Test-Taking Tips Easy items are scattered all throughout the test. .Precision is important BUT do not spend too long on one item. One must develop a data-selection ability and ignore those unnecessary info. Skip difficult questions and solve easy questions first. Focus only on the sought data . tables and graphs which serves to confuse.Gives peace of mind when one knows he is prepared. Control the Timing .There could be excess data. Practice makes perfect! . Having an accurate expectation of examination questions is calming and provides quicker computation. It would be nice to allot about 2 minutes before the end of the exam to make good guesses on unanswered items. Watch out for tricky questions . .Do visualization and other relaxation techniques. But many test-takers fail to fill-in those unanswered items. Remain Calm .These questions will ask about something not stated from the problem. Don't leave blank spaces . Knowing how to detect them will spare you time.Many tests are really lengthy that no one could finish them all. Topics Logical & Spatial Reasoning Clerical Ability Test Analogies Numerical Reasoning . Logical Reasoning is a system that we use to construct an argument from observation and known facts. . They are: Induction Abduction .Deduction • means determining the conclusion • using the rule and its precondition to make a conclusion Logical Reasoning .Are classified into three. Deduction • means determining the rule. They are: Induction Abduction .Are classified into three. Logical Reasoning . • Knowing the rule after several events prove a consistent idea. Are classified into three. They are: • means determining the precondition.Deduction Logical Reasoning . • using the conclusion & the rule to support that the precondition could explain the conclusion. Induction Abduction . All nuns are prayerful.Logical Statements have the following: Precondition Conclusion Maria is a nun. Maria is prayerful. Rule . .determining the conclusion (Precondition) “It rained. Therefore.Deduction .” (Conclusion) ? Ans. the grass gets wet. the grass is wet.” (Rule) "When it rains. " . the grass gets wet. Therefore.Induction .” Ans. the rule is.determining the rule (Precondition) "The grass has been wet” (Rule) ? (Conclusion) “every time it has rained. “when it rains. determining the precondition. the grass is wet. “It rained. the grass gets wet.” . (Precondition) ? (Rule) "When it rains.Abduction .” (Conclusion) Therefore. Ans. Logical Reasoning Given: Argument or Explanation Task: To Analyze Product: • • • • Description of the Argument Draw Conclusion Contradict or Defend the Argument Draw an Assumption . • Draw rough diagrams.Avoid being influenced by your own personal opinions. charts *Follow the line of reasoning then use the Common Sense standard of logic. • Note: You don’t need to have a masteral or doctorate degree to answer logical questions How to answer logical reasoning questions? . Read the passage. Of the remaining answer choices. choose the best answer Suggested Answering Approach . or beyond the scope of the passage. Read the question again. V. focus on elements important to the question III. Do the analysis of the answer choices by eliminating those that are irrelevant. Read the question first before reading the passage and mark the keyword II. inconsistent. IV.I. Types of Logical Questioning Conclusion Determination • Supposition • Argument Enhancement / Reduction • Error Identification • Error Correction Appraisal Harmonizing Construction • Inference • Divergence • Process • Standard • Parallel Reasoning • Underlying issue . Appraisal Questions . Argument Enhancement/Reduction • These problems require the examinee to make a selection that will either enhance or reduce the validity of a stated argument.Supposition • These questions require the examinee to make an assumption about a missing portion of the argument presented. Appraisal Questions . Error Correction • These problems require the examinee to choose the selection that best corrects the problems in a reasoning statement or argument.Error Identification • These problems require the examinee to identify the logical error contained in the argument or scenario given. Inference •These problems require the examinee to follow the facts provided to a reasonable conclusion. Conclusion Determination . Harmonizing .Divergence • These problems require the examinee to follow two points of view on a particular topic and identify where the two points of view diverge. Process • These problems require the examinee to recognize the process(es) used by the exam writer to produce the problem. Parallel Reasoning • Examinee must identify identical reasoning used in different circumstances. Harmonizing .Standard • These problems require the examinee to correlate facts given to specific standards or provided standards to their necessary facts. Function: These problems require the examinee to identify the purpose of various statements given in a passage.Underlying issue • These problems require the examinee to identify the underlying issue and separate it from the facts. Construction . Syllogistic Reasoning basic logic is concerned with using syllogisms to draw conclusions from premises. . . Conclusion: Therefore. a form of deductive reasoning consisting of a major premise. the conclusion should follow from the two premises. . Major Premise • makes a general statement that the writer believes to be true. all black dogs are warm-blooded. and a conclusion. Minor Premise • presents a specific example of the belief Conclusion • If the reasoning is sound. a minor premise. Here is an example of a valid categorical syllogism: Major premise: All mammals are warm-blooded. Syllogistic Reasoning . . Minor premise: All black dogs are mammals. What Makes a syllogism valid? true? sound? true when it makes valid (or logical) when accurate claims--that is. a its conclusion follows when the information it syllogism must be both contains is consistent from its premises. valid and true. Syllogistic Reasoning . To be sound. with the facts. Is this syllogismValid? True? Sound? Major premise: All mammals are warm-blooded. Statement 2: Some animals are female. Conclusion: Therefore. How about statements A & B? Are they Valid. Ans. Statement 2: Some animals are aggressive. Invalid. Conclusion: Some men are female. true and sound. False. True. all black dogs are warm-blooded. Unsound Statement 1: All men are animals. it is valid. Minor premise: All black dogs are mammals. Syllogistic Reasoning . Unsound A) B) Statement 1: All men are animals. True and Sound Syllogisms? Valid. Conclusion: Some men are aggressive. Yes. The previous syllogisms were examples of Syllogistic traps. Simply, Syllogistic Traps mean “we are using what we know to be true as substitute for the logic of the statement.” Using Venn Diagrams Syllogistic reasoning uses rational logic and hence set theory applies and the best way to visualize it is to draw a Venn Diagram. Proof: The animals who are aggressive are not necessarily men. Syllogistic Reasoning Common Syllogistic Traps • • • • Affirming the Consequent: If A then B. B is true, so A is true. Denying the Antecedent: If A then B. A is false, so B is false. Four Terms: All A is B. All C is D. So all A is D. Illicit Major: All X is Y. No P (which is a subset of Y) is X. Therefore no P is Y. • Illicit Minor: All X are Y. All X are P. Therefore all P are Y. Unspoken assumption: All Y is X. • Undistributed Middle: All A is B. All C is B. Therefore all C is A. Unspoken assumption: All P are X. Syllogistic Reasoning Affirming the Consequent • I am in London, England. I am in England, therefore I am in London. Denying the Antecedent • If you give a man a gun, he may kill someone. If he has no gun, then he will not kill anyone. Four Terms • All dogs are mammals. All fish are animals. So all dogs are animals. [true, but not proven by the first two statements] • Man is an intelligent animal. No woman is a man. Therefore no women are intelligent animals. ['man' has two different meanings] Illicit Major • All Londoners are European. No Parisiens are Londoners. Therefore no Parisiens are European. Syllogistic Reasoning Therefore some boys are elephants. Therefore you are a fool. • All elephants are big. Syllogistic Reasoning . All women are beautiful. Undistributed Middle • All Californians are beautiful. Some boys are big. All New Yorkers are intelligent.Illicit Minor • All New Yorkers are beautiful. Therefore all intelligent people are beautiful. Therefore all women are Californian. You acted stupid. • All fools act stupid. Rules for Categorical Syllogism (a common type of syllogism) Rule 1: There must be three terms and only three – the major term, the minor term, and the middle term. (Sample Error) Animals are living beings. Plants are heavenly bodies. Therefore… Rule 3: The middle term Rule 2: Each term must must be distributed at occur twice in the least once. syllogism: the major must occur in the conclusion (Sample Error) and in one premise, the All sharks are fish. minor in the conclusion All salmon are fish. and in one premise; the middle in both premise Therefore, all salmons are but not in the conclusion. sharks. Syllogistic Reasoning Rules for Categorical Syllogism (a common type of syllogism) Rule 4: The major and minor terms may not be universal in the conclusion unless they are universal in the premises. Same applies for minor terms. (Samle Error) All horses are animals. All dogs are not horses. Therefore, all dogs are not animals. Rule 5: If both premises are affirmative, the conclusion must be affirmative. The reason for this rule is that affirmative premises either unite the minor or major terms. (Sample Error)All sins are detestable. All pretenses are a sin. Therefore, all pretenses are not detestable. Rule 6: If one premise is affirmative and the other negative, the conclusion must be negative. (Sample Error) All crows are birds. All wolves are not crows. Therefore, all wolves are birds. Syllogistic Reasoning Rules for Categorical Syllogism (a common type of syllogism) Rule 7: If both premises are negative – and not equivalently affirmative – there can be no conclusion. (Sample Error)Reptiles are not mammals. Dogs are not reptiles. Therefore… Rule 8: If both premises are particular there can be no conclusion. Syllogistic Reasoning Ready for some fun Logic Exercises? Lets GO!!!!!! . Heidi thinks that Rico failed the bar exams.The fact that the _______ of confrontation is no longer as popular as it once was _______ progress in race relations. Which can be inferred from the following conversation? Heidi: I have just have heard that Rico failed the bar exams. Mavic assumes that no witty individual can fail the bar exams.technique … presages E. Mavic thinks that Heidi got the wrong information.practice … inculcates C.insidiousness … reiterates B. Rico was very witty. E.reticence … indicates 2. Mavic: Impossible.glimmer … foreshadows D. A. C. Mavic thinks Heidi is telling a lie. Heidi thinks that Rico failed the bar exam. Logic Exercises .* D. B.1. A. Ruth C. Rochelle holds a position senior to Ruth. B. A. Kai D. C. It is either one of ours or one of yours. and Kai holds a junior post to Ruth. ______________. It is not one of yours. D. E. None of the above. Who holds the junior-most position? A. MSA E. Rochelle 4.3. no one Logic Exercises . Therefore. It is not one of ours. At MSA preschool. It is one of yours. It is not one of ours. It is one of ours B. Some of the artists belong to the AAP. This conclusion can be deduced from which of the following statements? A. E. Caloy is an artist. then he is not an artist.With the warning. At all concerts. the child may stop troubling her. A. Only assumption I is implicit B. Caloy is seated in the front row.Both I and II are implicit Logic Exercises .If Caloy was not asked to join the Senior’s Club.All children are basically naughty. Assumptions: I. Neither I nor II is implicit E. None of the above. 6. C. Caloy was asked to join the said club. Either I or II is implicit D. If one is an artist. everyone who is not an artist is seated in one of the back rows. I will slap you. he draws meaningful pictures. B. II. Only assumption II is implicit C.A mother warns her child. Caloy belongs to the AAP. Statement: "If you trouble me." .5. D. leaf C) 145 C. mangrove E) 121 E. Friday Logic Exercises . How many total number of hand shakes occurred? 8) The day after the day after tomorrow is four days before Monday. What day is it today? 9) Forest is to tree as tree is to ? A) 100 A. Wednesday D. Tuesday B. plant B) 132 B. 12 members shook hands with each other before & after the meeting.7) At a conference. branch D) 144 D. Monday A. Thursday C. (iv) D weighs half as much as E. (iv) D weighs half as much as E. 10) Which of the following is the lightest? (i) A weighs twice as much as B.D. (ii) B weighs four and a half times as much as C. C.A fisherman has 5 fishes (namely A. (i) A weighs twice as much as B. B. (v) E weighs less than A but more than C. (iii)C weighs half as much as D. (ii) B weighs four and a half times as much as C. (iii)C weighs half as much as D. Ans: (iii) C Logic Exercises . E) each having a different weight. (v) E weighs less than A but more than C. (ii) B weighs four and a half times as much as C.D (ii)D. (v) E weighs less than A but more than C.C Ans: (v) A. 11) In the same problem. (iv) D weighs half as much as E.A fisherman has 5 fishes (namely A. C. (i) A weighs twice as much as B.D (iv)B.C (v)A. E is lighter in weight than which of the following pairs? (i) B.B Logic Exercises . (iii)C weighs half as much as D.D. E) each having a different weight.B (iii)A. B. b B. c C. b C. castle D. d A. bloat C. i D. c D. a B. bald B.12) 6121135 is to flame as 21215120 is to ? 13) What is the missing letter in this series: h g ? e d 14) What is the missing letter in this series: c c d ? e f g g h A. e E. f E. f Logic Exercises . voice A. y Logic Exercises . b A. p C. k E. r E. q D. o B. c C. j D. w D. a B.15) What is the missing letter in this series: a z b ? c x 16) What is the missing letter in this series: f g e h d i c ? 17) What is the missing letter in this series: r q p r q p ? A. s C. x B. b A. l E. Max turns around and joins the pursuit. James C. false A. Max Logic Exercises . Ruby C. James is directly behind the dog. Eric is older than Cliff. Ruby is behind James. Ruby runs faster and is alongside the dog on the right. He runs in behind Ruby. As the children and dog pass. Max is ahead of the dog walking down the street in the opposite direction.18) Tanya is older than Eric. true B. Which child is directly behind the dog? A. Rachel is behind Ruby. Rachel D. James runs faster and is alongside the dog on the left. uncertain B. If the first two statements are true. the third statement is 19) Children are in pursuit of a dog whose leash has broken. Cliff is older than Tanya. • A.21): Each question given below consists of a statement.Either I or II is strong • D.Both I and II are strong Ans. 20 . It encourages the kidnappers to continue their sinister activities. a proper course of action? Arguments: Yes.Only argument I is strong • B. 21) Statement: Is paying ransom or agreeing to the conditions of kidnappers of political figures.Direction (for Q.Neither I nor II is strong • E.Only argument II is strong • C. No.Nos. The victims must be saved at all cost. Logic Exercises . E Both the arguments are strong enough. followed by two arguments numbered I and IL You have to decide which of the arguments is a 'strong' argument and which is a 'weak' argument. Further. It will help in eliminating tensions among the nations. a world government cannot eliminate tensions among nations because it will also have the ruling group and the opposition group.Only argument II is strong • C.21) Statement: Should there be a world government? Arguments: Yes.Either I or II is strong • D.Both I and II are strong Ans. Then.Only argument I is strong • B. only the developed countries will dominate in the government. No. only argument II holds. the more powerful and diplomatic shall rule the world to their interests. • A.Neither I nor II is strong • E. B Clearly. Logic Exercises . So. 22. All toffees are chocolates.Nos.Only conclusion I follows • B.Both I and II follow Ans. • A. Conclusions: Some chocolates are toffees.Direction (for Q. Read the conclusion and then decide which of the given conclusions logically follows from the two given statements. A Logic Exercises .Neither I nor II follows • E.Only conclusion II follows • C.Either I or II follows • D. Some toffees are not pastries. You have to take the given two statements to be true even if they seem to be at variance from commonly known facts. disregarding commonly known facts. Statements: Some pastries are toffees.23): In each question below are given two statements followed by two conclusions numbered I and II. II. Conclusions: I.Neither I nor II follows E. No rich man is poor. • • • • • A.Only conclusion I follows B.Either I or II follows D.Both I and II follow Ans. All gentlemen are rich. No poor man is rich. D Logic Exercises .23) Statements: No gentleman is poor.Only conclusion II follows C. 25) tadpole lamb frog sheep amphibian ? C. rung Directions: The words in the bottom row are related in the same way as the words in the top row. cushion D. leg • A) animal • B) wool • C) farm • D) mammal Ans. For each item. Logic Exercises . find the word that completes the bottom row of words. D.24) Which word does NOT belong with the others? A. seat B. .Spatial Reasoning is the ability we use to position and orientate ourselves in everyday environments. cube views in 3-dimensions. Spatial Reasoning . shape rotation. • and the manipulation of other solid shapes in 2 and 3 dimensions. Spatial reasoning ability questions cover: • shape matching. • combining shapes.Spatial reasoning consists of two main abilities: • spatial visualization ability which is your ability to call up images in your mind • and the ability to reason with these images. One of the shapes has been ‘cut up’ into pieces. Spatial Reasoning . one of which may have been rotated. You are then asked to say which symbol is on the opposite face. In these types of question you will be presented with a number of objects only two of which are identical. The questions presents you with the pieces and you are asked to work out which of the shapes has been ‘cut up’. markings or symbols on each face. You will need to identify the identical shapes.Spatial Reasoning – Combining Shapes • These questions show you a series of 2-dimensional shapes. Spatial Reasoning – Matching 2-dimensional shapes • These are speed questions. Spatial Reasoning – Cubes in 3-dimensions • These questions show you views of a 3-dimensional cube with unique figures. each face of the solid shape has a shape of its own rather than just being square. Spatial Reasoning . You will need to identify the identical groups. Spatial Reasoning – Solids in 2 and 3-dimensions • These questions use solid shapes which may be irregular.Spatial Reasoning – Matching Rotated Groups • In these types of question you will be presented with a series of groups of objects. only 2 of the groups are identical. military and law enforcement jobs where the ability to give or follow directions based on a map or street plan is essential. Spatial Reasoning – Maps and Plans • These questions often appear in tests for emergency services. In other words. one of which will have been rotated. How to Improve on Spatial Reasoning Tests . Find similarities and differences between shapes and patterns. and Retain the pattern/rule. How to Answer Spatial Reasoning Tests .Identify relationships. Recognize visual sequences and relationships between objects. B.2 . A. Spatial Reasoning Exercises 1. 4 . C. blue square. blue square + red circle underneath. blue square + red circle + green triangle + black circle underneath.E. blue square + red circle + green triangle + black circle + red square on top: C is the answer Spatial Reasoning Exercises 3. blue square + red circle + green triangle on top. D. Hint: Mind the gap Spatial Reasoning Exercises 5.6 . D. Hint: Colour Cycling B.8 .B. Hint: Count everything! Spatial Reasoning Exercises 7. C.10 . Hint: Count the lines E. Hint: Rectangle orientation Spatial Reasoning Exercises 9. 12 . Hint: Blue squares D. Hint: Clockwise Spatial Reasoning Exercises 11.E. 14 . Hint: Lines Spatial Reasoning Exercises 13. Hint: Follow the leader C.B. If you do not think any of the figures is the same as the target shape then choose the answer option (e) ‘none of these’.16 . c Spatial Reasoning Exercises 15. Your task here is to look at the target figure and decide which of the rotated figures below is identical to it. Ans. e Ans. B Spatial Reasoning Exercises 16 .Ans. A Spatial Reasoning Exercises 17 .Ans. Ans. D Spatial Reasoning Exercises 18 . D Spatial Reasoning Exercises 19 .Ans. C Spatial Reasoning Exercises 20 .Ans. Ans. B Spatial Reasoning Exercises 21 . Ans. D Spatial Reasoning Exercises 22 . Ans. A Spatial Reasoning Exercises 23 . Ans. West Ans. B) N Spatial Reasoning Exercises 24.25 . Clerical Ability Test This part of the Civil Service Exam will only cover two abilities i.e. . Alphabetization and Matching Ability. Alphabetization Exercise: Job Jack Fragrance Indecent Hill Heel Flamboyan Fragrant . Abbreviations. Designation. Be careful with: • Spelling. Special Symbols.Matching Ability • Requires one to match an exact duplicate of the given set of words or phrase to the choices given. Salutations . Numbers. Punctuations. Central London w1D3Qb Matching Ability Exercises . Smith Po Box 2354* Chico. John L. Smith Po Box 2354 Chico.Travel Agency7 Soho Square West Central London W1D 3QB A. Box 2854 Chico. John L. John L. CA 95927 2. Expedia.Travel Agency 7 Soho Square West Central London W1D 3QB C. Expedia. Expedia. John L.Travel Agency 7 Sobo Square West Central London W1D 3QD D. Smith Po Box 2354 Chico.Com Ltd . Smith Po Box 2354 Cico.Travel Agency 7 Soho Square W.1. CA 95927 D. Ca 95927 B. Smith P. Jonn L. Expedia. CA 95927 B. Expedia.Com Ltd .O.Com Ltd .Com Ltd .Com Ltd . CA 95927 C.Travel Agency 7 Soho Square West Central London WLD 3QB A. .Analogies These types of questions ask you to determine the relationship between a pair of stem words and find the same relationship in one of the answer pairs. Let's try one. The capitalized words are the stem words. SKYSCRAPER:SHACK:: A) elevator:escalator (B) house:building (C) village:town (D) jetliner:biplane (E) chimney:fireplace Analogies .Working Analogy Questions When reading the analogy questions you can interpret the colons like this: (:) translates to "is to" and (::) translates to "as". (A) elevator:escalator What's their relationship? (B) house:building A skyscraper is a large. Comparing the Stem Words SKYSCRAPER:SHACK:: The stem words . modern structure vs.skyscraper and shack.So what’s the answer? D. small and old-fashioned structure (C) village:town (D) jetliner:biplane (E) chimney:fireplace So what’s the answer? . modern structure. A shack is a small oldfashioned structure So the relationship is: large. The first word was a modern and big version of the second word. NOT same CATEGORIES. but the correct answer has nothing to do with buildings. (D) jetliner:biplane (E) chimney:fireplace .SKYSCRAPER:SHACK:: Finding the Answer Notice something? The stem words are about buildings. You're looking for (A) elevator:escalator (B) house:building (C) village:town same RELATIONSHIPS. E. (A) fish:river (B) volleyball:net (C) field:fun (D) stadium:game (D) stadium:game Start with the second word instead of the first. See example below. Hence the answer is…. . "Soccer is a kind of sport. 1." Let’s do the same for the other word pairs.SPORT:SOCCER:: Defining the Relationship Here are some helpful tricks to determine the relationship. (B) pollen:bee (C) farm:tractor (D) automobile:traffic (E) requirement:limitation . See left. brings rain. Choice (A) is the right answer.SPRING:RAIN:: (A) suitor:gifts Defining the Relationship 2. Nouns or Verbs? Identifying what part of speech the words are help in defining the relationship of the stem words. Spring. in the same way that a suitor brings gifts. the season. It is to your advantage to memorize them so you can approach the analogy questions on the with confidence.The following are the eleven most common analogy relationships. Common Relationships . remember? Soccer is a type of sport. delay is what a procrastinator does. Whatever order you use for the stem words is the order you must use for each of the choices. or minor crime. Here's another example: JAYWALK:MISDEMEANOR:: Jaywalk is a type of misdemeanor. Type 2: “Definition” • PROCRASTINATOR:DELAY:: A procrastinator is someone who delays. Common Relationships . Type 3: “Opposites” • STARVATION:BINGEING:: Starvation is the opposite of bingeing. Or you could say.Type 1: “Type Of” • SOCCER:SPORT:: You saw one like this before. The first word lacks the second word. Common Relationships .Type 4: “Lack Of” • PAUPER:MONEY:: A pauper lacks money. the two words are synonyms. Type 5: “Same” • PERSUASIVE:CONVINCING:: Someone who is persuasive is also convincing. Type 6: “Extremes” • HOT:SCALDING:: The second word is the extreme of the first word. The first word is used for the purpose of the second word. Common Relationships . Type 8: “Use” • GILLS:BREATHING:: Gills are used for breathing.Type 7: “Part to Whole” • PLATOON:SOLDIER:: The second word is part of the first word. Type 9: “Place” • DESERT:OASIS:: The second word is located in the first word. Type 10: “Sign Of” • SNARL:ANGER:: The first word is a sign of the second word. Common Relationships . The second word is something that is done during the first word. CONSTRUCTION:CARPENTER:: The second word is someone who performs the first word. The first word is a tool used for doing the second word. Type 11: “Job-Related Pairs” • SURGERY:INCISION:: An incision is performed in surgery. SCALPEL:SURGERY:: A scalpel — which is a doctor's cutting tool — is used in surgery. DOCTOR : HOSPITAL :: (A) sports fan : stadium (B) cow : farm (C) professor : college (C) professor : college (E) food : grocery store 5. ANGLE : DEGREE A. Select the lettered pair of words.1. BIRD : NEST :: (A) dog : doghouse (B) squirrel : tree (C) beaver : dam (D) cat : litter box (E) book : library 3. DALMATIAN : DOG :: (A) oriole: bird (B) horse : pony (C) shark : great white (D) ant : insect (E) stock : savings 4. followed by five lettered pairs of related words. . area : square inch B. society : classes D. CUB : BEAR :: (A) piano : orchestra (B) puppy : dog C) cat : kitten (D) eagle : predator (E) fork : utensil Exercises : Each of the questions below consists of two words that have a certain relationship to each other.letter : alphabet E. milk : quart C. time : minutes 2. careful: punishing E. PARENTHESIS : EXPLANATION A. danish : Dutch E. financial : bankrupt B. . credible : incredible D.6. followed by five lettered pairs of related words. fish : vehicle B. TENET : THEOLOGIAN :: (A) predecessor : heir (B) hypothesis : biologist (C) recluse : rivalry 7. DORY : VAN 9. dairy : cow B. knowledge : supposed A. Select the lettered pair of words. CONFIRMED : INVETERATE 8. asterisk : exaggeration C. apostrophe : annotation (E) guitarist : rock band E. ellipsis : omission A. synthesis : interpolation Exercises : Each of the questions below consists of two words that have a certain relationship to each other. freighter : caisson C. immature : callow C. synopsis : affectation (D) arrogance : persecution D. runners : wheels D. unlike those for personality and psychological assessment. one can learn and improve the skills necessary for success by completing practice tests with similar questions. .Numerical Reasoning For numerical reasoning tests. you need to work out how to get the answer. rather than just doing the necessary calculations. Definition . In other words.What’s a Numerical Reasoning Test? • A numerical reasoning test is a power test rather than a speed test because the questions require you to interpret the information provided and then apply the appropriate logic to answer them. charts and tables. powers. currency conversions and more What are to be expected in the exam? • Arithmetic Questions – includes: • addition. etc) Number Sequences – find missing numbers in a sequence. statistical and economic topics and they specifically include: • • • • • • • • • • percentages. sales data. Alphabet letters as numbers is another variation to this type of questioning. Data Interpretation – information is provided and requires the test-taker to exert the right logic to answer the question.The tests are based mainly on financial. proportions. means. comparisons. Eg. costs. trends. multiplication and division • number sequences • simple mathematics (percentages. subtraction. fractions. Table and graph interpretation Numerical Reasoning . indices. 5 x 16 = A) 80 B) 86 C) 88 D) 78 4. 139 235 = A) -69 B) 96 C) 98 D) -96 3.1. ½ + ¼ x 3/4 = A)3/8 B) 13/8 C) 9/16 D) 3/4 Exercises on Arithmetic Questions .5 B) 4 C) 5 D) 6 5. 15% of 300 = A)20 B) 45 C) 40 D) 35 6. 139 + 235 = A) 372 B) 374 C) 376 D) 437 2. 45 / 9 = A) 4. . This missing number may be at the beginning or middle but is usually at the end.Number Sequences Numerical Reasoning These questions require you to find the missing number in a sequence of numbers. ..7) 4…8…16…32…____ 8) 4…8…12…20…____ 9) 54…49…____.39…34 A) 48 A) 32 A) 47 B) 64 C) 40 D) 46 B) 34 C) 36 D) 38 B) 44 C) 45 D) 46 Number Sequences: Find the next number in the series . 10) B…E…H…K…--- i) L ii) M i) C ii) X i) Y ii) B iii) N iv) O iii) D iv) Y iii) A iv) W .” Be very extra careful while keeping a good pace when doing these items. Find the next letter in the series 11) A…Z…B…Y…--12) T…V…X…Z…--- Number Sequences A variant of number sequences is the use of “Alphabet as Numbers. com/3452410 . Article Source: http://EzineArticles.Data Interpretation Numerical Reasoning "the application of statistical procedures to analyze specific observed or assumed facts from a particular study". 13) Below are the sales figures for 3 different types of network server over 3 months. 13a) In which month was the sales value highest? 13b) What is the unit cost of server type ZXC53? 13c) How many ZXC43 units could be expected to sell in April? A) January B) February C) March A) 12 A) 56 B) 13 C) 14 B) 58 C) 60 Data Interpretation . comparisons. trends. means.percentages. indices. sales data. currency conversions and more Numerical Reasoning Topics . proportions. costs. charts and tables. Percentage a percentage is a way of expressing a number as a fraction of 100 (per cent meaning "per hundred" in Latin). . the second quantity.06. relative to another quantity.Percentages are used to express how large/small one quantity is. an increase of $ 0.50 = 0.50 is an increase by a fraction of 0. this is therefore a 6% increase. or a change in. which should be greater than zero. The first quantity usually represents a part of.15 on a price of $ 2. Percentage . For example.15/2. Expressed as a percentage. Convert Decimals to Fractions Convert Fractions to Percents Convert Percents to Decimals Percentage . . Convert Decimals to Fractions Step 1: Write down the decimal divided by 1.. Divide both the top and bottom of the fraction by the Greatest Common Factor. like this: decimal/1 How do I Simplify a Fraction ? Step 2: Multiply both top and bottom by 10 for every number after the decimal point.7. Percentage . Method 2.5. Step 3: Simplify (or reduce) the fraction Method 1.. Try dividing both the top and bottom of the fraction until you can't go any further (try dividing by 2. etc).3. or 100. Convert Percent to Decimals Just move the decimal point 2 places to the left and remove the "%" sign! Step 1: Find a number you can multiply by the bottom of the fraction to make it 10. Step 3. Then write down just the top number. Percentage . Step 2: Multiply both top and bottom by that number. or any 1 followed by 0s. Convert Fraction to Decimals and Percents Let’s Try! Convert 3/8 to decimal and percent. putting the decimal point in the correct spot. or 1000. 20 C) 0. A) 0.13 E) 0.069 C) 0.00105 % B) 0. 5) Convert 1.25 B) 0. 3) Express 17.5% as a fraction.69 D) 69 E) 0.1) Convert 2/5 decimal.5% E) 6/7 E) 1% Percentage Exercises . 4) Express 260% as a fraction.35 A) 6. 2) Convert 69% to decimals.0105% C) 105% A) 0.0069 A) 17/100 B) 1/5 C) 9/40 D) 7/9 E) 7/40 A) 2 3/5 B) 1 3/5 C) 13/50 D) 5/13 D) 10.15 D) 0.9 B) 0.05 to percent. charts and tables. means. indices. proportions. currency conversions and more Numerical Reasoning Topics . sales data. trends.percentages. costs. comparisons. Proportions A proportion is a name we give to a statement that two ratios are equal. . a:b = c:d There are three kinds of proportion. Twice the soup costs twice he money Indirect/ Inverse Proportion • this is when one quantity decreases as another increases by the same factor. How much will each of the four children receive? Proportions . Direct Proportion • is defined as increase in one quantity causes increase in other quantity or decrease in one quantity causes decrease in other quantity. or. Partitive Proportion • Partitive proportion involves identifying parts of a whole based on a given ratio of these parts. A father wants to leave $4675 to his four children in the ratio of 1:3:3:4. indirect and partitive. E. using a colon. They are direct. • Eg.It can be written in two ways: two equal fractions.g. 50. how many pencils can you buy with $9.8 each from the same amount? 5) Jane ran 100 meters in 15 seconds. How long did she take to run 1 meter? A) Direct A) Direct A) Direct A) Direct A) Direct B) Indirect B) Indirect B) Indirect C) Partitive C) Partitive C) Partitive C) Partitive C) Partitive B) Indirect B) Indirect Identify what kind of proportion is given. Proportions .1) John plans to donate his collection of 3042 books to three libraries in the ratio of 1:3:5.14. How many toys Imran can buy at Rs. How many books will each library get? 2) If two pencils cost $1.00? 3) Four pipes can fill a tank in 70 minutes. How long will it take to fill the tank by 7 pipes? 4) Imran brought 40 toys each cost Rs. Put the #s with the same quantities together on the left. the smaller # on top. The remaining number is kept together with one of the first two numbers. 2. Proportions . How to solve direct proportion? 1. 50 3 3.15 2.1) For every 3 students. 16 2 15 25 27 33 2. 2) The recipe says 6 cups cereal for every 5 cups of marshmallows. The class has 42 students. we need a computer. But we only have 3 cups of cereals.25 Proportions . How to solve Inverse Proportion? 1. Proportions . the smaller # on top. Put the #s with the same quantities together on the left. The remaining # is not kept together with one fof the first two numbers. 2. 5 hrs.5 hrs. Proportions . 115mins. 6 people cleaned the stadium in 3 hours. 4 hrs. 4. How long will it take 4 people? 100mins. If we drive 100 km/hr. how long will the trip be? 2. 45mins. 5.75 hrs. It took 175 mins.1. 6 hrs. To reach the cottage at 80 km/hr. 3. 120mins. 140mins. divide the number representing the total. multiply the quotient by each of the term in the ratio. by the sum of the terms in the ratio then. How to solve partitive proportion? To get the answer. Proportions . How many books will each library get? Proportions . 2.1. How much will each of the four children receive? 3. A father wants to leave $4675 to his four children in the ratio of 1:3:3:4. Divide 1035 in the ratio of 2:3:4. John plans to donate his collection of 3042 books to three libraries in the ratio of 1:3:5. means. trends. indices. charts and tables. currency conversions and more Numerical Reasoning Topics . proportions. comparisons. costs. sales data.percentages. .Indices The index of a number shows you how many times to use the number in a multiplication. It is written as a small number to the right and above the base number. In this example: 82 = 8 × 8 = 64 The plural of index is indices. (Another name for index is exponent or power) 1o = 1 181 = 18 22=4 32=9 4 2 = 16 5 2 = 25 6 2 = 36 7 2 = 49 8 2 = 64 9 2 = 81 10 2 = 100 11 2 = 121 12 2 = 144 13 2 = 169 14 2 = 196 15 2 = 225 23=8 3 3 = 27 4 3 = 64 5 3 = 125 6 3 = 216 7 3 = 343 8 3 = 512 9 3 = 729 Indices . trends. indices. means. proportions. currency conversions and more Indices . costs. charts and tables. sales data.percentages. comparisons. Mean, Median, Mode, and Range Mean, median, and mode are three kinds of "averages“. Mean, Median, Mode, and Range The "median" is the "middle" value The "mean" is the in the list of The "mode" is the "average" you're numbers. To find value that occurs used to, where you the median, your most often. If no add up all the numbers have to number is numbers and then be listed in repeated, then divide by the numerical order, so there is no mode number of you may have to for the list. numbers. rewrite your list first. The "range" is just the difference between the largest and smallest values. Example: Find the mean, median, mode, and range for the following list of values: 13, 18, 13, 14, 13, 16, 14, 21, 13 percentages, proportions, indices, charts and tables, means, comparisons, costs, sales data, trends, currency conversions and more comparisons . comparisons . Math Shortcuts . Divide it by 2 3. B. Divide the result by 2 3. Choose a 2-Digit Even # 2. Multiply the result by the next number Eg. Square this number Eg. 22 x 23 = 506 ans. Choose a 2-digit odd number then add one to the number 2. Add all even numbers from 2 to 44 1. 41 x 41 = 1681 Shorcuts for Addition . Add all odd numbers from 1 to 81. 81 + 1 = 82 1.A. 82/2 = 41 2. Adding Even Numbers from 2 to another 2-Digit Even Number 1. Adding a Sequence of Consecutive Odd Numbers 1.44/2 = 22 2. 2. Adding a Sequence from 1 to a selected 2-Digit Number 1. then multiply 17 x 35. The next number is 35. Eg. 34/2 = 17. D . The number to add is from 1 to 34. 1. Multiply the 2-digit number by half of the next number. Suppose you are to add numbers from 1 to six and back. Choose a 2-digit number. Square it. 1+2+3+4+5+6+5+4+3+2+1 = 36 Shortcut: (6)2 = 36 Shorcuts for Addition . 2. Choose a 1-digit number 2. Eg.C. Adding a Sequence from 1 to a Selected 1-Digit Number and Back. or multiply half of the 2-digit number by the next number. 1. and 2-Digit Number Multiplied. 7 ( 43) = 7 ( 40 + 3 ) = ( 7 .A. 57 (815) = ( 50 + 7 ) ( 800 + 10 + 5 ) = ? Shorcuts for Multiplication . 3 ) = 360 + 21 = 381 Eg. Multiplying 1-Digit Number with 2-Digit Number. -Use the Distributive Property of Multiplication over Addition A (B+C)=(A. 40 ) + ( 7 .C) Eg.B)+(A. Rather than pay the hefty surcharge to have the supplier make a 15% solution. you decide to mix 10% solution with 30%solution. to make your own 15% solution. You need a 15% acid solution for a certain test. This time. suppose you work in a lab. 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