- Math haters are grave diggers
- Mathematics: What to ignore?
- CSAT Math doesn’t not fall from sky but NCERTs
- High priority topics
- H1: Linear Equations
- H2: Number system
- H3: Percentages, Profit Loss, SI- CI
- H4: Ratio Proportion Variation Partnership (RPVP)
- H5: Speed Time Distance Work (STDW)
- H6: Averages, Allegations
- H7: Data Interpretation (DI)
- H8: Geometry: Area volume perimeter (AVP)
- Appendix: Download links
So far in the CSAT paper-2 study plan
- Comprehension and Reasoning
- Mathematics & Data Interpretation: high priority topics You’re here
- Decision Making + Mathematics: Medium & low priority topics
Many of you have this mindset / strategy:
- 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.
- 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!
- xyz person on xyz forum said he managed to crack CSAT without preparing maths. Same Cinderella story will repeat in my case.
- 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:
|% 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 = = ~1/5th of paper.|
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.
26th 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.
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).
In April 2014, UPSC wrote a letter to DoPT, requesting more officers to be deployed for exam duty because:
- more than 10 lakh people expected to apply for CSAT-2014
- 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.
- 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.
|STDW||Speed Time Distance Work||2||1||4|
|Data Interpretation (DI)||Pie chart||2||0||5|
|oddballs||Permutation combination (how many figures possible etc.)||3||0||0|
|Subtotal: Odd balls||5||0||1|
|% 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
- UPSC hasn’t completely revamped its question bank.
- 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.
|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|
|Clock Angles||indirectly||YES||Asked in 98, 2002, 2000 etc.|
|Divisibility||YES||YES||Asked in 2010.|
|Probability||YES||Yes||Routinely asked this topic up to mid-2000s.|
|Permutation &Combination (Pnc)||NO||YES|
|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:
- Linear Equation
- Number System
- %, profit loss, SI-CI
- Ratio Proportion Variation
- Speed Time Distance Work
- Averages, Alligiations
- Data Interpretation
- Geometry: Area Volume Perimeter
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.
- Arithmetic Progression => only have to do one chapter in NCERT.
- Coordinate Geometry => only have to do one chapter in NCERT.
- Polynomials factorization => only have to do two chapters in NCERT.
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.
- Geometry theory: Triangles, Quadrilaterals, Circles (TQC)
- Trigonometry: only height n distance
- Permutation Combination Probability
Anyways, let’s begin preparation:
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.
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:
- 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.
- They’re Useless for CSAT and higher level exams. Because they don’t cover all variety of tricky MCQs asked in such exams.
- Even banking & insurance exams – Rajesh Verma’s techniques are faster & easy to understand.
- 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.
If you already know such tricks then good, but now is not the right time to learn them fresh.
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:
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’.
|x2+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 x1 but for our understanding purpose, take it as just “x”). This is high priority topic for CSAT.|
Linear equations are very important for aptitude exams, from two angles
- direct MCQs about age, coins, salary, expenditure related problems
- 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
(this is the most common mistake)
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
|A and B|
20 years ago, so make a column on left side:
|Age 20 years ago:||present age|
|A and B|
Then make second equation: 20 years ago, Bhootnath was 12 times the age of Abdul
|age 20 years ago (-20)||present age|
|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. ”
|avoid this approach||use this approach|
L3: Cannot be determined
Suppose you end up with two equations like this:
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|
|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.|
|Class||Ch.||What to focus for CSAT?|
|10||3||Everyone should do this, irrespective of how strong / weak in maths.|
|Rajesh Verma||Sarvesh Kumar|
|First solve chapter 27 then chapter 7.Chapter 27 linear equation|
Chapter 7: Word problems based on numbers
|Ch13. Elements of Algebra|
Sample Questions from previous prelims
- (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.
- (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.
- (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
- (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|
|NCERT||Chapter||Topic to focus for CSAT|
|7||2.Fractions and Decimals|
|9. rational numbers|
|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|
|NCERT||Chapter||Topic to focus for CSAT|
|7||13.Exponents & powers|
|8||6. squares and square roots|
|7. Cube and Cube roots|
Related articles under my [Aptitude] series:
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.
Sample Qs. from previous prelims
- (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.
- (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.
- (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”,
- (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%
- (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%
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:
- Concepts of Marked Price and Successive Discounts (Profit-Loss) without (stupid) formulas
- Compound Interest Rate, Population Growth without Formulas
- Alligation: Advanced applications in Interest rates, Profit-loss, Average Wages (Wine-Water Concept)
- 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.
Sample Qs. from previous prelims
- (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)
- (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
- (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
- (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
- (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.
- (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.
- (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.
- (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.|
Then solve your Quant book. Refer appendix for what to prepare, what to skip.
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
- (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
- (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
- (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
- (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
- (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
- (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
- (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
- (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
- (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
|cars, trains, platforms, boats etc.|
|“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:
Once you’ve understood this STD table concept, then apply it while solving the illustrations and exercises given in your quant book.
- (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
- (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
- (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.
if you really want to learn the basics, consult following NCERT chapter (although quite unnecessary because everyone knows this much basic.)
|8||5, 15 (These are useful for data interpretation though)|
[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?
- During heating, liquid P remained hotter than liquid Q throughout
- At no point of time during heating did the two liquids have the same temperature
- P attained the temperature of 100 degree C faster than Q
- Q attained the temperature of 100 degree C faster than P
[Prelim 1996] Following graph represents a race among four persons.
Consider following statements
- A stood first in the race
- C led all the way
- D ran faster than others in the later part of the race.
- 1 and 3 false, while 2 correct
- 1 and 2 false, while 3 correct
- 1 and 3 correct while 2 false
- 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.
[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?
- 1,2 and 4
- 3 and 4
- 2 and 3
- 1,3 and 4
[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?
- R started slowly in the beginning but got ahead of Q to complete learning the lesson
- Q started slowly and finished learning the lesson earlier than R
- R was always faster than Q in learning Mathematics
- Q was always faster than R in learning Mathematics
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 digging through all previous papers of CDS, CAPF and SCRA = too time consuming exercise. Anyways, you will find a few such question under
- aptitude manuals
- 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.
- 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.|
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?
- SSC sets far easier than CSAT. so avoid
- CAT sets will be an overkill. so avoid
- 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
- go through monthly issues of Pratiyogita Darpan or banking service chronicle
- CST (Civil service times) magazine gives demo CSAT papers with DI
- 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.
Sample questions from previous prelims:
-  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
-  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
-  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%
- [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:
- logical Venn diagrams (we saw in previous article)
- mathematical Venn diagrams (that we’ll see here)
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.)
Sample questions from previous prelims 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|
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 :
- Reduce expenditure on defence
- Spend more and more on interest payments
- Reduce expenditure on subsidies
- Spend more and more as grants-in-aid to State government/Union Territories
- (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
- (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|
- 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
- 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.
- 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.
Sample questions from previous prelims
- 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
- 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
- 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)m3
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|
|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
|203||Q.3 to 6; Example 4|
|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|
|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.
except CSAT-2013, all contain official answerkey from UPSC
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:
- Fast track to Arithmetic Rajesh Verma What to prepare what to skip for CSAT
- Quantam CAT Sarvesh Kumar What to prepare what to skip for CSAT
Visit Mrunal.org/aptitude for more articles on aptitude, maths, reasoning.