In same direction their combined speed = s1 ~ s2. Example 4: Two people start moving from the same point at the same time at 30 kmph and 40 kmph in opposite directions. Find the distance between them after 3 hrs. Soln: Speed = 30 + 40 = 70 kmph (since in opposite directions) Time = 3 hrs So distance = speed X time = 70 X 3 = 210 km. Example 5: A starts from X to Y at 6 am at 40 kmph and at the same time B starts from Y to X at 50 kmph. When will they meet if X and Y are 360 km apart? Soln: Distance = 360 km Speed = 40 + 50 = 90 kmph. Time = distance / speed = 360 / 90 = 4hrs from 6 am => 10 am. Example 6: A starts from X to Y at 6 am at a speed of 50 kmph. After two hours B starts from Y to X at 60 kmph. When will they meet if X and Y are 430 km apart? Soln: By the time B started A traveled for 2 hrs => 2 X 50 = 100 km. So at 8 am, distance = 430 – 100 = 330 km Speed = 50 + 60 = 110 kmph. Time = distance / speed = 330 / 110 = 3 hrs from 8 am => 11 am. Note: When a train crosses a negligible length object (man / pole / tree) the distance that it has to travel is its own length. When a train has to cross a lengthy object (train / bridge / platform) the distance it has to travel is the sum of its length and the length of the object. Example 7: If a train traveling at 40 kmph crosses another train of length 100m traveling at 14 kmph in opposite direction in 30 s find the length of the train. Soln: Let length of train be d. Distance to be covered = d + 100. Speed = 40 + 14 = 54 kmph = 54 X 5 / 18 = 15 m / s Time = 30 s. Distance = speed X time => d+100 = 15 X 30 => d = 350 m. Note: If a man rows a boat along the stream flowing at speed S2 then it is termed downstream speed and is given by S down = S1 + S2 , where S1 is speed of boat in still water. If a man rows a boat opposite to the stream flowing at S2 then it is termed upstream and is given by S up = S1 – S2. Exercise: 1. A car moves at a speed of 80km/hr. What is the speed of the car in meters per second? 1) 9 2 12 2) 9 2 22 3) 9 1 20 4) 2 9 21 2. If a man can cover 12 meters in one second, how many kilo meters can be cover in 3 hours 45 minutes? 1) 168 km 2) 162 km 3) 150 km 4) 156 km 3. If a man running at 15 kmph. Crosses a bridge in 5 minutes, then the length of the bridge is 1) 1230 m 2) 1240 m 3) 1250 m 4) 1220 m 4. Walking at th 4 3 of his usual speed a man is late by 2 hours 30 minutes. The usual time would have been 1) 2 1 7 hrs 2) 2 1 3 hrs 3) 4 1 3 hrs 4) 8 7 hrs 5. In a 1 km race, A beats B by 100 m and C by 150 m. In a 2700 m race, by how many meters does B beat C? 1) 100 m 2) 120 m 3) 150 m 4) 180 m 6. Traveling at a speed of 8 kmph a student reaches school from his house 10 minutes early. If he travels at 6 kmph, he is late by 20 minutes. Find the distance between the school and the house. 1) 12 km 2) 1 km 3) 10 km 4) 13 km 7. A man takes 5 hours 45 minutes in walking to a certain place and riding back. He could have gained 2 hours by riding both ways. The time he would take to walk both ways is _________ 1) 12 hrs 2) 11 hrs 45minutes 3) 7 hrs 45 minutes 4) 3 hrs 8. The ratio between rates of walking of two persons is 3:4. If the time taken by nd 2 person to cover a certain distance is 36 minutes, then the time taken by the first person to cover the same distance is ___________ 1) 36 minutes 2) 48 minutes 3) 27 minutes 4) none 9. If the speed of a vehicle changes in the ratio a : b, then the ratio of times taken is 1) a : b 2) 1 ÷ b a 3) b : a 4) 1 ÷ a b 10. A car driver makes his journey by the speed of 75km/hr and returns to initial place with 50 km/hr. Then his average speed of journey is ___________ 1) 30 km/hr 2) 40 km/hr 3) 50 km/hr 4) 60 km/hr 11. A vehicle travels 715 km at a uniform speed. If the speed of the car is 10 kmph more, it takes 2 hours less to cover the same distance. The original speed was _______________ 1) 45 kmph 2) 65 kmph 3) 55 kmph 4) 75 kmph 12. Two persons P and Q run at 8 kmph and 12 kmph on a circular track of length 6 km in the same direction starting at same time from same place. After how many hours will they meet each other any where on the track? 1) 1.5 hours 2) 2 hours 3) 2.5 hours 4) 3.5 hours 13. A car driver driving at a speed of 68kmph locates a truck 40 meters ahead of him. After 10 seconds, the truck is 60 meters behind. The speed of truck is ____________ 1) 30 km/hr 2) 32 km/hr 3) 23 km/hr 4) 3 km/hr 14. Rajan is traveling on his cycle and has calculated to reach a point at 2 p.m. if he travels at 10 kmph. He would reach there by 12 noon if he travels at 15 kmph. At what speed must he travel to reach the same place at 1.p.m? 1) 12 kmph 2) 14 kmph 3) 15 kmph 4) 13 kmph 15. Two persons start running simultaneously around a circular track of length 300m from the same point at speeds 15 and 25km/hr. When will they meet first time on the track, when move in opposite direction? 1) 21 sec 2) 22 sec 3) 27 sec 4) 24 sec 16. A robber steals a Maruthi car at 2.30 pm and drives at 60 kmph. The theft is discovered at 3 p.m. and the owner sits in Police jeep running at 75 kmph. When will he catch the thief? 1) 5.30 pm 2) 5.15 pm 3) 5 pm 4) 5.45 pm 17. Two planes move along a circle of circumference 1.2 km with constant speeds. When they move in different directions they meet every 15 sec and then they move in the same direction one plane over takes the other every 60 sec. The speed of slower plane is 1) 0.04 km/s 2) 0.03 km/s 3) 0.05 km/s 4) 0.02 km/s 18. A 150 m long train crosses a man walking at a speed of 6 kmph in his opposite direction in 6 sec. The train (in kmph) is: 1) 66 2) 84 3) 96 4) 106 19. A train of length 150 m takes 10 sec to pass over another train 100 m long coming from the opposite direction. If the speed of the train is 30 kmph. Then the speed of the second train in kmph is _________ 1) 54 2) 60 3) 72 4) 36 20. If a train 110m long passes a signal pole in 3 sec. Then the time taken by it to cross a railway platform 165m long is : 1) 3secs 2) 4secs 3) 7.5secs 4) 5secs 21. An Engine of 10 m length travels at 60 kmph. How long does it take to cross another train 170 m long, running at 54 kmph in the same direction? 1) 16 sec 2) 16.8 sec 3) 108 sec 4) none 22. Two trains starting at the same time from two stations 200 km apart and going in opposite directions cross each other at a distance of 110 km from one of the stations. What is the ratio of their speeds? 1) 9:11 2) 11:9 3) 10:9 4) 9:10 23. A train M leaves Mumbai at 5am. And reaches Delhi at 9am. Another train leaves Delhi at 7am. And reaches Mumbai at 11.00am. At what time do the two trains across each other? 1) 8 a.m. 2) 9 a.m. 3) 7 a.m. 4) 6 a.m. 24. Train P leaves Hyderabad at 6.00am. And reaches Vijayawada at 10.00am. Train Q leaves Vijayawada at 7.00am. And reaches Hyderabad at 1.00pm. At what time do the trains meet? 1) 8.48 a.m. 2) 8.12 a.m. 3) 8.42 a.m. 4) 9.00 a.m. 25. A train running at 52kmph takes 36 seconds to pass a platform. Next it takes 24 seconds to pass a man walking at 10 kmph in the same direction. Find the length of the train and that of the platform? 1) 800 m; 440 m 2) 280 m; 440 m 3) 280 m; 240 m 4) 420 m; 300 m 26. Two trains running in the same direction at 40 kmph and 22 kmph completely pass one another in 60 seconds. If the length of the first train is 125 meters, then the length of second train is? 1) 125 m 2) 128 m 3) 175 m 4) 900 m 27. Two trains 220 meters and 380 meters in length respectively are running in opposite direction. One at the rate of 35 kmph and other at 25 kmph. In what time they will cross each other? 1) 36 seconds 2) 30 seconds 3) 60 seconds 4) None 28. A man misses a train by 40 minutes if he travels at 30 kmph. If he travels at 40 kmph, then also he misses the train by 10minutes. What is the minimum speed required to catch the train on time? 1) 44 kmph 2) 45 kmph 3) 48 kmph 4) 49 kmph 29. A boat traveled from A to B and back to A from B in 5 hours. If the speed of boat in still water and the speed of stream be 7.5 kmph and 1.5 kmph, then what is the distance between A and B? 1) 80 km 2) 45 km 3) 18 km 4) 19 km 30. A man can row downstream at 18 kmph and upstream at 10 kmph. Find the speed of the man in still water and the speed of stream (in kmph) 1) 13; 3 2) 15; 3 3) 12; 6 4) 14; 4 31. A man can row at 9 kmph in still water. He takes 4 ½ hours to row from P to Q and back. What is the distance between P and Q if the speed of the stream is 1 kmph? 1) 32 km 2) 28 km 3) 20km 4) 24 km 32. A man can row 30 km downstream in 3 hours 45 minutes, and 11 km upstream in 2 hours 12 minutes. What is the speed of the man in still water and speed of stream (in kmph)? 1) 6; 2 2) 6.8; 1.8 3) 6.5; 1.5 4) 7; 3 33. A man rows 22 km upstream in 4 hours and 45 km downstream in 6 hours. In 10 hours how much more distance can he row downstream than the distance he can row upstream? 1) 24 km 2) 22 km 3) 20 km 4) 18 km 34. A person can row 10 km in 1 hour in still water. If the speed of the water current is 2 kmph and it takes two hours for him to go to a certain place and back. Find the distance he traveled in upstream? 1) 9 ½ km 2) 9.6 km 3) 48 km 4) 5 km 35. A person can row 5 3 of a km in upstream in 10 minutes and return in 6 minutes. Find the speed of man in still water? 1) 4.4 kmph 2) 4.5 kmph 3) 4.8 kmph 4) 4.9 kmph 36. A boat can travel 10 kmph in still water. It traveled 91 km downstream and then returned, taking altogether 20 hours. Find speed of the stream? 1) 4 kmph 2) 5 kmph 3) 8 kmph 4) 3 kmph 37. The time taken for a boat to cover certain distance in upstream is equal to the time taken by the boat to cover three times the distance in downstream. If the speed of current is 5 kmph, what is the speed of boat in still water? 1) 14 kmph 2) 15 kmph 3) 10 kmph 4) 19 kmph 38. The time taken by a person to row upstream is twice the time taken by him to row the same distance downstream. If the speed of the boat in still water is 42 kmph, find the speed of current? 1) 14 kmph 2) 32 kmph 3) 12 kmph 4) 8 kmph 39. A man rows his boat to a certain place covering a distance of 72 km and back again in 15 hours. He finds that he takes same time to row 3 km in downstream as much he takes for 2 km in upstream. Find the speed of the stream? 1) 4 kmph 2) 3 kmph 3) 1 kmph 4) 2 kmph 40. A man can row 6 km/hr in still water. If the speed of stream is 2km/hr, it takes him 3 hours to row to a place and back. How far is the place? 1) 16 km 2) 10 km 3) 12 km 4) 8 km Time and Work If a person can complete a work in ‘n’ days then he can do 1/n part of the work in one day. The amount of work done be a person in 1 day is called his efficiency. Example: A can do a work in 10 days. Then the efficiency of A is given by A = 1 / 10. Note: Number of days required to do a work = work to be done / work per day. Example 1: If A can do a work in 10 days, B can do it in 20 days and C in 30 days in how many days will the three together do it? Soln: The efficiencies are A = 1/10, B = 1/20 and C = 1/30 So work done per day by the three = 1/10 + 1/20 + 1/30 = 11/60 => No of days = 60/11 = 5.45 days. Example 2: If A and B can do a work in 10 days , B and C can do it in 20 days and C and A can do it in 40 days in what time all the three can do it? Soln: A+B = 1/10 B+C = 1/20 C+A = 1/40 Adding all the three we get 2(A+B+C) = 7/40 => A+B+C = 7/80 => No of days = 80/7 days. Note: If all the people do not work for all the time then the principle below can be used: mA + nB + oC = 1. (1 is the total work) Here, m=no of days A worked n=no of days B worked o=no of days C worked A,B,C = efficiencies Example 3: If A can do a work in 12 days, B can do it in 18 days and C in 24 days. All the three started the work. A left after two days and C left three days before the completion of the work. How many days are required to complete the work? Soln: Let the total no of days be x. A worked only for 2 days, B worked for x days and C worked for x-3 days. So, mA + nB + oC = 1  2(1/12) + x(1/18) + (x-3)(1/24) = 1  12 + 4x + 3(x-3) = 72  x = 69 / 7 days. Note: The ratio of dividing wages = ratio of efficiencies = ratio of parts of work done Example 4: A can do a work in 10 days and B can do it in 30 days and C in 60 days. If the total wages for the work is Rs. 1800 what is the share of A? Soln: Ratio of wages = 1/10 : 1/30 : 1/60 = 6 : 2 : 1 (Multiplying each term by LCM 60) So total 9 equal parts in Rs. 1800 => each part = Rs. 200 => share of A = 6 parts = Rs. 1200. Note: When pipes are used filling the tank they are treated similar to the men working but some outlet pipes emptying the tank are present whose work will be considered negative. Example 5: A pipe can fill a tank in 5 hrs but because of a leak a the bottom it takes 1 hr extra. In what time can the leak alone empty the tank? Soln: Let the filling pipe be A. A = 1 / 5. But with the leak L, A – L = 1 / 6 ( A-L because leak is outlet) So, 1/L = 1 / 5 – 1/ 6 = 1/30 => Leak can empty the tank in 30 hrs. Example 6: A pipe A can fill the tank in 10 hrs, B can fill it in 20 hrs and C can empty in 40 hrs. All are opened at the same time. After how many hours shall the pipe B be closed such that the tank can be filled in 10 hrs? Soln: Let the pipe B be closed after x hrs. Then A worked for 10 hrs, B worked for x hrs and C worked for 10 hrs. mA + nB – oC = 1 (since C is outlet) 10(1/10) + x(1/20) – 10(1/40) = 1 x = 5 hrs. Exercise: 1. A alone can complete the work in 12 days while A and B together can complete the same work in 8 days. The number of days that B will take to complete the work alone is ___________ 1) 10 2) 24 3) 20 4) 9 2. A can do a work in 6 days and B in 9 days. How many days will both take together to complete the work. 1) 7.5 2) 5.4 3) 3.6 4) 3 3. A can do a piece of work in 4 hours, B and C can do it in 3hrs, A and C can do it in 2hrs. How long will B alone take to do it? 1) 10hrs 2) 12hrs 3) 8hrs 4) 24hrs 4. 10 men and 15 women finish a work in 6 days. One man alone finishes that work in 100 days. In how many days will a woman finish the work? 1) 125 2) 150 3) 90 4) 225 5. A completes a work in 12 days; B completes the some work in 15 days. A started working alone and after 3 days B joined him. How many days will they now take together to complete the remaining work? 1) 5 2) 8 3) 6 4) 4 6. 10 men can complete a piece of work in 15 days & 15 women can complete the same work in 12 days. If all the 10 men & 15 women work together, in how many days will the work get completed? 1) 6 2) 3 2 7 3) 3 2 6 4) None of these 7. A can do a certain work in the same time in which B & C together can do it. If A and B together could do it in 10 days and C alone in 50 days then B alone could do the work in 1) 15 days 2) 20 days 3) 25 days 4) 30 days 8. A& B under took to do a piece of work for Rs.4,500. A alone could do it in 8 days and B alone in 12 days. With the assistance of C they finished the work in 4 days. Then C’s share of the money is ____________ 1) Rs.2,250 2) Rs.1,500 3) Rs.750 4) Rs.375 9. A can finish a work in 24 days, B in 9 days and C in 12 days. B & C start the work but are forced to leave after 3 days. The remaining work is done by A in _____________ 1) 5 days 2) 6 days 3) 10 days 4) 2 1 10 days 10. If 3 men (or) 4 women can plough a field in43 days, how long will 7 men and 5 women take to plough it. 1) 10 days 2) 11 days 3) 9 days 4) 12 days 11. A can do th 4 3 of a work in 12 days. In how many days can he finish th 8 1 of work? 1) 1 day 2) 2 days 3) 4 days 4) 8 days 12. If 72 men can build a wall 280m. long in 21 days, how many men will take 18 days to build a similar type of wall of length 100m.? 1) 30 2) 10 3) 18 4) 28 13. A takes twice as much time as B or thrice as much time as C to finish a piece of work. Working together, they can finish the work in 2 days. B can do the work alone in 1) 12 days 2) 4 days 3) 8 days 4) 6 days 14. A does 5 4 of a piece of work in 20 days; he then calls in B and they finish the remaining work in 3 days. How long will B alone take to do the whole work? 1) 2 1 37 days 2) 37 days 3) 40 days 4) 23 days 15. A does half as much work as B in 1/6 of the time. If together they take 10 days to complete a work, how many days shall B take to do it alone? 1) 15 days 2) 30 days 3) 40 days 4) 50 days 16. A man, a woman and a boy can together complete a piece of work in 3 days. If a man alone can do it in 6 days and a boy alone can do it in 18 days, how long will a woman alone take to complete the work. 1) 9 days 2) 21 days 3) 24 days 4) 27 days 17. If the wages of 6 men for 15 days be Rs.700, then the wages of 9 men for 12 days will be ___________ 1) Rs.700 2) Rs.840 3) Rs.1050 4) Rs.900 18. A man is paid Rs.20 for each day he works, and forfeits Rs.3 for each day he is idle. At the end of 60 days he gets Rs.280. Then he was idle for _____________ 1) 20 days 2) 25 days 3) 30 days 4) 40 days 19. A team of 10 men can complete a particular job in 12 days. A team of 10 women can complete the same job in 6 days. How many days are needed to complete the job if the two teams work together? 1) 4 2) 6 3) 9 4) 18 20. A contractor undertook to finish a certain work in 124 days and employed 120 men on it. After 64 days, he found that he had already done rd 3 2 of the work. How many men he can discharge now so that the work may finish in time 1) 24 2) 56 3) 64 4) 80 21. A work could be completed in 100 days. However, due to the absence of 10 workers, it was completed in 110 days. The original number of workers was ___________ 1) 100 2) 110 3) 55 4) 50 22. A contractor under takes to make a road in 40 days and employs 25 men. After 24 days, he finds that only one- third of the road is made. How many extra men should he employ so that he is able to complete the work 4 days earlier? 1) 100 2) 60 3) 75 4) none of these 23. 30 men complete one third of a work in 30 days. How many more men should be employed to finish the rest of the work in 40 more days? 1) 15 2) 45 3) 20 4) 25 24. A and B under took to do a piece of work for Rs.900. A alone could do it in 60 days and B in 30 days. If A & B work together and complete the work, then the share of B _______ 1) Rs.600 2) Rs.400 3) Rs.300 4) Rs.200 25. 5 men or 6 women or 10 boys can do a work in 15 days. How long will it take to complete the work by a group of 5 men, 6 women and 10 boys? 1) 5 days 2) 6 days 3) 10 days 4) 45 days 26. A can do a piece of work in 30 days. B in 15 days and C in 10 days. They started the work all together but B put 2 1 time daily and C put 3 1 time daily to help A in doing the work. The work will last in ______________ 1) 30 days 2) 10 days 3) 20 days 4) 25 days 27. A can do a work in 15 days & B the same work in 12 days. B started the work and was joined by A, 5 days before the end of work. The work lasted for _____ days. 1) 8 2) 12 3) 13 4) 24 28. A and B can do a piece of work in 40 days while C & A can do it in 60 days. If B is twice as good as C, then C alone will do the work in ___________ days. 1) 120 2) 100 3) 80 4) 24 29. A hostel has provision for 800 men for 24 days at the rate of 2 kg per man per day. For how many men is the provision sufficient, for 20 days at the rate of 1.5 kg per man per day? 1) 1280 2) 1000 3) 1820 4) 1240 30. 12 men can do a work in 15 days working 8 hours a day. In how many days can 9 men do the same work, working 10 hours a day? 1) 10 2) 16 3) 18 4) 24 31. Two taps A and B can separately fill a tank in 20 and 30 hours respectively. If both the pipes are opened simultaneously, how much time will be taken to fill the tank? 1) 10 hrs 2) 11 hrs 3) 18 hrs 4) 12 hrs 32. A tap can fill a tank in 12 minutes and another tap in 15 minutes, but a third tap can empty it in 6 minutes. The three taps are kept open together. Find when the cistern is emptied or filled? 1) 60 min. to fill 2) 30 min. to fill 3) 60 min to empty 4) 30 min to empty 33. Two taps A & B can fill a cistern in 12 and 16 minutes respectively. Both fill taps are opened together, but 4 minutes before cistern is full, one tap A is closed. How much time will the cistern take to fill? 1) 9 1 / 7 min. 2) 3 1 / 7 min. 3) 11 1 / 7 min. 4) None. 34. A ship 55 km from the shore springs a leak which admits 2 tonnes of water in 6 minutes. 80 tonnes would suffer to sink her, but the pumps can throw out 12 tonnes an hour. Find the average rate of sailing that she may just reach the shore as she begins to sink. 1) 5.5 kmph 2) 2.5 kmph 3) 1.8 kmph 4) 4 kmph 35. A tap can fill a swimming pool in h hours. What part of the pool is filled in y hours? 1) yh 2) y h 3) h y 4) h – y 36. Three pipes A, Band C can fill a tank in 30 min, 40 min and 60 min respectively. A and B work in alternative minutes, A beginning the work whereas C works continuously. In how many minutes will the tank be filled? 1) 16.4 2) 21.8 3) 18.2 4) 19.6 37. A tank has a leak, which would empty it in 8 hrs. A tap is turned on which admits 6 litres of water a minute into the tank and it is now emptied in 12 hrs. How many litres does the tank hold? 1) 8640 2) 8460 3) 8064 4) 8406 38. A cistern is normally filled with water in 10 hours but takes 5 hours longer to fill because of a leak in its bottom. If the cistern is full, then the leak will empty the cistern in 1) 20 hours 2) 40 hours 3) 50 hours 4) 30 hours 39. Two pipes A and B can separately fill a cistern in 60 and 75 minutes respectively. There is a third pipe at the bottom of the cistern to empty it. If all the three pipes are simultaneously opened, then the cistern is full in 50 minutes. In how much time can third pipe alone empty the cistern? 1) 110 minutes 2) 100 minutes 3) 120 minutes 4) 90 minutes 40. A tap can fill a tank in 6 hours. After half the tank is filled, three more similar taps are opened. What is the total time taken to fill the tank completely? 1) 4 hours 2) 4 hours 15 minutes 3) 3 hours 15 minutes 4) 3 hours 45 minutes