1[Studyplan] CSAT Aptitude Paper 2: Comprehension & Reasoning, analysis, previous papers, free studymaterial, cutoffs (part 1 of 3) 1. Chart: Analysis of all CSAT papers so far 2. [Section I] Comprehension for CSAT 1. Step1: Finish theory 2. How to prepare high level reasoning? 3. Step#2: Move hands while reading passage 4. Step#3: Maximum practice 5. Comprehension: Why read Non-GS columns? 6. What about the English passages? 3. [Section II] Reasoning for CSAT 1. [Block 1] High level (HL) reasoning in CSAT 1. Sample questions: Logical Connectives 2. Sample questions: Syllogism 2. [Block2] Arrangement 1. A1: Blood relation 2. A2: Grouping: People vs clothing/city/occupation/relation 3. A3: Line Sequence / Comparison problems 4. A4: Arrangement: table Circular / Rectangular 5. A5: Conditional Team selection 6. A6: Scheduling lectures, events, journey 7. A7: Direction sense test 3. [Block 3] Reasoning: Non Verbal 4. [Block 4] Reasoning: Misc. Topics / Low priority 1. M1: Missing number pattern 2. M2: Sequence Series 3. M3: Coding decoding 4. M4: Logical Venn Diagrams 5. M5: Calendar 6. M6: Data Sufficiency (DS) 5. [Block 5] Reasoning: Totally Ignore these topics 4. Study schedule for the remaining days 5. Why people can’t finish paper? 1. P1: Start with English passages 2. P2: Don’t keep counting black circles in OMR sheet 3. P3: Don’t come back for “sets” 4. P4: Keep “sitter” Questions for the end 6. Become data processor NOT data collector 7. Booklist for CSAT exam Paper II? 1. Backup#1: Banking, insurance etc. 2. Backup#2: no competitive exam 3. Backup#3: higher difficulty exams 8. Book related doubts 9. Appendix1a: Sacred cutoffs of CSAT prelim exams 10. Appendix1b: Minimum Passing marks in CSAT prelims 11. Appendix2: Download links Prologue to a mile long article Yes, Just like YOYO Honey Singh, I’m also alive. and [Current] series will be resumed soon but first, How to prepare for CSAT paper II (aptitude) in a systematic and time-bound manner – that too via selfstudy? 1. Comprehension and Reasoning You’re here 2. Mathematics & Data Interpretation: high priority topics 3. Decision Making + Mathematics: Medium & low priority topics Structure of CSAT paper II (Aptitude) Total Questions: 80 Total Marks: 200 2 Marks for correct answer: 2.5 Negative marking: Yes MINUS 0.83 marks. i.e. -33% of correct answer. Sectional cutoffs: No. They combine marks for both paper I and paper II to select candidates for next stage the Mains exam. Four Sections of CSAT Paper II (Aptitude) 1. Comprehension (i) to test your understanding (ii) to test English 2. Reasoning 3. Mathematics 4. Decision making (without negative marking) Chart: Analysis of all CSAT papers so far From above charts, it is evident that in all three years, maximum number of questions have come from Comprehension. So, let’s start with that. [Section I] Comprehension for CSAT HL: High level reasoning (Find assumption, inference, central theme in the passage) Reading Comprehension 2011 2012 2013 Comprehension passages (printed in both Hindi and English) 28 32 24 Passages to test your English knowledge (printed only in English) 9 8 8 Total 37 40 32 UPSC comprehension passages are tougher than banking, insurance, staff selection and State PSCs because: 1. CSAT comprehension don’t ask straightforward who, when or where type of MCQs. 2. Even when they ask “what” and “why”, you can’t find answer directly from a single sentence of the passage. They test your understanding of the entire passage. 3. In CSAT 2011 and 2012, one passage would contain set of 5-6 MCQs. But in 2013, one passage contains barely 2-3 questions. Hence you’ve to read more number of passages to get same amount of MCQs. Similar trend in sitting arrangement and data interpretation sets. [Same trend in CAT- upto mid-2000s, one passage 5 MCQs, nowadays 1 passage contains barely two MCQs.] 4. They even ask High level reasoning questions within the passages. (Find assumptions / inferences) Step1: Finish theory You’ll encounter the High level reasoning topic within Comprehension segment, for example: Assumptions 1. Which of the following assumptions are valid? then 2-3-4 statements given 3 2. With reference to the passage, which of the above assumptions is/are valid? Interferences 3. What does the author imply? 4. What does the passage imply? 5. Which one of the following statements conveys the inference of the passage? 6. Which of the following inferences can be made from the passage? Central theme* 7. Which of the following statements constitute central passage of the theme? 8. What is the essential message being conveyed? 9. Which of the following best describes the thoughts of the author? 10. Which one of the following statements constitutes the central theme of this passage? These are examples of HIGH LEVEL REASONING. *as such “central theme” is not high level reasoning question, but to confuse you, they provide assumptions and inferences as wrong options. Passages Questions 2011 2012 2013 Comprehension passages High level reasoning (HL) Find assumption, inference, central theme 10 8 8 other MCQs e.g. finding meaning of a phrase, cause-effect etc. 14 24 20 A. Subtotal: Comprehension 28 32 24 B. English passages i.e. those easy passage given before Decision Making segment, and only printed in English. No Hindi translation give. 9 8 8 Total MCQs A+B 37 40 32 Many candidates don’t need to practice comprehension at home. And in the exam, they make silly mistakes by mixing up facts, assumptions, and inferences with the central theme. You need a strong grip over high level reasoning theory to tick correct option in this section. How to prepare high level reasoning? Recommended Book: Analytical Reasoning by MK Pandey (BSC Publication) RS Aggarwal also covers these topics but MK Pandey’s explanations and examples are much more refined and lucid, particularly for comprehension angle. CSAT Manuals by TMH, Pearson, Arihant etc. also cover, but not in a thorough manner. As such MK Pandey is written for Bank exams, hence not all chapters are important for UPSC. Do selective study in following sequence Chapter Title Topics to focus 1 basic of logic How to identify conclusion?– he has given list of keywords on page 6. 2 some information tips Logical connective theory explained on page 19 and 20. He did not use the word “Logical Connective”. He calls them “hypothetical reasoning”. But either way it’s important for both CSAT and CAT. After that read following article: [Reasoning] Logical Connectives (if, unless, either or) for CSAT, CAT shortcuts formulas approach explained 3 Assumptions Page 29. When assumption is invalid? Page 30. When assumption cannot be out rightly rejected? page33. Difference between implications and assumption. All the practice exercises + read the full explanation given in the answers- why he classified something as “Assumption”? Otherwise in the comprehension you’ll always endup in 50:50 doubt. Page 53: Exercise 3C, particularly the end part questions dealing with assumption in passages. 5 Evaluating inference Page 119-122: how to avoid confusion while deriving inference? Page 127 onwards: all the question passages. Also read full explanation given in the answers. 10 Cause Effect Page 287 onwards: differentiating between immediate cause vs principle cause. It’ll help particularly in the passages related to science, environment or economy. 6 evaluating the given course of action This will also help indirectly in the Decision Making Questions: Page 168: how to determine whether a suggestion action reduces or solves the problem? 4 Page 171: how to determine if suggestion solution is practical or not? Page 172: are you solving the problem or creating a new one? After above “Core” theory is done, go through following: Ch.4 Forcefulness of the arguments. Ch.9 Strengthening and weakening the arguments Ch.8 Punch line. So far, UPSC hasn’t asked GMAT like questions about “strengthen/weaken arguments in the given passage”. But nonetheless, above theory will help you digest the passages better. Step#2: Move hands while reading passage ManhattanGMAT TM is a prominent coaching class in USA(!) Their comprehension tips are worth implementing for CSAT. While reading the passage, do two things: 1. Note down the assumption & premises on the margin, in a short-hand note. 2. Highlight the important phrases. (GMAT/CAT done online, their software has this facility. You can do the same even on paper question paper via pen / highlighter) This helps quickly eliminating options without having to re-read the whole passage again and again, thus saving precious time during the exam. To see practical demo, go to following links. Their instructor Stacey Koprince showed her own notes and thought process while reading the passage: 1. Passage: Language of the leader 2. Passage: Meteor showers part I; Part II 3. Passage: Multinational corporations Additional tips from the same instructor: 3. How not to read the passage? 90% focus vs 20% focus 4. How to find the “central theme” / “central point”? Once this is over, time for maximum practice. How? Step#3: Maximum practice for Comprehension? As such every publication house has released a separate book on comprehension. But I’m not impressed with their content vs MRP. Most of their tips are just “bolbachhan” without telling specifically do this or do that. Then they give 20-30 practice passages and charge 200-300 rupees. But the quality of their passages doesn’t even justify 50 rupees for the book. If you can get such books from library then do borrow and practice. Otherwise don’t waste money buying such ‘special comprehension books for CSAT’. For practice you can use following resources: 1. Last three years CSAT papers- to get a taste of the difficulty level of UPSC. (download links given in appendix of this article) 2. 500 passages gathered from pagalguy.com’s old threads related to CAT preparation for year 2011 and 2012. (download links given in appendix of this article) 3. Pagalguy thread for CAT RC discussion 2013 4. this website got another 250 passages: codecoax.com/grerc/ You can find many more resources by just a google search. e.g. just type “1000 comprehension passages” But keep in mind just ~3 months left. Don’t get fixated over RC. You’ve to prepare & practice other topics as well. Comprehension: Why read Non-GS columns? UPSC examiner doesn’t write new passage himself. He merely cut-pastes the passages from prominent English newspapers and academic books. From his side, he only designs the MCQs, and gives Hindi translations. Therefore, irrespective of your medium in mains exam, you have to read English newspapers and magazines. Just because you finished college in English medium, doesn’t automatically make you master of English. Avoid such overconfidence. The English textbooks you’ve read for engineering, medicine, pharma or commerce – they’re *NOT* the same English that UPSC passages will contain. Therefore, you’ve to get yourself familiar with the sentence flow and vocabulary of such academic / column type passages. Otherwise, in the exam, you’ll take 15 minutes just to read one passage, while other players finish the same within 3 minutes. In past exams, many candidates failed to finish entire paper, only because of this reason. 5 To get a taste of comprehension passages, the best place is the Book review segment within Hindu, Indian express, Frontline and EPW. Because they first talk about the book, then about the contemporary issue dealt in the book e.g. arts, economics, science, environment, philosophy etc. Links: 1. indianexpress.com/tag/book-review/ 2. thehindu.com/books/ 3. epw.in/book-reviews 4. frontline.in/books/ (requires free registration) of course it doesn’t mean you’ve to read all four each day. Just keep an eye as and when you get time. Most candidates avoid such articles/columns in newspaper, thinking“this is not important for General studies syllabus”. But Keep in mind-Comprehension is a perishable skill that must be polished with regular reading of such “non-GS” English columns. By the way, What about the English passages? Yes, what to do with those easy passages given before decision making questions? (i.e. printed only in English and not in Hindi) As such no separate preparation necessary. Because MK Pandey is entirely in English. So once you’re done with that theory, you’ve automatically gained knowledge of such easy English passages. But still for practice of such passages, you may go through papersets of Bank and SSC exams (only if you’ve time left!) Anyways, enough of comprehension, let’s move to the next segment of CSAT paper II: [Section II] Reasoning for CSAT Type Reasoning Topics 2011 2012 2013 High Level Syllogism 3 5 0 Logical connectives 0 2 0 assumption / inference / conclusion 0 5 0 Subtotal: High level Reasoning 3 12 0 Arrangement 1 case vs. many questions 0 5 11 1 case 1 question 1 7 5 blood relation 3 1 0 Direction sense test 1 0 0 Sub Total: Sitting Arrangement 5 13 16 Non-Verbal reflection from mirror 1 0 0 min. colors required to paint 1 0 0 which figure next 0 2 3 Cube figure 0 2 1 Subtotal: Non-Verbal 2 4 4 Misc Venn Diagrams 1 1 1 Missing number pattern 1 0 3 Subtotal: Misc 2 1 4 Total Final Total Reasoning 12 30 24 % weightage in Paper II 15 37.5 30 [Block 1] High level (HL) reasoning in CSAT UPSC asked no syllogism / logical connectives in 2013, but they filled up the quota of “high level reasoning” by asking 8 such MCQ (find assumption, inference etc) within 32 comprehension MCQs. High level reasoning (HLR) 2011 2012 2013 Standalone MCQs within reasoning section 3 12 0 HLR-MCQs within comprehension section 10 8 8 6 total HL reasoning 13 20 8 % weightage in CSAT Paper II (out of 80) 16% 25% 10% We’ve already prepared the high level reasoning for comprehension i.e. logical connectives, assertion, reasoning, central theme – from MK Pandey’s book. Only one important topic left = Syllogism. Syllogism For this, refer to MK Pandey’s Chapter 11 page 301 onwards. Start with mastering “two statements”. e.g. all cats are dogs, all dogs are pigs then which of the following conclusion is valid? then move to three statement and four statement syllogism. MK Pandey has explained two methods to solve syllogism: AEIO method vs Venn diagram. I prefer AEIO, some prefer Venn diagram, and you can pick whichever you find more comfortable. Either way, do all the exercises and read the answer explanations in his book. If you prefer AEIO method, then: Mug up the tables given on 306, 307, 311, 321 (short form of table6) and read following articles(they’re based on AEIO method) [Reasoning] Syllogism (All Cats are Dogs): Method, approach, techniques, shortcuts explained for IBPS, SSC, CSAT and CAT [Reasoning] Three-Statement Syllogism: technique, method, shortcuts for IBPS, SSC, CSAT, CAT, CMAT [Reasoning Q] 3-Statement Syllogism doubt Question: Apples, Mangoes, Vegetarians [Reasoning] 4-Statement Syllogism: Approach, Techniques, explained for SBI PO (High level reasoning) and UPSC CSAT paper 2 If you still have time and mood, you can get additional practice from RS Aggarwal’s book. But that’d be an overkill because only ~3 months left. Sample questions: Logical Connectives (Prelim 1995) Which of the following can be inferred from the statement that “Either John is stupid or John is lazy”? a. John is lazy/therefore, John is not stupid b. John is not lazy/therefore, John is stupid c. John is not stupid/therefore, John is lazy d. John is stupid/therefore, John is not lazy (CSAT 2012) Examine the following statements: 1. I watch TV only if I am bored 2. I am never bored when I have my brother’s company. 3. Whenever I go to the theatre I take my brother along. Which one of the following conclusions is valid in the context of the above statements? A. If I am bored I watch TV B. If I am bored, I seek my brother’s company. C. If I am not with my brother, than i’ll watch TV. D. If I am not bored I do not watch TV. (CSAT 2012) Consider the following statements: 1. Either A & B are of same age or A is older than B 2. Either C & D are of same age or D is older than C 3. B is older than C Which of the following conclusions can be drawn from the above statements? a. A is older than B b. B and D are of the same age c. D is older than C d. A is older than C Sample questions: Syllogism (Prelim 1998) consider following statements: 1. all members of Mohan’s family are honest 2. some members of mohan’s family are not employed 3. some employed persons are not honest 4. some honest persons are not employed. Which of the following inferences can be drawn from above statements? a. all members of Mohan’s family are employed. b. all employed members of Mohan’s family are honest c. the honest members of Mohan’s family are not employed 7 d. the employed members of Mohan’s family are not honest. (CSAT 2011). Examine the following statements: 1. All animals are carnivorous. 2. Some animals are not carnivorous. 3. Animals are not carnivorous. 4. Some animals are carnivorous. Codes: a. 1 and 3 b. 1 and 2 c. 2 and 3 d. 3 and 4 (CSAT 2011) Examine the following statements: 1. All trains are run by diesel engine. 2. Some trains are run by diesel engine. 3. No train is run by diesel engine. 4. Some trains are not run by diesel engine. Codes: A. 1 and 2 B. 2 and 3 C. 1 and 3 D. 1 and 4 (CSAT 2012) Consider the following statements: 1. All artists are whimsical. 2. Some artists are drug addicts. 3. Frustrated people are prone to become drug addicts. From the above three statements it may be concluded that: a. Artists are frustrated b. Some drug addicts are whimsical c. All frustrated people are drug addicts. d. Whimsical people are generally frustrated (CSAT 2012) Consider the following statements: 1. Only those who have a pair of binoculars can become the member of the birdwatcher’s club. 2. Some members of the birdwatcher’s club have cameras. 3. Those members who have cameras can take part in photo-contests. Which of the following conclusions can be drawn from the above statements? a. All those who have a pair of binoculars are members of the birdwatcher’s club. b. All members of the birdwatcher’s club have a pair of binoculars. c. All those who take part in photo-contests are members of the birdwatcher’s club. d. No conclusion can be drawn. [Block2] Arrangement Within arrangement, I also include blood relation and direction sense test because in all such sums, you’ve to drag a chart/diagram in the rough sheets to get the answer. MK Pandey has covered them under Chapter 20 “Problem solving”. For additional practice you can use RS Aggarwal’s chapter 5, 6 and 8. A1: Blood relation (1998) A to F are members of a family consisting 4 adults and 3 children. A and D are brothers, A is doctor. E is an engineer married to one of the brothers and has two children B is married to D and G is their child. Who is C? (2009) There is a family of 6 persons A, B, C, D, E and F. There are two married couples in the family. The family members are lawyer, teacher, salesman, engineer, accountant and doctor. D, the salesman is married to the lady teacher. The 8 doctor is married to the lawyer. F, the accountant is the son of B and brother of E. C, the lawyer is the daughter-in-law pf A. E is the unmarried engineer. A is the grandmother of F. How is E related to F? (CSAT 2011) A is the brother of B, C is the father of A, D is brother of E, E is the daughter of B Then, the uncle of D is? MK Pandey Chapter 20 from Page 612 onwards. Understand the concept of “backtracking” and how to draw family tree- especially for complex problems like “A is wife of B who is not an engineer” etc. then do all exercises in 20A (page 628 onwards). but it is only for “warmup”. The real UPSC level sets begin from Exercise 20B and 20C. First solve them on your own, then understand the full explanation and technique shown by MK Pandey. Page Questions combined problem of blood relation plus __. Explanation 633 12-19 intelligence comparison 670 635 27-31 Weight comparison. 673 638 51-55 Sitting arrangement + age comparison. 680 (but he did not explain this one, just gave answer) 643 79-83 Trait comparison. 687-688 653 50-54 occupation 705 653 55-59 occupation 705 655 70-73 nothing 706 660 111-115 nothing try yourself 662 132-135 surnames 709 For additional practice, you may refer RS Aggarwal Ch. 5 Blood relations (page 261 onwards) . To complicate the question, often the examiner doesn’t ask straightforward blood relation but embeds it in the problem related to grouping- people vs. relation vs occupation vs car color and so on. Hence our next preparation should focus on: A2: Grouping: People vs clothing/city/occupation/relation (Prelims 2010) Gopal, Harsh, Inder, Jai and Krishnan have Ahmedabad, Bhopal, Cuttack, Delhi and Ernakulam as their hometowns (Not necessarily in that order). They are studying in Engineering, Medical, Commerce, Economics and History Colleges (Not necessarily in that order). None of the five boys is studying in his hometown, but each of them studies in one of the cities given above.Further, it is given that: i. Gopal’s hometown is Ernakulam. ii. Harsh is not studying in Ahmedabad or Bhopal. iii. Economic college is in Bhopal. iv. Inder’s hometown is cuttack. v. Krishnan is studying in Delhi. vi. Jai is studying in Ernakulam and the History College4 is in his hometown Ahmedabad. vii. Engineering College is situated in Ernakulam. **then you’ve to solve four MCQs about who belongs to which city and college. (CSAT 2012) Three persons A, B & C wear shirts of Black, Blue and Orange colours (not necessarily in the order). No person wore shirt and pant of the same colour. Further, it is given that, A did not wear shirt of black colour. B did not wear shirt of blue colour. C did not wear shirt of orange colour. A did not wear the pants of green colour. B wore pants of orange colour. What were the colours of the pants and shirts worn by C respectively? (CSAT 2013) In five flats, one above the other, live five professionals. The professor has to go up to meet his IAS officer friend. The doctor is equally friendly to all, and has to go up as frequently as go down. The engineer has to go up to meet his MLA friend above whose flat lives the professor’s friend. From the ground floor to the top floor, in what order do the five professionals live? How to prepare? In MK Pandey Chapter 20: Page Questions understand his technique explained in page __ 599 ex1 602 632 1-5 667 638-39 51-55 680 although has no explanation 657 88-92 707 658 98-102 707 663 140-144 710 664 145-149 710 A3: Line Sequence / Comparison problems You’re given information about people standing in a line / cars parked / marks or height or wealth of people in a sequence, then you’ve to solve the MCQs. observe samples: 9 (Prelims 2010) P, Q, R and S are four men. P oldest but not poorest. R richest but not oldest. Q older than S but not than P or R. P richer than Q but not S. Arrange these men in descending order of their age and richness. (CSAT 2011) In a queue, Mr. X is fourteenth from the front and Mr. Y is seventeenth from the end, while Mr. Z is exactly in between Mr. X and Mr. Y. If Mr. X is ahead Mr. Y and there are 48 persons in the queue, how many persons are then between Mr. X and Mr. Z? (CSAT 2012) Rama scored more than Rani. Rani scored less than Ratna. Ratna scored more than Rama. Padma scored more than Rama but less than Ratna. Who scored the highest? How to prepare? In MK Pandey Chapter 20: Page Questions understand his technique explained in page __ 608-09 Point (3), Ex.7 609-10 633 12-19 670 635 27-31 673 644-45 91-95 689 645-46 96-100 690 649-51 25-36 699-700 654 65-69 706 660 116-121 708 661 122-126 708-709 Additional practice: RS Aggarwal ch.6 on puzzle tests. A4: Arrangement: table Circular / Rectangular (2000) A to F are sitting on a circular table. A is between D and F. C opposite of D. D and E are not on neighboring chairs. Which of the following must be true? (then various possibilities given (CSAT 2013) Five people A, B, C, D and E are, seated about a round table, every chair is spaced equidistant from adjacent chairs. C is seated next to A. A is seated two seats from D. B is not seated next to A. Which of the following must be true? I. D is seated next to B. II. E is seated next to A. III. Both 1 and 2 IV. Neither 1 nor 2 How to prepare? In MK Pandey Chapter 20: Page Questions understand his technique explained in page __ 604- 05 Ex5, Ex6 606-608. pay attention to definite information vs comparative information vs negative information and how he utilizes all three of them to make the arrangement. 637 39-43 677-678 observe how he prepares diagram to accommodate complex info- gender vs marital status vs position on a circular table 640 62-71 681-684. again observe how he prepared diagram to accommodate complex info of gender vs profession vs intelligence vs position on a rectangular table. 654 60-64 This is for self-exercise. 655 74-77 this is for self-exercise 659 108-110 708 661 122-126 708-709 Then RS Aggarwal Ch 6 A5: Conditional Team selection (CSAT 2013) A tennis coach is trying to put together a team of four players for the forthcoming tournament. For this 7 players are available: males A, Band C; and females W, X, Y and Z. All players have equal capability and at least 2 males will be there in the team. For a team of four, all players must be able to play with each other. But, B cannot play with W, C cannot play with Z and W cannot play with Y. Then 3 MCQ given (CSAT 2013) The music director of a film wants to select four persons to work on “different aspects of the composition of a piece of music. Seven persons are available for this work; they are Rohit, Tanya, Shobha, Kaushal, Kunal, Mukesh and J aswant. Rohit and Tanya will not work together. Kunal and Shobha will not work together. Mukesh and Kunal want to work together. the only MCQ given. How to prepare? MK Pandey Chapter 20: Page Questions understand his technique explained in page __ 10 621 Ex14 621-623. Obverse his shortcut method, he focuses on the options that are blatantly violating the selection rules, thus he eliminates wrong options quickly. 636 32-38 674 to 676 643 84-90 688- important don’t misread the last condition! 652 44-49 703 to 705 658 93-97 this is for self-exercise Then RS Aggarwal Ch.6 Type 5: from page 356 onwards. A6: Scheduling lectures, events, journey Observe the pattern of MCQs asked in previous CSAT exams: (CSAT 2012) Guest lectures on five subjects viz., Economics, History, Statistics, English and Mathematics have to be arranged in a week from Monday to Friday. Only one lecture can be arranged on each day. Economics cannot be scheduled on Tuesday. Guest faculty for History is available only on Tuesday. Mathematics lecture has to be schedules immediately after the day of Economics lecture. English lecture has to be scheduled immediately before the day of Economics lecture. ***then MCQs start** How to prepare? In MK Pandey Chapter 20: Page Questions understand his technique explained in page __ 634 20-26 671-673 638 44-50 678-679 641 72-78 684-687 651 37-43 702 656 78-82 706 659 103-107 708 662 127-131 709 For additional practice, RS Aggarwal Ch6 “Puzzle test” (page 288) A7: Direction sense test Sample questions from previous prelims (2009) A person travels 12 km due North, then 15 km due East, after that 15 km due West and then 18 km due South. How far is he from the starting point? 1. 6 km 2. 12 km 3. 33 km 4. 60 km (2010)In a meeting, the map of a village was placed in such a manner that south-east becomes north, north-east becomes west and so on. What will south become? 1. North 2. North-east 3. North-west 4. West (2011) The houses of A and B face each other on a road going north-south, A’s being on the western side. A comes out of his house, turns left, travels 5 km, turns right, travels 5 km to the front of D’s house. B does exactly the same and reaches the front of C’s house. In this context, which one of the following statements is correct? a. C and D live on the same street. b. C’s house faces south. c. The houses of C than 20 km apart. d. None of the above How to prepare? MK Pandey doesn’t deal with “Direction sense test” topic. For this consult RS Aggarwal Chapter 8. [Block 3] Reasoning: Non Verbal 11 Non-Verbal 2011 2012 2013 reflection from mirror 1 0 0 Min. colors required to paint the given figure. 1 0 0 which figure next (similar to those SSC/Bank question) 0 2 3 Cube figure – which side will have what color / number / alphabet. 0 2 1 Subtotal: Non-Verbal 2 4 4 MK Pandey doesn’t cover non-verbal reasoning Preparation source: “A modern Approach to verbal and non-verbal reasoning, RS Aggarwal” (S.Chand Publication) solve all the chapters given under in the non-verbal reasoning section of that book-Even chapters related to paper cutting and paper folding type MCQs. Reason: UPSC is full of uncertainty. Similarly nothing prevents them from asking “paper cutting / paper folding” type questions. So practice a few sum from each variety. Reserve the practice quota of non-verbal, for the last month before exam. Because even if you begin right now (June), your skill/dexterity will perish by August end. Besides you cannot really makes revision “notes” for this topic. (Except a few points in cube theory- number of faces, how many smaller cubes if “x” number of cuts are made etc.) Just like “find missing number” MCQs, these should also be done at last during the exam. Sometimes particularly in the cube questions, candidates cannot crack the pattern and unnecessarily waste 10-15 minutes for a one MCQ. Avoid doing that. Save these non-verbal reasoning questions for the end. [Block 4] Reasoning: Misc. Topics / Low priority Odd ball topics = Not regularly asked in large amount. You cannot see a ‘pattern’ over the years- unlike sitting arrangement or assumption-inference. Reasoning Misc. 2011 2012 2013 Missing number pattern 1 0 3 Venn Diagrams 1 1 1 total 2 1 4 M1: Missing number pattern (Prelim 2006) find the missing number “X” in following series fig1 fig2 fig3 16 64 64 9 18 25 25 18 1 9 18 1 36 16 X Answer choice: 4 / 16 / 25 / 36. (CSAT 2013) find the missing number “X” in following series figure 1 figure 2 figure3 84 81 88 14 12 18 9 ? 11 The missing number (?) in figure 3 is? Answer choice: 7/16/21/28 Preparation source: RS Aggarwal Ch16: “Inserting the missing character” Page 628 and practice the sums Tip: in the exam, solve these sums in the end. Because sometimes it may take 10 seconds, and sometimes even after 10 minutes of trial-error you may not see the pattern. So don’t waste too much time. M2: Sequence Series (1995) consider the series given below. 4/12/95, 1/1/96, 26/2/96,… The next term of the series is a. 24/3/96 b. 25/3/96 c. 26/3/96 d. 27/3/96 12 (1998) .Which one of the following satisfies relationship Dda:aDD:Rrb: ? a. DDA b. RRR c. bRR d. BBr In the missing number questions we saw UPSC asked it twice- 2006 and 2013. So far UPSC hasn’t asked sequence/series- but nothing prevents them from asking, especially under the aegis of Chairman DP Agarwal, to break the backs of coaching classes and senior players. Therefore, you should prepare such ‘chillar’ topics as well. Don’t live under overconfidence that “just because xyz topic was not asked in last three exams, so UPSC will never ask it in future exams.” Preparation Source: RS Aggarwal, Chapter 2 number analogy, following types Type 8: number analogy Type 9: Alphabet Analogy Chapter 3: Classification, following types Type 4: choosing odd numerical (indirectly helpful in missing number) Type 5: choosing the odd letter group M3: Coding decoding (1999) In a code language, ‘SOLID’ is, written as ‘WPSLPIMFHA’. What does the code ‘ATEXXXQIBVO’ refer to? a. EAGER b. WAFER c. WAGER d. WATER (2000) In a certain code, MARCH is written as OCTEJ, how is RETURN written in that code? A. TFUVSM B. QGSTQM C. TGVWTP D. TGRVSO Preparation Source: RS Aggarwal, Chapter 4. Optional: MK Pandey Chapter 17 and 19 on coded relationships and inequalities M4: Logical Venn Diagrams There are two type of Venn diagram questions 1. Mathematical: in a society 30% people drink coffee and 50%….we’ll see about this in next article under Maths strategy. 2. Logical: you’re given a complex Venn diagram, without any quantity or percentages. It contains overlapping of squares, rectangles, circles and triangles, then you have to identify which of them are both singer and painters etc. In last three exams, UPSC asked both type of Venn diagrams. They also asked such MCQs in 1996, 1998 and 2001. Hence should be prepared. Preparation Source: RS Aggarwal, Chapter 9 Logical Venn diagrams. What to do with mathematical Venn diagrams? we’ll see in next article under Maths strategy. M5: Calendar Sample questions from previous prelims (2008) March 1, 2008 was Saturday. Which day was it on March 1, 2002? a. Thursday b. Friday c. Saturday d. Sunday Preparation source: My article under Aptitude series- click me By the way, I consider Permutation, combination, probability, clock angles and mathematical Venn diagrams as part of mathematics. We’ll see them in next part. M6: Data Sufficiency (DS) Not seen in recent times, but has been asked in pre-CSAT era, as part of age / sitting arrangement / blood relation type problems. Observe (2006) P, Q, R, S and T live in a five storied building (ground+4), and each of them resides on a separate floor. Further, 1. T doesn’t reside on topmost floor 2. Q doesn’t reside on ground floor 3. S resides on one story above P, and one below R. 13 To know which person resides on ground floor, which of the above statements are sufficient? a. only 1 and 3 sufficient b. only 2 and 3 sufficient c. 1, 2 and 3 are sufficient d. 1, 2 and 3 are insufficient. (2006) they gave four dice figures. and asked which of them are sufficient to find out the numbers opposite to each other. How to prepare DATA SUFFICIENCY? Prepare data sufficiency ONLY after learning all the theories in reasoning and mathematics- particularly age problems and number system. MK Pandey Chapter 7, Page 203 onwards (optional) RS Aggarwal’s chapter 17 on data sufficiency. Although that’ll be overkill, because MK Pandey’s chapter is far better and thorough than RS Aggarwal. [Block 5] Reasoning: Totally Ignore these topics You may “Ignore” because these topics are not seen in UPSC exams so far. They’re mainly reserved for Bank exams. Again I use the word “may” because DP Aggarwal may ask It for breaking the backs. but sometimes you’ve to take calculated risk hahaha Topic What does it contain? RS Aggarwal MK Pandey 1. Analytical decision making or 2. Eligibility Tests In a big paragraph, first you’re given recruitment conditions. Then 4- 5 “Cases” where you’ve to take appropriate action e.g. select candidate, refer to manager etc. This type of questions not seen in UPSC, hence ignore. 18 Ch.12 3. Input-Output or 4. Sequential Output Tracing First you’re given an example: input, step I, II, III, IV, V then output. Then you’re required to do similar for given 4-5 MCQs. 7 Ch. 13, 14, 15 and 16 Study schedule for the remaining days Random preparation based on mood swings = road to #EPICFAIL. Proceed in following manner. Month What To Prepare Why? June upto Mid July high level reasoning + comprehension Comprehension practice & mock tests will only cause frustration IF you don’t finish high level reasoning theory first. maths: with emphasis on recording all the calculation errors and shortcuts in your “diary of mistakes”. Because it has so many topics, you’ve to start early. Besides, concepts related to HCF, LCM, Time-speed-distance etc will remain for longer duration in memory -Compared to dexterity over non-verbal reasoning or data interpretation. Mid July to August 9 Data interpretation (DI) sitting arrangement Nonverbal reasoning misc. topics under maths & reasoning Comprehension practice Hardly contain any theory. Even if you ‘finish’ entire DI today itself, your skill/ dexterity will get rusted by August. Hence reserve the quota for Mid-July to Mid-august. August 10 to 23 rd (14 days) should be spent in revision. Practice aptitude after dinner. That way your hands keep moving and brain doesn’t feel sleepy. Allot your fresh hours in daytime to general studies preparation. For comprehension, make a resolve to solve at least 3-5 passages on daily basis. Download zip file from bottom. Why people can’t finish paper? In past exams, many candidates have failed to finish entire aptitude paper within two hours duration. Why? 1. They don’t read columns in Hindu, IE, frontline, EPW etc. Hence they take 10-15 minutes to read a passage, which a CAT/GMAT-master can finish in barely 3-5 minutes. 2. At home, they don’t study high level reasoning theory. So for every assumption /inference type question they’re 50:50 doubtful. YET they don’t skip it, they just keep pondering over it for another 10-15 minutes. 3. At home, they don’t study maths out of fear, and study reasoning in a casual manner. So to cross the imaginary cutoffs they come back again and again on same comprehension passages, even when they’re unable to solve it, and repeat point #2. 14 4. They take too much time solving non-verbal reasoning and sitting arrangement questions. Even after creating the diagram for sitting arrangement / blood relation- their diagram doesn’t match with any of the answer choice, so they spend another 10-15 minutes in fixing It, re-reading the entire caselet. 5. At home they only “read” the sums from books and mugup formulas. But in real life exam, they make silly mistakes in every multiplication, addition, subtraction and division. So they’ve to redo the same question multiple times. To avoid such firefighting and epicfails: 1. Be thoroughly prepared for Maths, reasoning and English. 2. Keep a wrist watch in the exam hall. 3. Observe following principles: P1: Start with English passages Donot start with first page of the question paper. But, immediately open 4 th or 5 th last page…it’ll contain those “English testing passages” (= those passages without Hindi translations). Solve them first because it’s the easiest section in the entire paper. Let’s assume cut off is xx. Then you’ve already filled up your tank by 8 correct questions. Now your brain and hands are warmed up, open first page and start with 1, 2, 3, 4… For the first ~65 questions, UPSC doesn’t have ‘sections’. You’ll come across comprehension, reasoning and maths questions at random intervals. Some people first mark the page number / Question numbers of comprehension passages on the rough-page. Then begin solving all passages one by one. I don’t recommendthis method because: 1. You’ll end up wasting precious moments in just flipping through pages. 2. You might accidentally miss a single maths /reasoning question hiding between two comprehension sets. So, just move with the flow Q no. 1, 2, 3, 4…so whatever maths, reasoning or comprehension question you face in that sequence, either solve or skip or put on ‘mark-n-review’. P2: Don’t keep counting black circles in OMR sheet Ideally you should count the black circles in OMR sheet only once, in those last 5-7 minutes before exam ends. But most candidates keep counting their black circles, after every 20-30 MCQs or every 30-45 minutes- “how many did I attempt? (imaginary) cutoff cross hogaa ki nahi?” This is a bad habit because: 1. You are wasting precious time in a non-productive activity. 2. Creates stress on your subconscious brain, prompts you to tick answers based on “gut-feeling”, even where you’re 50:50 doubtful. 3. You try to “Fit” wrong formula/ logic in to solve tough MCQs in maths/ reasoning. 4. You keep coming back to the “sets” again and again. P3: Don’t come back for “sets” Scenario: a passage contains 3 questions. You solved 2 MCQs confidently, but in one MCQ you’re 50:50 undecided. You mark its number on the last page of question paper, hoping “I’ll come back at the end of the exam”. This is a bad idea for two reasons 1. When you come back, the understanding of that passage would have evaporated from your short term memory just like Amir Khan in Ghajni. You’ll have to spend another 3-5-7 minutes re-reading the passage. 2. In the last few minutes before exam ends, person is usually under fear-factor of “Cutoffs” so, even if he is 50:50, he ticks answer on “Gut feeling” just to overcome that imaginary cutoff. In UPSC, usually Gut-feeling answers are wrong answers. So don’t dig your grave in negative marking. Same applies to blood relation, sitting arrangement, Data interpretation type “sets”. Solve the entire set in one go. Avoid coming back for a single unsolved MCQ from such set. P4: Keep “sitter” Questions for the end Whenever you come across find missing number, find coding-decoding, find analogy; OR Non-verbal questions like find next figure in the diagram, what will be the number / color on xyz face of dice…. For all such questions, note their page number on the rough space. Only when you’re finished with other questions, begin solving these questions. (this is one type of “marks and review” in online exams) Reason: sometimes it may take 1 minute, sometimes 10 minutes to crack the pattern in such MCQs. You don’t want to break mental-rhythm during middle of the paper with such bumpy-road MCQs, reserve them for the last lap. Same advice for any unconventional maths/reasoning questions. Donot break rhythm to solve something that you’ve never encountered before at home. or you’ll end up throwing good money after bad money. Remember: You’re not required to tick 80/80 MCQs to qualify for Mains. UPSC will give you only 2.5 marks whether you solve a given question in 1 minute or in 10 minutes. So learn to prioritize and make best use of time. *you’re welcome to add more principals in the comments below* 15 Become data processor NOT data collector 1. UPSC introduced aptitude paper in 2011. At that time, people spent countless hours on net, gathering tonnes on PDFS and webpages related to other higher level aptitude exams (CAT, GMAT etc.) hoping that UPSC will ask tough questions from it. 2. But now three years have gone, the paper analysis so far reveals that yes UPSC asks tough aptitude questions, but they’re not that tough. You can solve most of them through traditional aptitude books. You don’t have to download terabytes of material, pdfs, movies, softwares meant for CAT/GMAT etc. You don’t have to be on 24/7 internet gathering material for aptitude. So stop that material collection activity and get start practicing from the traditional books. Booklist for CSAT exam? Aptitude Book choice depends on career backup (in case you fail UPSC). Don’t waste on money separate set of books for every exam. CSAT Aptitude is a curious combination of both higher and lower level exams than UPSC. So, books meant for both type of exams, work just fine with slight jugaads. Backup#1: Banking, insurance etc. Jobs: IBPS, SBI, Staff Selection (SSC), CAPF (Assistant Commandant), AFCAT, LIC, NICL-AAO, ACIO, FCI, State PSC lower level, & other central government or PSU jobs. In that case, use following book combination for the CSAT paper II Maths: Fast track to Objective Arithmetic by Rajesh Verma Reasoning: RS Aggarwal OR BS Sijwali o if you’re buying second hand then RS Aggarwal because contains more practice Qs than Sijwali. o if you’re buying brand new then BS Sijwali – because ~Rs.200 cheaper than RS Aggarwal and yet covers all topics with good number of practice questions. Comprehension: MK Pandey’s Analytical Reasoning (for assumption –inference and high level reasoning) then maximum practice using online resources. English grammar: Objective General English by SP Bakshi (Mind it: this is not asked in CSAT Paper II but sentence correction / grammar important for non-UPSC aptitude exams.) Backup#2: no competitive exam Plan: If I cannot clear UPSC then I’ll simply go back to private sector job/ business. In that case use any CSAT Manual by Tata Macgraw Hill (TMH), Arihant or Pearson etc. (Whichever you can find cheaper second hand.) As such I don’t have good opinion about such aptitude manuals because they’re hardly useful for non-UPSC exams: 1. They don’t contain detailed trigonometry, quadratic equation= useless for SSC, CDS, SCRA, CAT etc. 2. No logarithms, no coordinate geometry, no geometry beyond area-volume-perimeter = useless for CAT, CDS and SCRA. 3. Their Data interpretation sets don’t have lengthy calculations and peculiar problems seen in banking exams = useless for IBPS and SBI exams. Then you’ll have to buy another paperset or DI book. 4. They usually avoid input-output, eligibility test topic asked in banking exam. = useless for IBPS, SBI and LIC/NICL exam, you’ll have to buy another book or paperset at that time. 5. Very few questions on non-verbal reasoning = not sufficient practice for SSC, insurance and Banking. Therefore, if you’re planning to give ‘non-UPSC’ exams as career backup, then avoid purchasing Aptitude manuals. At max, these manuals will help in CAPF (Assistant commandant) but not much outside that. Backup#3: higher difficulty exams CDS, CAT, CMAT, SNAP, XAT & other higher level exams. 1. Maths: Quantum CAT by Sarvesh Kumar (OR Arun Sharma) a. IF you’re already good at maths then Arun Sharma b. If you’re weak at maths then Sarvesh Kumar. 2. Reasoning: depends a. In CDS they don’t ask reasoning. So, for CSAT use the reasoning books mentioned under backup#1 (because CSAT asks reasoning questions!) b. For CAT you may use Gajendra Kumar (Disha publication). And then maximum practice from pagalguy.com threads for reasoning. 3. Comprehension: depends a. CDS: Passages easier than CSAT. But they fill-up the difficulty quota by giving tough sets on sentence arrangement and sentence correction. (Mind it CSAT doesn’t ask verbal ability /grammar). Hence use the sources given in backup#1. b. Arun Sharma OR Ajay Singh then maximum practice from pagalguy.com threads for comprehension and verbal ability. (Mind it CSAT doesn’t ask verbal ability –like those sentence correction or sentence arrangement). Book related doubts 16 Q. I already have purchased CSAT paper II Manual by xyz publication, do I need to refer those separate books on maths and reasoning? Ans. No need. If you already have bought such manual, just study the topics listed in this article, from respective chapters. You can also try desi-Jugaad: find a friend in your city with RS Aggarwal, exchange books for 10-15 days. That way he can practice new stuff from your book while you get to practice the important sections from his. Q. I already have RS Aggarwal, do I need MK Pandey? MK Pandey’s high level reasoning concepts are far better than others. Particularly useful for comprehension section of UPSC for those assumption / inference type of questions. RS Aggarwal’s chapters on logic-assumption-inference are just “practice workbook”, hardly explaining the theory/ concepts in detail. MK Pandey’s puzzle test/ sitting arrangement chapter contains good number of UPSC level question sets, along with useful explanations and tips. + highly useful for SBI and IBPS exams. Q. I already have MK Pandey, do I need RS Aggarwal? Yes because MK Pandey doesn’t cover many of the low- level reasoning topics such as analogy, non-verbal reasoning, and direction sense test. Anyways, you don’t need a brand new RS Aggarwal, try to find second hand used copy. Aggarwal is in the market since 90s, you shouldn’t have much trouble finding its second hand copy even in tier II cities. Q. I already have CAT books OR CAT coaching material for reasoning. DO I need others books? Ans. CAT material will work just fine. But with conditions- 1. CAT material usually doesn’t cover non-verbal reasoning beyond those cube color, dice face questions. But UPSC is asking “which figure next”?… so for that much practice, download SSC/ bank papers or borrow someone’s RS Aggarwal. 2. You may Ignore / low-prioritize following topics from CAT reasoning material, because they’re not seen in UPSC so far: i. games and tournaments ii. pipe-network iii. Data sufficiency (asked but low priority) Q. I’ve CSAT books from xyz jholachhap publication house exclusively in Hindi medium. Can I rely on them? No. Hindi maadhyam aptitude books are bogus waste of time and money because 1. They complicate even easy concepts by using too much shuddha Hindi terminology 2. They’re full of printing mistakes in answers. it ruins the mood and tempo while practicing sums at home. Therefore, when it comes to aptitude books, better go for English books of reputed publication houses. Appendix1: Sacred cutoffs of CSAT prelim exams Only for the informative purpose. DONOT enter the examhall with ‘cutoff’ mindset. Each UPSC paper is unique, each year’s demography is unique. If some baba or “Sir” has adviced that you must tick minimum 55 MCQs in aptitude, ignore them. If you can’t solve an MCQ then you CANNOT solve that MCQ, don’t dig your grave with guess work or gut feeling just to cross 55. Exam CS (Prelim)* CS (Main)# CS(Final) General 241 564 775 OBC 222 534 742 SC 207 518 719 ST 200 510 707 PH-1 Ortho 199 510 725 PH-2 Visual 184 502 718 PH-3 Hearing 163 410 613 Total 400 1750 2025 Minimum passing marks: Prelims From the above * and # , now we know UPSC’s official system of “minimum passing marks” (this was never disclosed in RTIs so far). it implies that if you failed to reach minimum passing marks in any one paper then they won’t select you for next stage, even if you get best marks in other papers. BUT overall merit list prepared by combing scores of both GS + Aptitue paper. MAX marks Minimum passing marks Must get atleast __ MCQs correct* 17 CSAT (GS) 200 30 12 CSAT (Aptitude) 200 70 28 total 400 *1 MCQ worth 2.5 marks. And assume no MCQs is wrongly attempted. PS: unlike Bank exams there is no sectional cutoffs within an individual paper. (This is confirmed via RTI many times) Sectional cutoff: no. Paperwise cutoff: no. They combine marks of GS+aptitude: total out of 400 Preliminary (CSAT) marks counted only for shortlisting candidates to next stage (i.e. Mains examination). Final selection depends on the combined score of mains + interview. Appendix2: Download links #1: UPSC CSAT: Aptitude papers of 2011, 2012, 2013 Link: https://files.secureserver.net/0s4I32bAjTl3bm UPSC uploaded these papers on its official site but PDF quality very bad. Hard to read the passages, and size too big especially 2013 paper pdf alone is 22 MB. Hence I’ve collected better quality PDFs from testkafunda.com + included official answerkey from UPSC. 2013’s answer key will come only after final result, because again Lord Curzon stonewalled my RTI. IF you want topicwise sorted question papers, refer CSAT Topicwise solve papers (1995-2013) by Disha Publication. #2: 500 Reading comprehension (RC) from Pagalguy.com Link: files.secureserver.net/0sSHBgG2lnFPwx In the next article, we’ll see the studyplan for mathematics and decision making. For more on aptitude, visit Mrunal.org/Aptitude. URL to article: http://mrunal.org/2014/06/studyplan-csat-aptitude-paper-2-comprehension-reasoning-analysis-previous-papers- free-studymaterial-cutoffs-part-1-2.html Posted By Mrunal On 03/06/2014 @ 18:20 In the category Aptitude Click here to print. [Studyplan] CSAT Aptitude Paper 2: Maths & Data Interpretation-High priority topics, Sample Questions, free studymaterial (part 2 of 3) 1. Math haters are grave diggers 1. #1: 2012 unlikely to repeat 2. #2: GS Strength doesn’t compensate math weakness 3. #3: One lakh Delhi aspirants 4. #4: Maths = competitive edge + peace of mind 2. Mathematics: What to ignore? 1. Doubtful syllabus topics in Mathematics 2. Highest priority (finish them first) 3. Medium priority 4. Low Priority 3. CSAT Math doesn’t not fall from sky but NCERTs 1. Gather the weapons 2. Which Quant book? 3. Don’t waste time learning Speed maths / Vedic maths 4. High priority topics 5. H1: Linear Equations 1. NCERT: Linear Equations 2. Quant book: Linear Equations 6. H2: Number system 1. NCERT: Number system 2. NCERT Powers & Exponents 18 7. H3: Percentages, Profit Loss, SI- CI 8. H4: Ratio Proportion Variation Partnership (RPVP) 9. H5: Speed Time Distance Work (STDW) 10. H6: Averages, Allegations 11. H7: Data Interpretation (DI) 1. DI-1: odd- graphs 2. DI-2: bar graphs, pie charts 3. DI-3: Venn Diagrams 4. Don’t assume A+B=total 5. DI-4 Tabulation questions 12. H8: Geometry: Area volume perimeter (AVP) 13. Appendix: Download links 1. A1: Last three years official CSAT papers 2. A2: NCERT Mathematics Topicwise Sorted free download 3. A3: Quant books: What to prepare, what to skip? So far in the CSAT paper-2 study plan 1. Comprehension and Reasoning 2. Mathematics & Data Interpretation: high priority topics You’re here 3. Decision Making + Mathematics: Medium & low priority topics Math haters are grave diggers Many of you have this mindset / strategy: 1. I hate maths / I’m weak in maths. Therefore, I’ll pump extra hours in General studies to compensate for my poor command over mathematics. 2. Prelim marks not counted in final merit list, and maths is not going to be asked in mains. so why bother. Besides, in 2012 only 3 questions were asked! 3. xyz person on xyz forum said he managed to crack CSAT without preparing maths. Same Cinderella story will repeat in my case. 4. In last three years, average cutoff was ___. So, so if I tick __ Questions in GS paper I and __ questions in comprehension /reasoning, I can easily reach cutoffs, without bothering about maths. To all such aspirants, I’ve four things to say: #1: 2012 unlikely to repeat % of questions CSAT-2012 Paper II CSAT 2013 comprehension 40 MCQs. (=50% of the paper) reduced to 32 MCQs. maths only 3 MCQs = dream come true for math haters. 17 MCQs = = ~1/5 th of paper. only THREE questions from Maths in 2012! Will those “Acche din” come again? Ok so why did the “Achhe din” end? Why didn’t UPSC ask just three Maths MCQs in 2013, like they did in 2012? You can unravel this mystery by looking at “Behind the curtains timeline” and joining the dots 20 May 2012 CSAT-2013 exam held. Only 3 maths and 40 comprehension. 30 August 2012 Prof. Nigvekar submits report & recommends following In CSAT Paper II: too many questions were asked from comprehension section, it needs to be reduced slightly in favor of other type of aptitude questions.(e.g. reasoning, maths) It will be better to reduce the English part in CSAT, and instead set bit tougher questions in the compulsory English paper at mains level. 26 th May 2013: CSAT 2013 exam. Comprehension reduced from 50% to 40%, consequently, maths questions increased from 3 to 17, to fillup the total 80 questions quota. Even in mains-2013, compulsory English paper was lengthier than previous exams, and hence tougher. In other words, Maths is here to stay. 2012 scene unlikely to repeat. UPSC unlikely to ask only 3 maths MCQs in 2014. 19 #2: GS Strength doesn’t compensate math weakness Prof.Nigvekar Committee observed: CSAT Paper-I (General studies) is difficult compared to paper-II (Aptitude test). The candidates who are good in general studies, are at disadvantage, because they can’t get any edge with general studies. On the other side, candidates good in paper-II(Aptitude) gets advantage, & they can make though the exam even without much study of general studies. (Therefore) Aspirants with engineering background formed the major chunk of aspirants who qualified the prelims in the first attempt. In other words, It takes far more effort to get 60 correct in GS, than it takes to get 60 correct in aptitude. Given the large influx of Engineer-UPSC aspirants post sub-prime crisis and mushrooming self-financed colleges, IF you (non-Engineers) think you can compensate your weakness in maths/aptitude by pumping more hours in General studies => then you’re making a grave mistake. You have to tame the bull (maths) by the horns (continuous practice). #3: One lakh Delhi aspirants In April 2014, UPSC wrote a letter to DoPT, requesting more officers to be deployed for exam duty because: 1. more than 10 lakh people expected to apply for CSAT-2014 2. Out of them more than 1 lakh people from Delhi alone. (This is UPSC’s estimation!). 10 lakh is not worrisome, because most of them are non-serious people applying just because papa said (JBPS). But 1 lakh from Delhi alone= that is a disturbing number. Because majority of them would be full-time dedicated aspirants migrated to Delhi for the sole purpose of UPSC preparation. Therefore, competition will be cutthroat than ever before. In recent years, even Hyderabad, Bangalore, Chennai, Indore, Lucknow and A’bad are also fast turning into Delhi like centres i.e. where many aspirants rent a room and full time dedicate to UPSC preparation with or without coaching. In this environment, you’ve to extract every mark you can, from every section you can. Hating maths is not a good idea. Remember: Sincere candidates don’t fail prelims by 100 marks, they fail by a margin of just few marks below the cutoff. And in most cases, they could have avoided failure by keeping alert on negative marking, and extracting a few easy questions from the subjects they disliked. #4: Maths = competitive edge + peace of mind Today every sincere player knows he has to prepare NCERT, Laxmikanth, and Economic Survey. So command over those books = just minimum height n chest requirement in military recruitment. Not a competitive edge, doesn’t automatically ensure selection. Last year pretty much every regular reader of Mrunal.org ticked 12-15 correct in Economy. Again, no longer a competitive edge, it’s just a ‘minimum system requirement’ (MSR). People have been trying to get competitive edge over others by doing PH.D on Culture, science, environment. But given the tough nature of GS-MCQs, all that labour barely translates to additional 10-15 marks, that too after spending months in mugging up fifty dozen festivals, tribes, caves, algae/biofertilizers and critically endangered species. On the other side, maths can easily help raise your score by atleast 30** marks than the crowd, and ensure peace of mind until prelim result comes. Then, you can completely focus on mains preparation, rather than worrying about cutoffs in online forums. **based on 2011 and 2013 trend, if UPSC asks 15-17 maths questions, then at least 12 of them will be solvable even with moderate preparation. 12 x 2.5 = 30 marks. Mathematics / Basic Numeracy: How much upto ClassX? Maths internal breakup in last 3 CSAT Maths Topic Subtopic 2011 2012 2013 Basic HCF,LCM 1 0 1 Ratio Proportion 1 1 4 Linear EQ 1 0 1 Subtotal: Basic 3 1 6 STDW Speed Time Distance Work 2 1 4 Stat averages 1 1 0 Data Interpretation (DI) Pie chart 2 0 5 Tabulation 3 0 0 Speedgraphs Interpretation 3 0 1 Bacterial growth 3 0 0 Age pyramid 1 0 0 Subtotal: DI 12 0 6 20 oddballs Permutation combination (how many figures possible etc.) 3 0 0 geometry 1 0 0 AP, GP 1 0 1 Subtotal: Odd balls 5 0 1 Maths Total Basic+Stat+STD+DI 23 3 17 % out of 80 MCQs 28.75 3.75 21.25 UPSC’s official syllabus doesn’t specifically say “we’ll not ask this, this and this.” It only says: Basic numeracy (numbers and their relations, orders of magnitude, etc.) (Class X level) Data interpretation (charts, graphs, tables, data sufficiency etc. – Class X level) This “etc.” word is dangerous. Because upto class X level NCERT textbooks include statistics, probability, trigonometry, parallelograms and even coordinate geometry. Should we prepare such topics or not? CSAT system is just three years old. So far ~43 total maths questions asked in 2011, 12 and 13. This sample size too small to make projections that “x” topic will always be asked and “y” topic will never be asked. 2011: UPSC introduces CSAT system, public believed that UPSC will completely “revamp” its Aptitude Question bank in its secret computer database. But UPSC is still asking stuff they used to ask way back in the 90s. Observe: CSAT paper II q. (maths / DI upto class X level) similar asked in pre-CSAT era 2011 they gave a graph of A,B,C running and asked who won the race, who was very slow etc. 1996- with four athletes A,B,C,D 2011: water contamination, various phases 1999: fertilizer input vs yield 2011: comparing speed of two trains 1995: comparing temperature of two liquids time speed distance Questions Regularly asked between 1995-2012, with almost identical difficultly level. linear equations, HCF-LCM questions same as above This is just tip of an iceberg- even reasoning, syllogism, assumption-inference, Venn diagram, sitting arrangement- if you look at all the aptitude questions from 1995 to 2013- history is repeating itself from pre-CSAT era to CSAT era. Many questions are mirroring themselves only names, numbers and wording changed. if previously they gave time-distance & asked you to find speed; this time they give speed and time and ask you to find distance and so on …..meaning 1. UPSC hasn’t completely revamped its question bank. 2. Just because xyz topic is not asked in last three CSAT = it doesn’t mean UPSC will never ask it in future exams. If something is taught upto class10, AND it has been asked in previous prelims (Even before Pre-CSAT era), then we should prepare. Doubtful syllabus topics in Mathematics Topic Taught up to NCERT std.10? Prepare for CSAT? why? Statistics (Cumulative frequency, median, mode etc.) YES YES Yes, because in 1999 they asked Data interpretation (DI) about cumulative frequency and average for grouped data with class interval. Arithmetic progression YES YES asked in CSAT 2011 itself. Geometric progression NO NO GP starts from Class11. They did ask “water doubles every five minute” question in 2001, but it could be solved without formulas. At max, mugup the “ball rebounding” formula. Irrational numbers YES No it’s not asked from 1995 till 2013. Coordinate Geometry YES YES Asked in 1995 and 1999 prelims. Non-AVP Geometry Theory YES YES Non-AVP Geometry theory= interior angle, parallelogram sides, cyclic quadrilaterals etc. topics beyond simple area- volume-perimeter (AVP). YES should be prepared, because asked in 1995, 96, 97, 98, 99, 2000, 2001. Trigonometry YES YES height-n-distance problem has been asked in past. Ignore radian, maximum minimum values of sin/cos/tan- because that starts from class11-12 and never asked in pre- CSAT or CSAT era. Clock Angles indirectly YES Asked in 98, 2002, 2000 etc. 21 Divisibility YES YES Asked in 2010. Probability YES Yes Routinely asked this topic up to mid-2000s. Permutation &Combination (Pnc) NO YES Yes. they routinely asked this topic upto mid-2000s, (may be Examiner considers this a “reasoning” topic and not maths) Even in CSAT 2011, they asked a question on fundamental counting- that topic is the mother of PnC, and starts only from class11 NCERT. in same CSAT 2011, they even asked image based PnC e.g. how many routes possible in 2×2 square diagram to reach from point A to B. Polynomials,Quadratic Equations YES YES Polynomial factorization related problems asked in 1995,96, 99, 2001 Pure mathematical questions related to Quadratic equation (e.g. nature of roots, find “k” etc. not asked so far) Logarithms NO NO Never asked between 1995-2013. Venn Diagram NO YES Venn Diagram starts from NCERT Class11. But they were regularly asked both in pre-CSAT and CSAT era. Perhaps examiner considers them part of “reasoning” and not mathematics or DI. dang…these are way too many odd topics, can’t we just focus on time speed distance, linear equation, HCF-LCM? Hardly two months left before exam!! Ans. No. You’ve to be prepared for all possible topics. UPSC examiner has no moral obligations to follow last year’s topic trend. 2011 he asks arithmetic progression, then ignores this topic for 2012 and 2013. If you aim to tick 10+ MCQs for a given subject, you’ve to be thoroughly prepared- whether its polity, geography, economy or aptitude. Nonetheless, it may not be feasible to give justice to all the maths topic within ~2 months, so study-priority order should be following: Highest priority (finish them first) 1. Linear Equation 2. Number System 3. %, profit loss, SI-CI 4. Ratio Proportion Variation 5. Speed Time Distance Work 6. Averages, Alligiations 7. Data Interpretation 8. Geometry: Area Volume Perimeter Medium priority Following topics not frequently asked, but takes barely 2 hours to master. because You just have to mugup 3-5 formulas and variety of questions is very less. Therefore cost: benefit good, You should make room in your schedule to prepare them. 9. Arithmetic Progression => only have to do one chapter in NCERT. 10. Coordinate Geometry => only have to do one chapter in NCERT. 11. Polynomials factorization => only have to do two chapters in NCERT. Low Priority Low priority doesn’t mean UPSC will *NOT* ask them. Low priority means, within your study time table, do them at last depending on how much free time left after allotting time for other high priority topics such as history, polity, science, economy, environment (for Paper I) and those reasoning-comprehension & other high priority topics under Maths (for Paper II). Reason: following topics not frequently asked. They’re not difficult but have many variety of questions and formulas=> each of them take more than 4 hours to master. Therefore, put under low priority in terms of study time allotment. 12. Geometry theory: Triangles, Quadrilaterals, Circles (TQC) 22 13. Trigonometry: only height n distance 14. Permutation Combination Probability 15. Statistics Anyways, let’s begin preparation: CSAT Math doesn’t not fall from sky but NCERTs Some questions directly came from NCERT, just numbers changed. Observe CSAT paper II question similar question in NCERT 2011: contractor penalty Class 10, Ch 5, page 113, Q.15 2011: students who play neither cricket nor football. Class11, ch1, page 23, example 26 2013: food in garrison, how many days will it last? Class8, Ch13, page 212 example 7, 8 and 9. Even the remaining questions, most of them are just slightly difficult than the concepts taught at NCERT level. Meaning, you don’t have to be an IIT/CAT ranker……If you can understand even upto NCERT level mathematics, you can tick good number of MCQs. Gather the weapons ESSENTIAL 1. One book on quantitative aptitude (hence forth referred as “Quant Book”) 2. (For those really poor in maths)- NCERT Mathematics. Topicwise zip file given at bottom. 3. one separate notebook / file, to maintain “diary of mistakes”- whenever you find any new formula, shortcut, weird MCQ or make mistake, note it down in this diary. Night before the exam, just read this diary. No need to “revise” aptitude books or practice sums on that night. I did the same for CAT, got 96%ile. OPTIONAL 1. A folder and loose A4 sized papers-To maintain a diary of mistakes and shortcuts. This is better than a notebook because you can add new pages anywhere as per your requirement. 2. A black slate, like those poor kids use in government primary schools-It saves lot of paper wasted in practicing math & reasoning sums. 3. CSAT Topicwise solve papers (1995-2013) by Disha Publication. Contains all papers of GS and aptitude- topicwise separated for both pre-CSAT and CSAT era. Which Quant book? As such, CSAT maths is just slightly more difficult than NCERT exercises. BUT, since NCERTs alone don’t give all variety of questions and street-smart techniques to save time during exam. Therefore, you need a quant book. For example, consider this (2007) A person has to fill three liquids – 403 lit. Petrol, 465 lt. diesel and 496 lt. motor oil in bottles of equal size without mixing any of above liquids. What is the least possible number of bottles required? While NCERT teaches HCF in class10, but doesn’t dwell into this concept. Concept is: you’ve to find HCF (31), then divide each number with HCF, then you’ll get total number of bottles required = 44. To learn all such variety of questions and concepts, you need a book on quantitative aptitude. NCERT are good to learn basic concepts, but NCERT alone are insufficient for CSAT. Choice of Quantitative Aptitude book, depends on your career backup apart from Civil Service Exam. IBPS, Bank, Staff Selection (SSC), AFCAT, LIC, NICL-AAO, ACIO, FCI & other PSU jobs. Fast-track to Objective Arithmetic by Rajesh Verma going back to private sector / business CSAT Aptitude Manual by Tata Macgraw Hill (TMH), Arihant or Pearson or xyz publication- whichever you can find cheapest or second hand :-) CDS, SCRA, CAT, XAT & other higher level exams. Quantum CAT Sarvesh Kumar (OR Arun Sharma) Avoid following books RS Aggarwal’s book on Quantitative Aptitude, M.Tyra’s book on quicker Maths, and any other 90s era book that bookstorewalla recommends you, because: 1. They’re Useless for SSC, CDS and SCRA because they don’t give detailed coverage of Trigonometry, geometry theory (parallelograms, circle-tangent etc.) OR quadratic equations. 2. They’re Useless for CSAT and higher level exams. Because they don’t cover all variety of tricky MCQs asked in such exams. 3. Even banking & insurance exams – Rajesh Verma’s techniques are faster & easy to understand. Don’t waste time learning Speed maths / Vedic maths For CSAT-Just memorize multiplication tables from 2 to 9. At max, mugup squares upto 19. It is sufficient. unlike Bank and CAT exam, the UPSC data interpretation questions don’t test your speed mathematics or long division skill, unlike CDS and SSC, UPSC questions on divisibility, number theory or HCF-LCM, don’t test your skill over prime number tables (13, 17, 19, 23, 29). Therefore, don’t waste time in Vedic maths tricks for speed maths, addition, multiplication, subtraction, division, cube roots, square roots etc. 23 If you already know such tricks then good, but now is not the right time to learn them fresh. High priority topics High priority topics doesn’t mean UPSC will definitely ask majority of the questions from here. It only means while you plan your study schedule, you should finish them first: H1: Linear Equations Sample questions from previous prelims (1998) in a family, age of father is three times that of his daughter, and age of son is half of his mother. If wife is nine years younger than husband, and brother is 7 years older than sister, what is the age of mother? (Ans.60) (2009) A gave half of his coins to B and 4 more besides. B gave half of his coins to C and 4 more besides. C gave half of his coins to D and 4 more besides. Both B and D end up with same number of coins. How many coins did A have originally? (Ans.72 coins) (2011) a person has only Rs. 1 and Rs. 2 coins with her. If the total number of coins that she has is 50 and the amount of money with her is Rs. 75, then find the number of Rs. 1 and Rs. 2 coins with him? (Ans. 25 and 25) What is Linear Equation? Linear equation means unknown variable (x or y) doesn’t have anything above their ‘head’. x 2 +2x+1 This is not linear equation because x has “2” above its head. Infact this is a quadratic equation. It is also part of “upto classs10” syllabus. But comes under “low priority” for CSAT. 2x+1 This is linear equation because x doesn’t have anything above its head. (Actually its x 1 but for our understanding purpose, take it as just “x”). This is high prioritytopic for CSAT. Linear equations are very important for aptitude exams, from two angles 1. direct MCQs about age, coins, salary, expenditure related problems 2. Indirect applications in time-speed-distance-work; profit-loss-SI-CI; Geometry problems etc. L1: Age problems: silly mistakes Q. 20 years ago, Bhootnath was 12 times the age of Abdul. At present, Bhootnath is twice as old as Abdul …blah blah blah we’re presented with two conditions Condition Wrong Right I. 20 years ago, Bhootnath was 12 times the age of Abdul B-20=12A or B=12(A-20) (this is the most common mistake) B-20=12(A-20) II. Bhootnath is twice as old as Abdul 2B=A B=2A Many candidates make wrong equations as shown above, then get wrong answer. Examiner would have even listed wrong answer in option. So junta happily ticks such option, “my paper went so good”, then they fail & blame nepotism, corruption and DP Agrawal for everything. How to avoid silly mistake? In age problems, always prepare a table beginning with present age. Observe At present, Bhootnath is twice as old as Abdul present age A and B Eq1. B=2A 20 years ago, so make a column on left side: Age 20 years ago: present age A-20 B-20 A and B Eq1. B=2A Then make second equation: 20 years ago, Bhootnath was 12 times the age of Abdul age 20 years ago (-20) present age A-20 B-20 A and B Eq2. B-20=12(A-20) Eq1. B=2A Now plug the value of B from Eq1. into Eq2 and you’ll solve this effortlessly. L2: keep minimum variables Suppose the question is like this “The sum of present ages of Abdul and Bhootnath is 56. 5 years ago Abdul’s age was……….blah blah blah….find the present age of Bhootnath. ” 24 avoid this approach use this approach assume Abdul present age “A” Bhootnath present age “B” assume Bhootnath’s present Age “B” assume Abdul’s present age =(56-B) Here you assumed two variables “A” and “B”= lengthier calculations and increased chances of silly mistakes. Here you’ve to worry about only one variable “B”. The moment you solve B, you get answer. L3: Cannot be determined Suppose you end up with two equations like this: I. x+y=5 II. y+z=6 Here you’ve two equations but three variables (x, y and z). You can never find out the unique value of x, y, z in such situation. Hence answer = “Cannot be determined”. But sometimes, even two variable-two equation set can be impossible to solve. For example No solution infinite solution I. x+ 2y=4 II. 2x+ 4y= 12 2x+ 3y=94x+ 6y=18 To learn more about ^this, refer to NCERT Maths Class 10, Chapter3, table given on the page #9. Examiner will test this by offering you both choice “Cannot be determined”; sometimes even data sufficiency (DS) question. Make sure you pick the right answer in right situation. Anyways, let’s proceed with preparations: @Those weak in maths @Those good at maths Following NCERT 7, 8 and 10, then refer your Quant book. NCERT Class10. (Because it has some good CSAT level sums) Then refer your Quant book: Rajesh Verma or Sarvesh Kumar (not both). NCERT: Linear Equations Class Ch. What to focus for CSAT? 7 4 How to convert statements into simple equation. example 10 age problem on page 90 Exercise 4.4 question no. 2 and 3 7 12 12.5 Monomials, Binomials, Trinomials & Polynomials (page 233) 12.6 adding-subtracting simple equations. Solve the four questions given immediately. (page 235) 12.8 formula and rules. page 243 Formula for no. of diagonals in a figure. Page 246 Page 247 summary. 8 2 Point 2.3 the example given in it page 24 Page 25 Example 7 age problem page 26 Example 8 coin problem Page 26-27 examples 9 to 11 Exercise 2.2 do all the sums Page 30: Example 14 digit reversal Page 31: Example 15 about age problem Exercise 2.4 do all sums Page 35: example 19 age problem Page 35: Exercise 2.6 only do Problem 6 and 7. 10 3 Everyone should do this, irrespective of how strong / weak in maths. Page 46: In what situation, infinite solution / no solutions? Table 3.4 most important for MCQs. Algebraic method to solve equations Page 50 understand the substitution method given in point 3.4.1 Page 52 Example 9: understand why the answer is “cannot be determined”. Page 53 Exercise 3.3 only solve Question No.3 25 Page 54 understand elimination method from example 11 Page 56 example 13: digit reversal problem Page 57 Do all the sums under Q.2 of exercise 3.4 Page 57: solve the apple sum under topic 3.4.5 but avoid the headache of that cross multiplication method. Stick to substitution & elimination methods. Page 60 ticket problem example 14 Page 63: do Q.(i) to (v) most important for CSAT. Page 65: example 19 avoid that stupid algebra method. Learn Boats and streams topic from my [Aptitude] article click me. Page 67 Quant book: Linear Equations Rajesh Verma Sarvesh Kumar First solve chapter 27 then chapter 7.Chapter 27 linear equation Understand the consistency system given on first page of this chapter. then solve all the questions in illustration and exercises you may avoid following type of questions because no asked in UPSC o Q.14 in Exercise1 o Q1 on Exercise2 Chapter 7: Word problems based on numbers Focus on digit reversal problems and age related problems. Ch13. Elements of Algebra in the initial part of this chapter he talks about polynomials, ignore it for the moment and directly move to page 525, “Linear Equation” He has explained all four methods to solve Linear equations. But stick to substitution and elimination method. Combined these two, you can handle pretty much every question. Ex.13: Do Question 10 to 18 Level 1: Do Question 23 to 31. Important: in Level1 exercises question No. 23 to 31: observe his explanations- how he solved them without assuming X or Y, or even framing equations. IF you master this technique, it’ll save a lot of precious minutes in the exam. H2: Number system Sample Questions from previous prelims 1. (2007) A person has to fill three liquids – 403 lit. Petrol, 465 lt. diesel and 496 lt. motor oil in bottles of equal size without mixing any of above liquids. What is the least possible number of bottles required? Ans. HCF will be 31. Then divide it with each number, you’ll get total number of bottles: 44. 2. (2009) while adding the first few continuous natural numbers, a candidate missed one of the number and wrote a wrong answer 177. Which number did he miss? Ans. Sum of the first “n” natural numbers is n(n+1)/2, but he missed “x”, so [n(n+1)/2] minus x = 177. Once you plug in the options, only x=13 will satisfy this equation. 3. (2011) three persons start walking together and their steps measure 40 cm, 42 cm and 45 cm respectively. What is the minimum distance each should walk so that each can cover the same distance in complete steps? Ans. whether its bells ringing together or bulbs lighting together or people walking together-you’ve Find LCM of those numbers. 25 m 20 cm 4. (2013) A gardener has 1000 plants. He wants to plant them in such a way that the number of rows and the number of columns remains the same. What is the minimum number of plants that he needs more for this purpose? Ans. Whenever you have to arrange soldiers or flowers or trees in Equal Row n equal column, then you have to make it square. Add 24 more trees so it becomes 1024=32×32. These are not really difficult questions, most of them can be solved without mugging up any formulas. You just need a good grip over basic concepts. POOR IN MATHS GOOD IN MATHS begin with NCERT (chapter wise list given below) Then use Quant books. No need for NCERT. Directly use your Quant book. Refer to appendix of this article, for what to prepare and what to skip in the quant books. NCERT: Number system NCERT Chapter Topic to focus for CSAT 7 2.Fractions and Decimals 1. proper, improper, mixed fraction 2. Ex.2.1’s example 6 26 3. Example 5 on page35 4. Example 6 on page39 9. rational numbers 1. topic 9.7 comparison of numbers- page 179 2. example 6: direction sense test page 186 3. summary from page 191-92 8 1.Rational numbers Table 1.2 the properties of rational numbers.Topic 1.4 how to find rational number between two rational numbers. 16. Playing with numbers. Divisibility rules for 2,3,5,9 9 1.Number system basic concept of recurring decimals: example 8topic 1.6 laws of exponents for real numbers page 241.7 summary page 27 10 1.Real numbers HCF, LCM how to find Page 10 Example 6, 8 and the remark given at bottom of it. Page 11: Question 7 important concept for circular race tracks. Page 19 note to reader. Ignore Euler and irrational numbers. NCERT Powers & Exponents NCERT Chapter Topic to focus for CSAT 7 13.Exponents & powers comparing numbers with powers how even-odd powers change the sign of negative numbers 13.6 expressing large numbers in std.form 8 6. squares and square roots table in 6.2 Numbers between square numbers- the lines given in italics. 6.4.2 Pythagorean triplets 6.7 estimating square root. 7. Cube and Cube roots geometry angle- example 7.2.2 12.Powers 12.3 Laws of exponents, 12.4.1 Comparing very large and very small numbers. Related articles under my [Aptitude] series: 1. LCM-HCF Simplified 2. Remainders: one number and two divisors After this is done, you have to solve all questions from your quant book. Even solve the already solved sums given in the “illustrations”. Refer to bottom of this article“Appendix A3″, for what to prepare what to skip from Rajesh / Sarvesh. H3: Percentages, Profit Loss, SI- CI Sample Qs. from previous prelims 1. (1998) A man bought two clocks A and B for total Rs.650. He sold A at 20% profit and B at 25% loss. If he had kept selling price of both clocks the same, then what were the cost prices of each clock? Ans. It requires your understanding of linear equation, percentages and profit loss. A’s cost price 250, and B’s 400. 2. (2002) Trader fixed the price of an article in such way that by giving a rebate of 10%, he made profit of 15%. If the cost of the article is Rs.72, what is the selling price? Ans. 92 rupees. 3. (2005) Left pan of a faulty weigh weighs 100 gms more than the right pan. Shopkeeper keeps the weight measure in left pan while buying goods but keeps it in the right pan while selling goods. He only uses 1 kg weight. If he sells goods at the listed cost price, what is his profit? Ans. gist of the question is: he frauds 10% in buying and 10% in selling. So, on each trading sequence. Hint: Assume 1 gm costs 1 rupee. Find per unit price while buying and selling. buying fraud of 100 gm per 1000 gm = 1100 gm selling fraud 100 gm per 1000gm = 900 gm Unit cost price per gram= Rs.1000 paid/ per 1100 gm bought unit SP =Rs. 1000 got/ per 900 gm sold Effective cost price = 10/11 Effective selling price = 10/9 Profit % = (SP-CP/CP) x 100= 200/9% This is one of those weird/unique question, so note it in your “diary of mistake”, 4. (2010) two numbers X and Y are respectively 20% and 28% less than third number Z. By what % is the number Y less than number X. Ans 10% 27 5. (2010) Difference between simple interest from two banks on Rs.500 for two years is Rs.2.5, what is the difference between their rates? Ans. 0.25% Percentages-NCERT As such UPSC’s percentage related questions are complicated than the exercises given in NCERT, but still solve NCERT as warm- up exercise for multiplication and division. Class 7 Ch8 Class 8 Ch8 To learn how to solve such MCQs, without mugging up formulas, refer to following articles: 1. Concepts of Marked Price and Successive Discounts (Profit-Loss) without (stupid) formulas 2. Compound Interest Rate, Population Growth without Formulas 3. Alligation: Advanced applications in Interest rates, Profit-loss, Average Wages (Wine-Water Concept) 4. Product Consistency: If Sugar price increases then consumption should be Decreased by What %, Time-Speed-Distance problems, After this is done, you have to solve all questions from your quant book. Even solve the already solved sums given in the “illustrations”. Refer to bottom of this article, for what to prepare what to skip from Rajesh / Sarvesh. H4: Ratio Proportion Variation Partnership (RPVP) Sample Qs. from previous prelims 1. (1998) If 15 pumps of equal capacity can fill a tank in 7 days, then how many extra pumps will be required to fill the tank in 5 days? Ans.6 (you can solve this as “pipes n cisterns / speed-time-distance problem also. ultimately it’s a problem of inverse relation between speed vs time) 2. (2002) Amit Shah started a business with investment of Rs.30,000. Rahul Gandhi joined after some time and invested Rs.20,000. At the end of year, profit was divided in the ratio of 2:1. After how many months did Rahul join the business? Ans. 3 months 3. (2013) in a rare coin collection, there is one gold coin for every three non-gold coins. 10 more gold coins are added to the collection and the ratio of gold coins to non-gold coins would be 1: 2. Based on the information; the total number of corns in the collection now becomes what? Ans. 90 4. (2013) Out of 120 applications for a post, 70 are male and 80 have a driver’s license. What is the ratio between the minimum to maximum number of males having driver’s license? Ans. 3:7 5. (2013) the tank-full petrol in Arun’s motor-cycle lasts for 10 days. If he starts using 25% more every day, how many days will the tank-full petrol last? Ans. 8 days. 6. (2013) In a garrison, there was food for 1000 soldiers for one month. After 10 days, 1000 more soldiers joined the garrison. How long would the soldiers be able to carry on with the remaining food? Ans. Inverse variation topic. Ans. 10 days. 7. (NCERT Class8) There are 100 students in a hostel. Food provision for them is for 20 days. How long will these provisions last, if 25 more students join the group?Ans. 16 days. 8. (NCERT Class8) The scale of a map is given as 1:30000000. Two cities are 4 cm apart on the map. Find the actual distance between them. Ans.1200 Understand the partnership concept from this article: (Aptitude) Partnership and profit-sharing made Easy. PS: Even those good at Maths MUST do the sums from Class8 Chapter 13. Class Ch. What To Focus 7 8 Basics of Ratios. Although most of the chapter is focused on percentages. too rudimentary stuff, use it just for warm up exercise for multiplication and division. 8 13 Basics of variation. page 207 example5 interesting Page 208 exercise 13.1 Question 5 to 10 Page 212 example 7, 8 and 9. Question 8. MOST IMPORTANT- how long the food will last. This type of questions asked in CSAT. Understand the concept well. Exercise 13.2 Q4 to 11. Notice Q5, its identical to the ‘food lasting’ problem. Then solve your Quant book. Refer appendix for what to prepare, what to skip. H5: Speed Time Distance Work (STDW) This is fourth block, because these sums also test your understanding of Linear Equation (H1), LCM (H2), Percentages (H3) and ratios (H4). But Juntaa directly starts preparing STDW without learning first four blocks because last time UPSC asked many MCQs from STDW. Such quickfix-shortcut-moodswing based preparation usually lead to #EPICFAIL. You need good command over all those basic concepts from H1 to H4. Proceed in a systematic manner. Sample questions from previous prelims 28 1. (2001) A worker reaches his factory 3 minutes late if his speed from his house to the factory is 5 km/hr. If he walks at a speed of 6km/hr, then he reaches the factory 7 minutes early. The distance of the factory from his house is ___? Ans 5 km 2. (2004) Two cars X and Y starts from two places A and B respectively which are 700km apart at 9 a.m. Both the cars run at an average speed of 60 km/hr. Car X stops at 10 a.m. and again starts at 11 a.m., while the other car Y continues to run without stopping. When do the cars cross each other? Ans 3:20PM 3. (2005) Aryan runs at a speed of 40meters/minute. Rahul follows him after an interval of 5 minutes and runs at a speed of 50 meters/minute. Rahul’s dog runs at a speed of 60 meters/minute and starts along with Rahul. The dog reaches Aryan and then comes back to Rahul, and continues to do so till Rahul reaches Aryan. What is the total distance covered by the dog? Ans 1200m 4. (2007) A and B can complete work together in 5 days. If A works at twice his speed and B at half of his speed, this work can be finished in 4 days. How many days would it take for A alone to complete his job? Ans 10 days 5. (2010) Three men start together to travel the same way around a circular track of 11km. Their speeds are 4, 5.5 and 8 kmph respectively. When will they meet at the starting point for the first time? Ans 22 hours 6. (2012) Mr. Kumar drives to work at an average speed of 48km/hr. The time taken to cover the first 60% of the distance is 10 minutes more than the time taken to cover the remaining distance. How far is his office? Ans. 40 km 7. (2013) A person can walk a certain distance and drive back in six hours. He can also walk both ways in 10 hours. How much time will he take to drive both ways? Ans. 2 hrs 8. (2013) A thief running at 8 km/hr is chased by a policeman whose speed is 10 km/hr. If the thief is 100 m ahead of the policeman, then the time required for the policeman to catch the thief will be what? Ans. 3 min 9. (2013) A train travels at a certain average speed for a distance of 63 km and then travels a distance of 72 km at an average speed of 6 km/hr more than its original speed. If it takes 3 hours to complete the total journey, what is the original speed of the train in km/hr? Ans.42 kmph NCERT not much useful here, because it runs on the LCM method and doesn’t dwell on all varieties of questions. STDW is made up of two topics 1. Speed time distance cars, trains, platforms, boats etc. 2. Speed time work “A can complete a work in….”, “pipe A can fill the tank in …” etc. All of these can be solved through just one formula: STD (speed x time =distance). Go through following articles: Time-speed-Distance Time-speed-work 1. Trains, Platforms TSD (Time, Speed, Distance) made easy 2. Boats and Streams made-easy using our STD- Table Method 3. Average Speed made easy without Formulas 4. STD table : Application in train man bridge, time and work problems 5. Time n Distance: Early and late to office (shortcut using product consistency method) 6. Product Consistency: Time-Speed-Distance problems 1. [Speed Time Work] Two Men can finish a work, A is 3x more efficient than B, B leaves before completion & variety of cases 2. [Speed Time Work] Three men can finish a work in x days, A & B start work, C joins after x day, share in wages & other special cases 3. Time n Work: 4 men and 6 women can complete a work in 8 Days then Once you’ve understood this STD table concept, then apply it while solving the illustrations and exercises given in your quant book. H6: Averages, Allegations 1. (1996) If the average of A, B and C is 14. Twice the sum of B and C is 30. What is the value of A? Ans. 27 2. (1997) the average monthly income of a person in a certain family of 5 is Rs.1000. What will be monthly average income of person in the same family if the income of one person increased by Rs. 12,000 per year? Ans. 1200 3. (2011) A student on her first 3 tests received an average score of N points. If she exceeds her previous average score by 20 points on her fourth test, then what is the average score for the first 4 tests? (Ans. N+5) NCERTs don’t provide the street-smart techniques OR the requisite variety of questions asked in aptitude exams. They mainly deal from “Statistics” angle. (Statistics is asked but low-priority for CSAT). So, instead of NCERTS, first go through following articles: [Aptitude] Averages: Entry / Removal of 1 element => Increase / Decrease in Average Shortcut method explained [Aptitude] Averages: More than two elements added / removed : shortcut technique explained [Aptitude] Alligations,Mixtures,Alloys: Water,Milk,Wine mixing: Weighted Average Made Easy for CSAT,CAT,CMAT,IBPS Aptitude [Aptitude Q] Mixture and Alligiation: Change Alcohol concentration from 15% to 32% [Aptitude] Alligation: Advanced applications in Interest rates, Profit-loss, Average Wages (Wine-Water Concept) Then solve all the illustrations and examples from your Quant book. 29 if you really want to learn the basics, consult following NCERT chapter (although quite unnecessary because everyone knows this much basic.) class ch 7 3 8 5, 15 (These are useful for data interpretation though) 9 14 10 14 H7: Data Interpretation (DI) GRAPHICAL TEXTUAL 1. “Odd” speed graphs, bacterial growth graphs etc. 2. bar graphs, pie charts, line graphs 1. Venn diagrams 2. Tabulation DI-1: odd- graphs [Prelim 1995] The variations in temperatures form 0 degree C to 100 degree C with respect to time of two liquids P,Q are shown in the graph given below: Which one of the following statements is correct? a. During heating, liquid P remained hotter than liquid Q throughout b. At no point of time during heating did the two liquids have the same temperature c. P attained the temperature of 100 degree C faster than Q d. Q attained the temperature of 100 degree C faster than P ANSWER. (d) [Prelim 1996] Following graph represents a race among four persons. Consider following statements 1. A stood first in the race 2. C led all the way 3. D ran faster than others in the later part of the race. Answer choices 1. 1 and 3 false, while 2 correct 2. 1 and 2 false, while 3 correct 3. 1 and 3 correct while 2 false 4. 1 is correct; 2 and 3 false. Correct answer: (B) hint: you should add numbers on both axis, then find what time each took to finish the race. you’ll see “D” won the race. 30 [Prelim 1999]The yield versus fertilizer input is shown in the graph. Consider the following statements based on this graph: 1.Yield rate is zero at B and C 2.There is no yield with no fertilizer input 3.The yield is minimum at D 4.The yield is neither minimum nor maximum at C Which of the above statements are correct? a. 1,2 and 4 b. 3 and 4 c. 2 and 3 d. 1,3 and 4 ANSWER.(b) [Prelim 2000]The following figure represents time vs learning curves of two students,Q and R for learning a Mathematics lesson: Which one of the following can be drawn from the graph? a. R started slowly in the beginning but got ahead of Q to complete learning the lesson b. Q started slowly and finished learning the lesson earlier than R c. R was always faster than Q in learning Mathematics d. Q was always faster than R in learning Mathematics ANSWER.(a) Hint: add numbers on both axis, then you’ll see who is learning to what pace. You’ll also find odd graphs in last three CSAT papers (attached at bottom of this article). I’m not copying them here because more images=slower loading webpage. I call them odd graphs because usually unseen in other aptitude exams, even CAT. But these graphs are not falling from sky, topic is given in NCERT. First understand following concepts from NCERT Class8, Chapter 15 “Graphs” Page 234-35: Example1 two cricketers performance graph Page 235-36: Example2 car average speed graph Exercise 15.1: Q1 Patient’s temperature Page 237-38 Q3. growth of two plants A and B Page 238: Weather forecast vs actual temperature graph Page 239: understand the concept in Q7 In the real CSAT, usually they don’t give numbers on the axis. But if you want to solve them with NCERT technique, then you’ve to write numbers on your own understanding. Observe following image Once you add numbers like this, it becomes very easy to compare P vs Q and eliminate options accordingly. Where to get additional practice? You’re unlikely to find such ‘odd graphs’ practice questions easily. They’re usually not asked in Bank and CAT. Although they’re sporadically asked in CDS, CAPF and SCRA exams (For all four major exams of UPSC, the Examiner seems to be utilizing the same DI Question bank from the secret server in the basement of UPSC Headquarter). But again cost:benefit not that great IF you start 31 digging through all previous papers of CDS, CAPF and SCRA = too time consuming exercise. Anyways, you will find a few such question under 1. aptitude manuals 2. CST magazine’s mock tests. You don’t have to specifically buy them only for the “ODD graphs”. Borrow whatever you can from library / friend circle. DI-2: bar graphs, pie charts I’m not adding their samples questions here, because dozens of images =slow loading webpage, especially on mobile browser. But you’ll find the samples in the last 3 CSAT papers attached below the article. Difficulty wise- above SSC and little below BankPO Data Interpretation in BankPO/ CAT UPSC CSAT Often require lengthy calculation and long divisions, even prime numbers (17,19, 23,37 etc.). Usually calculations are easy – you’ve to do 10%, 20%, 25% of something and you’ll get the answer. requires you to find exact mathematical answer. often the four options are very close (16.5,16.7,16.55,16.67) so you can’t eliminate wrong choices by logic or guestimation, you’ve to do exact calculation without any mistakes. Usually give you 3-4 text statements and ask which one of them are correct as per the given chart. Meaning they don’t usually require you to find exact mathematical answer. Although you’ve to do maths /apply logic to eliminate the wrong statements. To make difficult questions from pie chart, they usually make a combo of o two pie charts OR o 1 pie chart + 1 bar graph or o 1 pie chart + 1 table. Same To get a basic overview of Pie charts, bar graphs etc you can consult NCERT class8 chapter 5. But as such it doesn’t contain any street smart tricks OR sums relevant to CSAT. Therefore, to gain command you’ve to get practice. Where to get practice DI sets? 1. SSC sets far easier than CSAT. so avoid 2. CAT sets will be an overkill. so avoid 3. Hence your best bet is bank PO exam papers. But even in them, avoid sets that require lengthy calculations and long divisions. Yes but where to get BankPO papers? Ans. hit the library and o go through monthly issues of Pratiyogita Darpan or banking service chronicle o CST (Civil service times) magazine gives demo CSAT papers with DI o Arihant/Kiran publication books papersets Quant books usually don’t give many DI sets –whether it’s Rajesh, Sarvesh or Arun Sharma. It’s a clever marketing trick to sell another separate book for DI. But for CSAT DI, you don’t need any separate book. Also don’t waste time on internet gathering bank papers – they’re usually too scattered and bad PDF quality. Just hit the library and go through those magazines. DI-3: Venn Diagrams Sample questions from previous prelims: 1. [1998] There are 50 students admitted to a nursery class. Some students can speak only English and some can speak only Hindi. 10 students can speak both English and Hindi. If the number of students who can speak English is 21, then how many can speak Hindi, how many can speak only Hindi and how many can speak only English ?Ans. 39,29 and 11 respectively 2. [2000] In an examination, every candidate took Physics or Mathematics or both. 65.8% took Physics and 59.2% took Mathematics. The total number of candidates was 2000.How many candidates took both Physics and Mathematics? Ans. 500 3. [2001] In a survey,it was found that 80% of those surveyed owned a car while 60% of those surveyed owned a mobile phone. If 55% owned both a car and a mobile phone, what percent of those surveyed owned a car and a mobile phone or both? Ans. 85% 4. [2011-II] There are 100 students in a particular class. 60% students play cricket, 30% student play football and 10% students play both the games. What is the number of students who play neither cricket nor football? Ans.20 There are two sub types: 1. logical Venn diagrams (we saw in previous article) 2. mathematical Venn diagrams (that we’ll see here) Don’t assume A+B=total 32 Q. In a society 10 people drink tea, 4 people drink both coffee and tea…..blah blah blah..find total people in the society. Wrong Approach Right Approach Total people in society =+ only tea drinkers+ only coffee drinkers+ (those who drink both tea & coffee) Total people in society =+ only tea drinkers+ Only coffee drinkers+ (Those who drink both tea & coffee) + Those who drink neither tea nor coffee (n) This is juntaa’s most common mistake in Venn diagram. they forget about “n” Read the question description carefully. If and when required take n=0. As such Venn diagram is class11 topic but UPSC has repeatedly asked it both in pre-CSAT and CSAT era. Perhaps, examiner considers it “Reasoning” and not “maths”. Nonetheless, Venn diagram is a very easy “NO EXCUSE” topic. At max it should take ~3 hours to finish this topic at home. Start preparation with Class11 NCERT Mathematics chapter1. page What to focus for CSAT? 16 Properties of intersections. you don’t have to mugup formulas, but understand the concept from those colored regions in those five image boxes. 17 Example 18. this is the “basic” of all 2 circle Venn diagrams. 21 Formula of n(AUBUC). As such you can solve 3 circle Venn diagrams with just logic of “this portion minus that portion”. but sometimes problems are trickier and you need this formula. 22- 26 All the illustrations and all the exercises. 27 Q.13 to 16 After this, solve all the sums in your Quant book (+ whatever sums you get in Pratiyogita, CST etc.) DI-4 Tabulation questions Sample questions from previous prelims [1996] The following table shows the percentage distribution of revenue expenditure of Government of India in 1989-90 and 1994-95 : Expenditure Head (percent to total) Years Defence Interest payments Subsidies Grants to State/UT other 1989-90 15.1 27.7 16.3 13.6 27.4 1994-95 13.6 38.7 8.0 16.7 23 Based on this table, it can be said that the Indian economy is in poor shape because the Central government continues to be under pressure to : a. Reduce expenditure on defence b. Spend more and more on interest payments c. Reduce expenditure on subsidies d. Spend more and more as grants-in-aid to State government/Union Territories ANSWER.(b) 3. (2000) A club has 108 members. Two-thirds of them are men and the rest are women. All members are married except for 9 women members. How many married women are there in there in the club? Ans.27 4. (2001) A city has a population of 3,00,000 out of which 1,80,000 are males. 50% of the population is literate. If 70% of the males are literate, the number of literate females is __.? Ans 24,000 You can solve Q3 and Q4 by directly framing linear equations. but table = less changes of error. Sometimes, question descriptions of tabular vs Venn diagram sound very similar, but the main difference: the players in a tabular questions will not have “overlapping”. Observe Tabular question Venn diagram question 1. In a company ** male, out of them ** union members. Total female are **, blah blah blah…..then find __. 2. in a company ** people work in HR, ** people work in R&D, ** people work in marketing blah blah blah….then find ___. 1. In a society 10 people drink tea, 4 people drink both coffee and tea…..blah blah blah..find total people in the society. 2. in a society ** people own car, ** own bike….blah blah blah Overlapping not possible. Man is man, woman is woman. You can make two columns: union vs non-union and further two sub columns man vs woman. same way, Person who works in HR cannot work in R&D at the same time. These are all separate columns. no overlapping circles. Overlapping circles are possible, people who like tea, may also like coffee. Those who own car, may also own bike. 33 This is not difficult, but juntaa doesn’t practice at home so in the exam they cannot decide which way to proceed- Should I make table OR Venn diagram? So, they simply start scribbling data either in table or in Venn diagram, until they get nowhere after 10-15 minutes of calculation. Then they try second approach, but make silly mistakes in addition / multiplication so finally after wasting 20 minutes they leave the sum. This is one of the main reasons why people cannot finish paper on time and fail in the CSAT. DONOT start scribbling numbers, UNLESS you know exactly how you’re going to reach the answer. Keep an eye on the wrist watch. DONOT spend so much time on a single question, even if it’s “Data interpretation”. Anyways where to get practice? NCERTs not much useful here. You’ll find some questions within Venn diagram chapter of your quant book. Beyond that 1. Previous papers of General Studies (Mains) paper II upto 2012. Because in those years, UPSC had statistics and DI section under Mains syllabus and they used to ask such tabulation questions. 2. Bank papers given in competitive magazines Pratiyogita, Banking chronicle etc. but keep in mind, UPSC’s tabulation MCQs don’t involve that lengthy calculations unlike IBPS/SBI. H8: Geometry: Area volume perimeter (AVP) Sample questions from previous prelims 1. [2005]A big rectangular plot of area 4320 meter square is divided into 3 square shaped smaller plots by fencing parallel to the smaller side of the plot. However some area of land was still left as a square could not be formed. So, 3 more square shaped plots were formed by fencing parallel to the longer side of the original plot such that no area of the plot was left surplus. What are the dimensions of the original plot? Ans. 120m x 36m 2. [2010]The diameters of two circular coins are in the ratio of 1:3. The smaller coin is, made to roll around the bigger coin till it returns to the position from where the, process of rolling started. How many times the smaller coin rolled around the bigger coin? Ans.3 times 3. [1998]A square pond has 2m sides and is 1m deep. If it is to be enlarged, the depth remaining the same, into a circular pond with the diagonal of the square as diameter as shown in the figure, then what would be the volume of the earth to be removed? Ans. (2pi-4)m 3 How to proceed? if you don’t have Sarvesh Kumar if you’ve Sarvesh Kumar First NCERTs then your quant book. No need to consult NCERT. Because he has neatly summarized all theorms, formula and special questions given in NCERTs. NCERT Class7 Chapter 11 206-208 all examples for area-perimeter related questions 220 example 15 221 example 16 223 do all exercises in 11.3 225-26 Example 20, 21, 22. Similar park-road question asked in 1997 226-28 all the sums and summary Class9 Chapter 12: Areas related to triangles: HERON’s formula 199 Heron’s formula 201 example 2 202 all questions 203 Q.3 to 6; Example 4 205 ex.6 207 all questions and summary Class9 Chapter 13: surface area volume. Proceed in following sequence: 237 first mug up all the formulas given in this summary 211-213 Cuboids area related sums 227-28 Cuboid volume related sums. 1995: UPSC asked question similar to example 11. 216-17 Cylinder area related sums 229-231 Cylinder volume related sums 220-21 Cone area related sums 232-33 Cone volume related sums 34 224-25 Sphere area related sums 235-37 Sphere volume related sums Class10 Chapter 12 225 example cost of ploughing the field 226 entire exercise 12.1 227 formula for area of a sector 230 Q3, 8, 9 231 Q10 to 14 231-238 all illustration and sums important for CSAT. They keep asking such combo images and shaded areas. Class10 Chapter 13 This chapter deals with volume of ‘combo’ figures. Semi-sphere above a cube & so on. Solve all the illustration and exercises given here. – next article, we see how to approach the medium and low priority topics under mathematics for CSAT. Appendix: Download links A1: Last three years official CSAT papers https://files.secureserver.net/0s4I32bAjTl3bm except CSAT-2013, all contain official answerkey from UPSC A2: NCERT Mathematics Topicwise Sorted free download https://files.secureserver.net/0fmaNqqBDslHlc A3: Quant books: What to prepare, what to skip? Beyond NCERT, you’ll need to practice maximum sums from your quantitative aptitude book. However, not all chapters / topics given in such books, are important for CSAT. So, consult following PDF files on what topics to focus and which topics to ignore: 1. Fast track to Arithmetic Rajesh Verma What to prepare what to skip for CSAT 2. Quantam CAT Sarvesh Kumar What to prepare what to skip for CSAT Visit Mrunal.org/aptitude for more articles on aptitude, maths, reasoning. URL to article: http://mrunal.org/2014/06/studyplan-csat-aptitude-paper-2-maths-data-interpretation-high-priority-topics- sample-questions-free-studymaterial-part-2-3.html Posted By Mrunal On 08/06/2014 @ 11:51 In the category Aptitude Click here to print. [Studyplan] CSAT Aptitude Paper 2: Decision Making + Maths Medium & Low priority topics, Sample Questions, free studymaterial (part 3 of 3) 1. Decision Making Problem solving & communication 1. Bad decision choices 2. Good decisions 3. Just eliminate two bad decision 4. CSAT 2013 Questions 5. Elimination doesn’t always work though! 6. Where to get practice? 2. Maths: Medium priority topics 35 1. M1: Arithmetic Progression (AP) 2. M2: Coordinate Geometry 3. M3: Polynomials & Quadratic equation 3. Maths: Low priority topics 1. L1: Geometry theory (TQC) 2. L2: Trigonometry 3. L3: Permutation Combination Probability 4. L4: Statistics 4. Appendix: Download links 1. A1: Last three years official CSAT papers 2. A2: NCERT Mathematics Topicwise Sorted free download 3. A3: Quant books: What to prepare, what to skip? So far in the CSAT paper-2 study plan 1. Comprehension and Reasoning 2. Mathematics & Data Interpretation: high priority topics 3. Decision Making + Mathematics: Medium & low priority topics You’re here Decision Making Problem solving & communication First read following articles: 1. [Decision Making] CSAT 2011: official question and answers 2. [Decision Making] CSAT 2012: official question and answers 3. [Decision Making] CSAT 2013: (official answer released and included in present article.) Overall we can see following pattern: Theme 2011 2012 2013 Office tension: project deadline, Khaddus Boss, idiot subordinates, colleagues seeking favors 2 4 1 Interaction with Goonda-log, corrupt babu 1 1 1 Roleplaying Govt. officer in situation where he could be blamed for corruption, apathetic 3 0 1 Distribution of precious commodity: sugar, vaccine, water, sarkari-house etc) 1 1 2 Communication 0 0 1 Misc. problems (dowry victim, sport chairman) 1 1 0 Total Questions 8 7 6 % weight out of 80 Questions 10% 9% 8% Bad decision choices From official answers, we can see UPSC hates following type of choices: 1. Pliable guy: 1. bribe giver 2. bribe taker 3. choses to look the other way while others are involved in wrongdoing, 4. Easily gets scarred or intimidated. 2. No discipline guy: 1. shows Arrogance 2. Insubordination: lack of respect towards authority, Goes on leave without telling boss etc. 3. liar, Gives excuses instead of doing his job. 3. Implausible, impractical choice e.g. free water or electricity to everyone irrespective of his income status. 4. “Take no action” guy: prefers status quo, takes no action, “Committee mindset” 5. Biased officer, apathetic officer, evasive officer. 6. Short term oriented. A decision that will break office discipline in long term. Good decisions From official answers, we can see UPSC hates following type of choices: 1. Humane e.g. giving free water / electricity but only to BPL 2. Punctuality, meets the deadlines 3. Upright Honest person 4. Atleast trying to do take some “positive action” rather than continue with status quo Just eliminate two bad decision In Decision Making questions, there is no negative marking. And as per official answerkey-two possible correct answers. (Which of them is best? UPSC doesn’t tell) 36 But still, this reduces the effort. Instead of looking for right answer, just eliminate two baddest worst answer choices using the list given above. Then you’re automatically left with right answers. Pick any one based on which you think is right for the given question. Let’s try… (2012) You are handling a priority project and have been meeting all the deadlines and planning your leave during the project. Your immediate boss does not grant leave citing the urgency of the project. You would ____. 1. Proceed on leave without waiting for the sanction (indiscipline) 2. Pretend to be sick and take leave (liar) 3. Approach higher authority to reconsider the leave application. 4. Tell the boss that it is not justified. So A and B automatically eliminated. We are left with correct answer C or D. Ok 2012’s official answerkey is available. So I or anyone can ‘fit’ the logic after knowing official answers! let’s apply this technique for CSAT 2013, where official answerkey is not available. (When official answerkey comes, after final result – we’ll see how apt this approach is. update Jun-26-2014: official answerkey released and all of following answers turned out to be correct, except slight difference at just one place in family planning.) CSAT 2013 Questions Q. House allotment problem: Secretary wants house because his father ill. But HQ said no. A. Call him over to your room and personally explain why the allotment cannot be done. B. Allot the house to him to win his loyalty. (biased, will break office discipline) C. Agree with the office note to show that you are not biased and that you do not indulge in favoritism. D. Keep the file with you and not pass any orders. (status quo guy) Thus we are left with two choices: A and C. (But are they really correct? we’ll see when answerkey comes.) Q. you’re passenger, Taxi driver gives bribe to transport office a. Go up to the counter and ask the clerk to give back the money which he has illegally taken. b. Do not interfere at all as this is a matter between the taxi driver and the tax authorities. (pliable) c. Take note of the incident and subsequently report the matter to the concerned authorities. d. Treat it as a normal affair and simply forget about it. (status quo) Again after eliminating bad decisions, we are left with A and C. Q. You’re DM, a village came long way to submit complaint but you’re busy with work. A. Tell him to wait for another two hours till you come back from your next meeting. (Apathetic) B. Tell him that the matter is actually to be dealt by a junior officer and that he should give the application to him. (Evader) C. Call one of your senior subordinate officers and ask him to solve the villager’s problem. (this is not evader because asking ‘senior’ subordinate to “solve” problem.) D. Quickly take the application from him, ask him a few relevant questions regarding his problem and then proceed to the meeting. We are left with C or D Q. You’re DM. There is sugar quota order but friend asking additional supply for marriage reception a. Release the extra amount of sugar which your friend has requested for. (biased officer) b. Refuse your friend the extra amount and strictly follow the rules. c. Show your friend the copy of the Government instructions and then persuade him to accept the lower amount as prescribed in the rules. d. Advise him to directly apply to the allotting authority and inform him that you do not interfere in this matter. (Evader. because friend may try to pursued that other officer saying “I’m best friend of DM”.) We are left with B or C Q. You are in-charge of implementing the Family Planning programme in an area where there is a strong opposition to the present policy. You want to convince the residents of the need for keeping small families. What would be the best way of communicating this message? A. By logically explaining to the residents the need for family planning to improve the health and living standards. B. By encouraging late marriages and proper spacing of children. (ya but how do you “communicate”?) C. By offering incentives for adopting family planning devices. (ya but he’s asking you to “Communicate” this message?) D. By asking people who have been sterilized or are using contraceptives to directly talk to the residents. We are left with A or D Update Jun-26-2014: UPSC uploaded official answerkey, the correct answer is “A or C”. Hence this is the only place where our technique didn’t work 100 accurately. Q. You’re setting university paper. Colleague asks you for this paper so his son can clear last attempt. he has done favors in past. A. In view of the help he had given you, extend your help to him. (biased guy) 37 B. Regret that you cannot be of any help to him. C. Explain to your colleague that this would be violating the trust of the University authorities and you are not in a position to help him. D. Report the conduct of your colleague to the higher authorities. (too extreme, given that he had helped in past). This one is hard for “two eliminations”. Because B, C and D all sound legit. “C” seems to be the best alternative though. Actually B=C. But C is “communicating” the message in better way than “B”. Anyways final judge UPSC’s official answerkey. Elimination doesn’t always work though! Sometimes statement is open to multiple interpretations and if you drag the logic then it leads to a track away from official answer key. Consider this problem: Q.You are a chairperson of a state sports committee. You have received a complaint and later it was found that an athlete in junior age category who has won a medal has crossed the age criteria by 5 days. You would… 1. Ask the screening committee for a clarification 2. Ask the athlete to return the medal 3. Ask the athlete to get an affidavit from the court declaring his/her age. 4. Ask the members of the committee for their views The statement says “later it was found that….he has crossed age by five days” => so on that interpretation even “B” seems a right answer because if he cheated on age, then chairman should take back his medal. But official answer is A or D. But such odd questions are in minority. And even in worst case you should tick an option anyways because there is no negative marking in the Decision Making questions. Where to get practice? Various Publication houses came up with separate books but hardly few UPSC level question. Most of them is just bolbachhan about Plato, Kautilya etc. (sometimes even copied from Wikipedia!) Hence their content doesn’t justify the price tag. (just like their comprehension books for CSAT) Nonetheless, hit the library go through following: 1. Pratiyogita Darpan’s SSB Group Task/Interview related articles. They don’t usually contain MCQs with 1,2,3,4 choices, but you’ll still get good problems and case studies. 2. Civil service Times (CST): their mock test papers 3. CSAT aptitude manuals TMH, Arihant, Pearson (whatever is available free in the library or temporarily borrow from a friend in exchange of some good book from your side.) 4. you’ll find some demo questions here too: Mrunal.org/ethics Anyways, moving to the next issue: Maths: Medium priority topics Medium priority =only while allot time for various topics in your study schedule for paper I and paper II. These medium priority topics are rarely asked in UPSC. But they’re are not difficult, very few variety of questions, you have to memorize just 3-5 formulas. require barely ~2 hours study practice for 1 or 2 NCERT chapters.Hence you should definately try to make time in your schedule for them. For UPSC examiner, there is no such “medium” priority, he is free to ask whatever he wishes from upto ClassX. M1: Arithmetic Progression (AP) (2011) A contract on construction job specifies a penalty for delay in completion of the work beyond a certain date IS as follows : Rs. 200 for the first day, Rs. 250 for the second day, Rs. 300 for the third day etc., the penalty for each succeeding day being 50 more than that of the preceding day. How much penalty should the contractor pay if he delays the work by 10 days? Ans.4250 NCERT Class10 chapter 5 Page what to focus 116 summary mugup the formulas 105 example 10 107 Q19 and 20 111 example 16 113 Q15. Similar question asked in CSAT 2011 113-14 Q.16 to 20 115 Q.3 to 5 Beyond that your quant book for additional practice. Geometric progression (GP) starts from Class11, so far not asked in prelims so you may ignore. M2: Coordinate Geometry 38 1. [1995] In the Cartesian plane, four points P,Q,R,S have co-ordinates (1,1), (4,2), (4,4) and (1,4) respectively. The area of the quadrilateral PQRS is __? Ans 7.5 2. [1999] At a given time, two players are standing on a play-field. The Cartesian coordinates of their locations are (20,60) and (-40,-20) units. What is the distance between the players? Ans. 100 units As such coordinate geometry is rarely asked in UPSC. But, Coordinate geometry is not tough. You just have to do one chapter in NCERT=At max, two hour study and calculation. So, from that angle, cost : Benefit is still quite good. You might get lucky finding one MCQ in the exam, in this cut-throat competition every mark counts. NCERT Class10 chapter 7 172 first mugup the formulas given the summary here 161 Q1, 2 167 Q6, 10 area problems 169 example 11 to 13: triangle areas 169 example 14: understand the technique to find collinear points 170 example 15: similar question asked in 1995 171 Q 1, 2 and 4 171 Question 2 to 4 M3: Polynomials & Quadratic equation It is part Class8, 9 and 10 NCERTs. Official UPSC syllabus says basic numeracy “upto class 10”. Although UPSC hasn’t asked this in 2011, 2012 or 2013. But such questions have appeared in pre-CSAT era, in 1995, 96, 99, 2001. Observe (1995) what is the value of (a-m)(b-m)….(y-m)(z-m).Ans. actually this one quite easy: m-m=0 so entire multiplication will be zero. (2001) if x 2 +y 2 =34 and x 4 -y 4 =544, then what is the value of x and y A. 4,3 B. 5,3 C. 3,5 D. 3,4 (1996) If A=x 2 -y 2 , B=20 and x+y=10 then A. A > B B. B > A C. A = B D. data insufficient (1999) if x+2y=2x+y, then x 2 /y 2 is equal to A. 0 B. 1 C. 2 D. 4 There is no need to fear, very easy questions based on basic formulas. You can finish learning the entire topic at maximum within 2 hours. Minimum prepare this: class ch. what to focus 8 Ch.9 Algebraic Expressions Polynomials: additions, subtraction, multiplication. 8 Ch.14 Factorization making Factors of the form (x + a) (x+ b); division of polynomials You may avoid following chapters because I’ve not such questions between 1995-2013. These chapters/concepts are typically reserved for the SSC, CDS, SCRA and CAT exam. 9 Ch.2 Polynomials remainders finding value of “k” in the polynomial equation 10 Ch.2 Polynomials sum of roots, product of zeros (given on pg.30) 10 Ch.4 Quadratic Equations factors of quadratic equations (QE) nature of roots of QE Maths: Low priority topics Low priority doesn’t mean UPSC will *NOT* ask them. Low priority means, within your study time table, do them at last depending on how much free time left. First allot time for 1. high priority topics such as history, polity, science, economy, environment (for Paper I) and those reasoning-comprehension & other high priority topics under Maths (for Paper II). 2. then medium priority math topics given above 3. and finally to the following low priority topics. Reason: following topics not frequently asked. They’re not difficult but have many variety of questions and formulas=> each of them take more than 4 hours to master. Therefore, put under low priority in terms of study time allotment. 1. Geometry theory: Triangles, Quadrilaterals, Circles (TQC) 39 2. Trigonometry: only height n distance 3. Permutation Combination Probability 4. Statistics L1: Geometry theory (TQC) Geometry image based Qs (Prelim 1998) LMNOP is a semicircle with centre at R and diameter LP. LSR and RQP are also semi-circles with centres at T and U respectively and diameters LR=RP=1/2 LP. What is the ratio of perimeter of LMNOP and LSRQP? Ans. 1:1 (Prelim 2000) in the given figure, all line segments of the shaded portion are of same length and at right angles to each other. What is the area of the shaded portion? Ans.52 cm 2 (Prelim 2001) in the given figure ABCD is a cyclic quadrilateral. if AB=BECAUSE and angle BAC=70, then what is the measurement of angle ADC? Ans. 140 Without images [1999] If the angle of triangle are in the ratio of 4:3:2, then the triangle a. Is obtuse angled triangle b. Has one angle greater than 80 degree c. Is a right triangle d. Is acute angled triangle (this is the right answer) [2000] Which one of the following has a greater perimeter than the rest? a. A square with the area of 36 sq.cm. b. An equilateral triangle with a side of 9 cm c. A rectangle with 10 cm as length and 40 sq cm as area. (this is the right answer) d. A circle with a radius of 4 cm These questions mostly deal with angle, side related theorems of triangle, circle and quadrilaterals. These type of sums have been asked in earlier prelims, but in less frequency than Area-volume-perimeter. As such the list of topics, will look quite daunting but in reality its not that difficult. Lengthy yes. Difficult no. Class_Ch Page Topic 7_6 131 summary of triangle properties 8_3 43 example 2 44 Q.3 and 4 51 Q7,8 and 9 56 Summary- properties of all quadrilaterals. 8_11 170 table for formulas 40 171 entire exercise 11.1 176- 178 all the sums related to area of trapezium, rhombus etc. 184- 185 Example 4 to 6. 186 entire exercise 11.3 190- 92 All illustration, examples and formulas given in the summary. 9_6 91 pair of angles 98 6.5 transversal 101 example 4 103- 04 all the angle finding questions 104 fig.6.33 fact that such mirror rays will be parallel 107- 08 all the angle finding questions 108 summary 9_7 – All the theorems given in this chapter. You don’t have to mug up the theorem itself but must understand how it they apply in the finding the sides and angles of any triangle. You’ll find their gist in the summary but without looking at figures, it won’t go in the head. 133 Q4 9_5 167 summary at area of triangles and parallelograms 9_8 146 Q1 151 Summary- the angle sum property and diagonals of quadrilaterals. 9_10 187 Summary-especially the properties of a cyclic quadrilateral. 10_10 213 Q.1,2 and3 214 Q12 215 summary 10_6 128 exercise 6.1 q.1 136 example 7 147 ex.11 151 q.10,11,12 153 q.10 154 summary Clocks 1. [1997] The number of times in a day the Hour-hand and the Minute-hand of a clock are at right angles, is __. Ans 48 2. [1998] An accurate clock shows the time as 3.00. After hour hand has 135 degree, the time would be __. Ans 7:30 3. (2000) A clock shows 8AM in the morning. Throughout how many degrees will the hour hand rotate when the clock shows 2 o’clock in the afternoon? Ans.180 4. [2009] How many times are an hour hand and a minute hand of a clock at right angles during their motion from 1.00 p.m. to 10.00 p.m.? Ans.18 5. (2002) When the time in the wall-clock is 3.25 p.m., the acute angle between the hours-hand and the minute- hand is ___? Ans 47.5 degrees. NCERT class7 deals with measuring angles, but that’s kid-stuff. For Clock problem, directly memorize the readymade formulas given in your Quant book, and practice sums from there. And in the exam, bring wrist watch and geometry compass for quick calculation (especially the 47.5 degree!) L2: Trigonometry I could notice only one MCQ so far (1999) A man is standing on a 6 meter pole whose shadow length is 8 meters. IF the length of his shadow is 2.4m, what is the height of this man? Ans. 1.8 metes There are two ways to solve above question 1. Similarity of triangles, then take two ratios of sides. => in that case it’s a Geometry TQC problem 2. TAN ratios (because there will be two angles with same measurement) => in that case it’s a Trigonometry problem. 41 Anyways, no need to consult NCERT or the Quant book for this. Because I made videos and incorporated all good sums from NCERTs within my subsequent articles. Links 1. Youtube lecture playlist Then articles: 2. Introduction, Types of Questions, Shortcut for memorizing 30,45,60 3. HnD Type #1: One Building One Angle finding height, distance or hypotenuse 4. HnD Type #2: Broken Trees and Telegraph Poles: Finding original height 5. HnD Type #3: One Building Two Angles 6. HnD Type #4: Two Buildings-Two Angles 7. HnD Type #5: Finding speed, time or distance Ignore the other articles under my [Trigonometry] section because they’re meant for SSC and CDS, and not asked in UPSC so far. L3: Permutation Combination Probability (1995) A table has three drawers. It is known that one of the drawers contains two silver coins, another contains two gold coins and the third one contains a silver coin and gold. One of the drawers is opened at random and a coin is drawn. What is the probability that the other coin in the drawer is a gold coin? Ans. 0.5 (2004) Nine letters are to be dropped in three different letter boxes. In how many different ways can this be done? Ans 3 9 (2006) In a tournament, each of the participants was to play one match against each of the other participants. Three players fell ill after each team had played three matches and had to leave the tournament. What was the total number of participants at the beginning, if the total number of matches played was 75? Ans. 15 (2006) digits are chosen at random 1,2,3,4,5,6,7,8 and 9 without repeating any digit. What is the probability that their product is odd? Ans. 5/42 (2006) How many numbers are there in all from 6000 to 6999 (Both 6000 and 6999 included) having all digits same ? Ans 496 (2007) If all the numbers from 501 to 700 are written, what is the total number of times does the digit 6 appear? ans. 140 (2007) In how many maximum different ways can 3 identical balls be placed in the 12 squares(each ball to be placed in the exact centre of the squares and only one ball is to be placed in one square) shown in the figure given below such that they do not lie along the same straight line? Ans. 200 (2009) In a carrom board game competition, m boys and n girls (m>n>1) of a school participate in which every student has to play exactly one game with every other student. Out of the total games played, it was found that in 221 games one player was a boy and the other player was a girl. Consider the following statements: 1. The total number of students that participated in the competition is 30. 2. The number of games in which both players were girls is 78. Which of the statements given above is/are correct? a. 1 only b. 2 only c. Both 1 and 2 d. Neither 1 nor 2 ans.C (2010) when ten persons shake hands with one another, in how many ways is it possible? Ans. 45 (2010) In a tournament 14 teams play league/matches. If each team plays against every other team only once then how many matches are played? Ans.91 (2011) there are four routes to travel from city A to city B and six routes from city B to city C. How many routes are possible to travel from the city A to city C? Ans. 24 (2011) Study the following figure.. (you’ll find the figure in CSAT paper attached below)…If, A person goes from A to B always moving to the right or downwards along the lines. How many different routes can he adopt? Ans. 6 How to proceed? 1. learn concepts from above articles, and you’ll able to solve most of the problems without needing any formulas: i. [Aptitude] Permutation Combination made easy without Formulas ii. [Aptitude] PnC: arrange such that two people Always sitting together? iii. [Aptitude] Probability Made Easy (Extension of Permutation Combination Concept!) iv. [Aptitude] PnC: How many Ways to arrange letters of word “RECUPERATE” (Permutation without Formulas) v. [Aptitude] PnC: All possible numbers using 012345, All possible words using ABCDE, Permutation Arrangement Made Easy with and without Formulas 42 2. Then solve NCERT Class11 Ch.7 for permutation – combination problems. (yes syllabus says is “maths upto ClassX” but UPSC has asked PnC questions in CSAT-2011 so perhaps examiner considers this topic part of reasoning and not maths. 3. Probability: up to class10 books cover very basic concepts, don’t have much CSAT quality questions. So go through NCERT class 11 Chapter 16. 4. Beyond that your quant book for additional practice. L4: Statistics (1999) the office distribution of working hours is following Members Work Hours 5 0-19 1 20-24 25 25-29 40 30-34 15 35-39 8 40-45 Consider following inferences drawn from the table 1. average number of working hours is 30 2. % of those who worked 35 or more hours, is less than 25 3. at least five staff members worked more than 44 hours Which of the inferences is/are valid? a. 1 alone b. 2 alone c. 1 and 2 d. 1,2 and 3 Above question tests your understanding of cumulative frequency and averages of grouped data with class intervals. Such pre-CSAT questions can be asked again, because this taught in Class10 NCERT chapter 14. And upto class10 is part of the new CSAT Syllabus. Anyways, topic not difficult all. Can be finished in less than four hours. (Hence cost: Benefit is still better than culture topic in Prelim GS.) First goto following playlist and Watch my video number 1, 3, 7, 8, 14, 17, 18 and 19. http://www.youtube.com/playlist?list=PL4D384E259F9ADECE Avoid videos related to mean deviation, quartile deviation and standard deviation they’re from class11 hence not part of syllabus. (They were part of old-mains syllabus. no longer relevant for new prelims or new mains) Also mugup this formula: 3 Median = Mode + 2 Mean Where to get practice? 1. Class 10 NCERT Chapter 14 a. Exercise 14.1, 14.2, 14.3, 14.4 b. understand the remark given on page 279 2. General studies (mains) paper II before 2013. Because they had these topics in syllabus. Appendix: Download links A1: Last three years official CSAT papers https://files.secureserver.net/0s4I32bAjTl3bm except CSAT-2013, all contain official answerkey from UPSC A2: NCERT Mathematics Topicwise Sorted free download https://files.secureserver.net/0fmaNqqBDslHlc A3: Quant books: What to prepare, what to skip? Beyond NCERT, you’ll need to practice maximum sums from your quantitative aptitude book. However, not all chapters / topics given in such books, are important for CSAT. So, consult following PDF files on what topics to focus and which topics to ignore: 1. Fast track to Arithmetic Rajesh Verma What to prepare what to skip for CSAT 2. Quantam CAT Sarvesh Kumar What to prepare what to skip for CSAT Visit Mrunal.org/aptitude for more articles on aptitude, maths, reasoning. URL to article: http://mrunal.org/2014/06/studyplan-csat-aptitude-paper-2-decision-making-maths-medium-low-priority-topics- sample-questions-free-studymaterial-part-3-3.html Posted By Mrunal On 08/06/2014 @ 11:41 In the category Aptitude Click here to print.