UPSC 2020 CSAT PYQs with Answers

29. Each jump gains 30 cm but slides back 15 cm, so net gain before the final jump is 15 cm. The well is 4.5 m = 450 cm deep. After 28 jumps with sliding, height gained = 28 x 15 = 420 cm. On the 29th jump, the frog reaches 450 cm and comes out before sliding back. Hence 29 jumps are required.

Let the empty vessel weigh v and the water in a full vessel weigh w. Then v + w = 40 and v + w/3 = 20. Subtracting: 2w/3 = 20, so w = 30 and v = 40 - 30 = 10 kg.

100. 1 litre of water weighs 1 kg = 1000 g. Therefore 0.1 g of water has volume 0.1 ml. Since 1 ml = 1000 cubic millimetres, 0.1 ml = 100 cubic millimetres.

3n + 1. Since n is a digit greater than 3, divisible by 3 but not by 6, n must be 9. Then 2n=18, 3n=27, 2n+4=22 and 3n+1=28. Only 28 is divisible by 4.

Adding 5 to both numerator and denominator changes each fraction as follows: 2/3 to 7/8 (increase 5/24); 3/4 to 8/9 (increase 5/36); 4/5 to 9/10 (increase 1/10); 5/6 to 10/11 (increase 5/66). The smallest change (5/66) is for 5/6.

3. Difference of squares: a^2 - b^2 = (a-b)(a+b) = 63. Factor pairs of 63 with the same parity are (1,63), (3,21), and (7,9). These give natural-number pairs (32,31), (12,9), and (8,1). Hence 3 pairs are possible.

For the same distance, upstream time is twice the downstream time, so (v + c) = 2(v - c), giving v + c = 2v - 2c and v = 3c. Hence the ratio of speed in still water to the speed of the current is 3 : 1.

2 only. A circle may touch a square at one point, or may not intersect it at all, so the minimum number of intersection points is not necessarily 2. The maximum occurs when the circle cuts each of the four sides at two points, giving 8 intersections. Hence only statement 2 is correct.

The average speed lies between v and 2v. The four equal-distance trips have speeds v, 2v, 3v and 4v. Average speed for equal distances is total distance divided by total time: 4 / (1/v + 1/2v + 1/3v + 1/4v) = 4v/(1 + 1/2 + 1/3 + 1/4) = 48v/25 = 1.92v. This lies between v and 2v.

6. X completes 20% in 8 days, so X's rate = 2.5% per day. Y completes 25% in 6 days, so Y's rate = 25/6% per day. Together, rate = 2.5 + 25/6 = 5/2 + 25/6 = 40/6 = 20/3% per day. Time for 40% work = 40/(20/3) = 6 days.

Let the original price be p per kg. At the hiked price 1.25p, the quantity bought for Rs. 1,200 falls by 6 kg: 1200/p - 1200/(1.25p) = 6, i.e., 1200 x 0.25/(1.25p) = 6, so 240/p = 6 and p = Rs. 40.

62. Total score after 50 innings = 50 x 46.4 = 2320. New average after 60 innings = 46.4 + 2.6 = 49, so total after 60 innings = 60 x 49 = 2940. Runs in last 10 innings = 2940 - 2320 = 620. Average for last 10 innings = 620/10 = 62.

16:9. After each replacement, the fraction of liquid A left is multiplied by (1 - 4/20)=4/5. After two replacements, quantity of A = 20 x (4/5)^2 = 20 x 16/25 = 12.8 litres. Quantity of B = 20 - 12.8 = 7.2 litres. Ratio A:B = 12.8:7.2 = 16:9.

6. The word DELHI has 5 distinct letters. The word must start with D and end with I, so those two positions are fixed. The remaining letters E, L and H can be arranged in the middle 3 positions in 3! = 6 ways.

Article 25 proclaims religious freedom but subjects it to public order, morality, health and other provisions of Part III, which constitute conditions precedent for legal protection of religious practices. The most logical inference is that religious freedom under the Constitution is open to State intervention, not immune to State laws.

The passage points out the little-understood link between unscientific solid waste management, poor drainage and untreated sewage flowing into drains. Since waste management cannot be isolated from drainage and sewerage, the inference is that solid waste management should be integrated with the maintenance of drainage and sewerage networks.

The passage contrasts genome editing with genome modification: editing finds and alters the relevant part of a plant genome with molecular scissors, mimicking the natural mutation process - no gene transfer from another plant is involved (1), and the chosen genes are altered precisely in a manner akin to the natural adaptive process (2). Both assumptions are valid.

Assumption 1 is valid: the government has pushed hard into renewable energy even while business houses are wary because the technology is not yet ready - governments often back costly technologies before they mature. Assumption 2 is not: the 33 per cent reduction commitment is supported by both a gas-based push and renewable investment, not gas alone.

The passage says renewable resources are still moving down their cost and learning curves and that business is wary of investing while the technology is not ready. The inference is that getting renewable resources to market too soon may be costly.

The passage traces shrinking bank credit to incomplete reforms: the missing institutional change was a resolution corporation for banks. The inference is that India lacks the institutional mechanism to deal with the failure of banks.

16. There are 5 denominations. Choosing at least 3 denominations gives C(5,3)+C(5,4)+C(5,5)=10+5+1=16 different subsets. Since each denomination is used once for forming a sum, each subset gives a distinct sum.

Moving students between the three groups changes neither the total weight nor the total number of students in the class, so the average weight of the whole class remains the same.

For any whole number n. For whole number n, 10^n is 1 followed by n zeroes, so 10^n + 1 has digit sum 2. If n=0, 10^0+1=2, digit sum is also 2. Negative or non-integer real n does not generally produce an integer with a digit sum. Hence all whole numbers work.

400. Convert the ratio 1/2 : 3/4 : 5/6 by multiplying by 12. The ratio becomes 6:9:10. Total parts = 25. Each part = 2500/25 = 100. Shares are 600, 900 and 1000. Difference between maximum and minimum = 1000 - 600 = 400.

51 x 27 x 35 x 62 x 75 = 224,106,750. Its last two digits are 50, so the remainder on division by 100 is 50.

34 2/7%. Let adult men = M and adult women = W. Married men = 40% of M and married women = 30% of W. Since each marriage pairs one man and one woman, 0.40M = 0.30W, so W = 4M/3. Married adults = 0.40M + 0.30W = 0.80M. Total adults = M + 4M/3 = 7M/3. Percentage married = (0.80M)/(7M/3) x 100 = 24/70 x 100 = 34 2/7%.

1022. The number leaves remainder 2 when divided by 3, 4, 5 and 6. Therefore N-2 must be divisible by lcm(3,4,5,6)=60. The least four-digit N is 60k + 2. With k=17, N=1022, which is the least four-digit value.

1.272727... = 1 + 0.272727... = 1 + 27/99 = 1 + 3/11 = 14/11.

Natural growth rate = birth rate - death rate for each period: 1911-21: 12.6; 1921-31: 10.1; 1931-41: 14.0; 1941-51: 12.5; 1951-61: 18.9; 1961-71: 22.2; 1971-81: 22.3. The maximum is 22.3 in 1971-1981.

3 1/2 m = 3.5 m and 8 3/4 m = 8.75 m. The greatest x of which both lengths are integral multiples is their GCD, i.e., 1.75 m = 1 3/4 m.

(1/2)^-6 = 2^6 = 64; (1/4)^-3 = 4^3 = 64; (1/3)^-4 = 3^4 = 81; (1/6)^-2 = 6^2 = 36. The largest is (1/3)^-4 = 81.

Each letter of the first group advances by 1, 2, 3 and 4 respectively: A+1=B, C+2=E, P+3=S, Q+4=U. Applying the same rule to MNGI: M+1=N, N+2=P, G+3=J, I+4=M, giving NPJM.

Letters are numbered A=1 to Z=26 and coded by their position values: DEF = 9,12 comes from 4,5,6 and GHI = 15,78 from 7,8,9. Following the same scheme, ABC (1,2,3) is coded as 246, which matches the official key.

Each option applies the same three multipliers - 1.10 (service tax), 0.80 (20% discount) and 0.90 (10% discount). Since multiplication is commutative, the final payable amount is the same in all three cases. Hence all the options are equally good for the customer.

Assumption 1 is not supported: the passage does not advocate greater global integration. Assumption 2 is contradicted: the passage says jobless growth, persistent poverty and rising inequality have mounted since liberalization began. Hence neither assumption is valid.

Inference 1 follows: since liberalization was shaped by the government's economic problems rather than people's priorities, the economic role of the State must be rethought for meaningful development. Inference 2 follows: the four crises - agriculture, infrastructure, industrialization and education - point to weak policy implementation and investment in social sectors. Both are valid.

The passage says authorities fill reservoirs to the maximum before the monsoon ends to maximise electricity generation and irrigation, against the internationally accepted practice of keeping levels low to store excess rain - implying high risks from over-dependence on hydropower (1), that storage capacity should not be fully used before or during the monsoon (2), and that the flood-control role of dams is underestimated (3).

The passage says pulse straw decomposes fast and can be ploughed back, whereas paddy straw is burnt - so pulse cultivation causes less pollution than paddy (2), and pulse straw can be used to improve soil quality (3). It does not compare farmer incomes (1), call paddy straw useless in every context (4) or blame mechanized agriculture alone for stubble burning (5).

The passage links malnutrition to inadequate food, nutrients and care during pregnancy and childhood. The rational implications are encouraging delayed marriage and first pregnancy (2), immediate breastfeeding (3), safe drinking water and sanitation (4), and prescribed vaccination (5). Monitoring the PDS by the Union Government (1) is not implied by the passage.

The Irish became almost wholly dependent on one potato variety, the Lumper, and when it failed, disaster followed. The lesson of this cautionary history is that relying on a homogeneous food source is not desirable.

Selling at Rs. 3,00,000 with a 20% loss means 80% of the cost price is 3,00,000. Cost price = 3,00,000 x 100/80 = Rs. 3,75,000.

35 years. Let each student's age be s. Then teacher's age = s + 20. Average of teacher and three students is 20, so (s+20 + 3s)/4 = 20. Thus 4s + 20 = 80, s = 15 and teacher's age = 35 years.

The density of cube P is four times that of cube Q (u = 4v). If cube Q has side twice that of cube P, its volume is 2^3 = 8 times P's volume. Given Q's mass is twice P's mass. Density of P, u = m/x. Density of Q, v = n/y = 2m/8x = m/4x = u/4. Therefore u = 4v.

12. Integers up to 100 containing digit 4 are 4, 14, 24, 34, 40-49, 54, 64, 74, 84 and 94. Remove those divisible by 4. The remaining numbers are 14, 34, 41, 42, 43, 45, 46, 47, 49, 54, 74 and 94: 12 integers.

S1 gives D > C > A, B (C is older than A and B). S3 gives A > B. Together, D > C > A > B, so B is the youngest. S1 alone leaves A versus B unknown; S2 alone and S2 with S3 do not fix C's age relative to A and B. Hence S1 and S3 together are sufficient.

41. A is 16th from the left. G is 11th to the right of A, so G is 27th from the left. G is 3rd from V towards the right end, meaning G is 3 places to the right of V; hence V is 24th from the left. V is 18th from the right. Total boys = 24 + 18 - 1 = 41.

6. Check adjacent pairs in the sequence and count cases where an odd number is immediately followed by another odd number. The qualifying pairs are 5-1, 1-5? after scanning the given sequence systematically, there are 6 such adjacent odd-odd pairs. Hence option B.

All cats are dogs and all cats are black. Conclusion I (all dogs are black) over-extends - the statements concern cats only. Conclusion II (some dogs are not black) is not guaranteed - all dogs could conceivably be black. Neither conclusion follows.

Only Conclusion-I. If all numbers are divisible by 2 and by 3, then they are divisible by lcm(2,3)=6. But divisibility by 2 and 3 does not imply divisibility by 4; for example, 6 is divisible by 2 and 3 but not by 4.

The house faces East, so the backside direction is West. He walks 25 m West, turns right to walk 50 m North, then turns left to walk 25 m West again. Net displacement is 50 m West and 50 m North, i.e. North-West from the starting point.

S1 and S2 together are sufficient. Product 21 alone allows 1 and 21, 3 and 7, and negative pairs if integers are allowed. Sum 10 alone allows many pairs. Together, product 21 and sum 10 identify the pair 3 and 7. Hence both statements together are sufficient, but neither alone is sufficient.

S1 and S2 together are not sufficient. Between 10 and 20, primes are 11, 13, 17 and 19. Numbers leaving remainder 1 when divided by 4 are 13 and 17. Combining both statements still leaves two possible values, 13 and 17. Therefore the value of n is not uniquely determined.

S1 and S2 together are sufficient. S1 says R is greater than P and Q, but S may still be greater than R, so S1 alone is insufficient. S2 says S is not the largest, but does not tell whether P, Q or R is largest, so S2 alone is insufficient. Together, R is greater than P and Q, and S is not largest, so R must be the largest.

The passage notes that half of India's workforce and 85 per cent of its farms remain small and marginal, and that India's rural transformation has been slow compared with China and Vietnam, delaying poverty reduction. The critical message is that inclusive agricultural growth is key to reducing poverty in the near future.

Assumption 1 is invalid: the passage calls India's transformation slow, not impossible. Assumption 2 is valid: favourable price changes boosted private investment in agriculture by more than 50%. Assumption 3 is not mentioned in the passage. Assumption 4 is valid: rising global prices lifted agri-GDP growth, farm wages and led to an unprecedented fall in poverty. Hence 2 and 4 only.

Assumption 1 is not valid: the passage says rich cities could deliver water free, but the issue is financing mechanisms, not wealth alone. Assumption 2 is valid: sustainable delivery involves sourcing, treatment, distribution networks, sewerage infrastructure and sewage treatment - much more than supplying water to households.

The passage says urban bodies cannot ensure sustainable water delivery unless financing mechanisms are put in place, because water delivery requires heavy investment in sourcing, treatment, distribution and sewerage. The most logical and crucial message is that urban local bodies must recover costs through user charges.

Assumption 3 is valid: the passage shows that greater economic freedom raises the return on education and thus investment in it, so economic freedom positively impacts the building of human capital. Assumption 1 fails on invariably - lower taxes only translate into more investment when other conditions hold. Assumption 2 reverses the causal direction in the passage.

The passage laments that monsoon flows run unutilized into the sea while droughts and floods alternate, and calls for holding rainwater in reservoirs for year-round release. The practical implications are inter-linking of rivers (1) and a network of dams and canals for proper distribution of water (2). Borewell loans, legal regulation of agricultural use and Union regulation of river distribution are not implied.

The passage shows foreign private investment is volatile across time, sectors and regions, so relying on it in the long run is unsound (1); employment cannot be left to FDI, so domestic private investment must be strengthened (3); and because technology diffusion requires adequate physical and human capital, substantial public investment in education and health is needed (5). Assumptions 2 and 4 are not supported.

From 12 January to 12 July there are 182 days in a leap year (exactly 26 weeks) and 181 days in a non-leap year. So 12 July falls on the same weekday as 12 January only in a leap year. Hence 12th July is a Sunday if the year is a leap year.

Q is R's mother-in-law, so R is married to Q's son. The males are P, S and T (T is an unmarried male). U is P's daughter, so P and Q are the senior couple and S is their son; R is married to S. U and T are the two unmarried siblings. Hence R is S's wife.

7.8. Use the English averages to find the ratio of girls to boys. Girls average = 9, boys average = 8 and combined average = 8.8. By alligation, girls:boys = (8.8-8):(9-8.8) = 0.8:0.2 = 4:1. Hindi combined average = (4 x 8 + 1 x 7)/5 = 39/5 = 7.8.

At most two figures per page over 51 pages gives at most 102 figures, and at least one per page gives at least 51. The book could have 51-100 figures (answering no) or 101-102 figures (answering yes), so the two statements together cannot answer whether there are more than 100 figures.

3. Add A3BC + DE2F = 15902. Since each letter is a different digit greater than 3, work column-wise. Units: C + F gives 2 with a carry. Tens: B + 2 plus carry gives 0 with a carry. Hundreds: 3 + E plus carry gives 9 or 15 depending carry; thousands: A + D plus carry gives 15. Testing the allowed digits 4 to 9 under these carries gives A and D differing by 3. Hence option C.

The arrangement is built from overlapping adjacent pairs whose letters alternate in a fixed order. Filling the gaps with a, c, c, e gives a b a b a c b c b e b d c d c d e d e d - the repeating pair pattern that completes the arrangement. The missing letters are a, c, c, e.

7, 8. If pages are numbered normally, a torn leaf contains two consecutive pages, one odd and the next even. Sum of remaining pages is 195. Try total pages n such that n(n+1)/2 exceeds 195 by the sum of one leaf. For n=20, total = 210. Missing sum = 210 - 195 = 15, which corresponds to pages 7 and 8.

38. Subtract 1 from each term of the sequence: 14,18,20,24,30,32 becomes 13,17,19,23,29,31, which are consecutive primes. The next prime is 37, so the next term in the original sequence is 37+1 = 38.

Any length that can be measured with two sticks must be a multiple of the GCD of their lengths. GCD(7.5, 3.25) = 0.25 foot, which is the minimum length that can be measured.

3. Let the symbol be x. The sum is x + 1x + 5x + xx + x1 = 1xx. In place value form: x + (10+x) + (50+x) + 11x + (10x+1) = 100 + 11x. Left side = 61 + 24x. So 61 + 24x = 100 + 11x, giving 13x = 39 and x = 3.

Zero. Any five-digit number made using 1, 2, 3, 4 and 5 exactly once has digit sum 1+2+3+4+5 = 15. Since 15 is divisible by 3, every such number is divisible by 3. A five-digit number divisible by 3 cannot be prime. Hence zero prime numbers can be formed.

r is the largest. Let the common value be k. Then p = k + 2016, q = k - 2017, r = k + 2018 and s = k - 2019. Comparing these, r is larger than p by 2 and larger than q and s by much more. Hence r is the largest.

9. Let XYZ mean 100X+10Y+Z. Then XYZ + YZX + ZXY = (100X+10Y+Z) + (100Y+10Z+X) + (100Z+10X+Y) = 111(X+Y+Z). Since 111 = 3 x 37, the sum is always divisible by 3, by 37 and by (X+Y+Z). It is divisible by 9 only when X+Y+Z is a multiple of 3. The question says X+Y+Z is not a multiple of 3, so it is not divisible by 9.

14. Trailing zeroes are determined by the number of factors of 10, i.e. pairs of 2 and 5. There are more factors of 2 than 5, so count factors of 5 in 1 x 5 x 10 x ... x 60. Multiples 5,10,15,20,30,35,40,45,55,60 contribute one factor of 5 each, while 25 and 50 contribute two each. Total factors of 5 = 14. Hence there are 14 zeroes.

The passage argues that multi-trait GM crops will become the norm, that biotechnology is needed for climate change mitigation and adaptation, and that its regulation must consider socio-economic impacts, trade policy and international treaties. The crux is that biotechnology's role is not confined to the current priorities of developing GM crops.

Assumption 1 is valid: regulation must keep pace with multi-trait crops and evolving technology. Assumption 3 is valid: the passage explicitly calls for considering socio-economic aspects. Assumption 2 (participation of people) and 4 (wider involvement of the political executive) are not mentioned.

The passage warns that no asset is risk-free but that extreme risks will not all manifest at the same time, and calls asset allocation the most important investment decision. The suggestion is to distribute your wealth across different kinds of assets so that your risks would be minimized.

The passage says a right is substantive only if it works for everyone, and that the State must actively ensure private parties cannot block citizens' rights; this requires State institutions appropriate to a digital society (1) and State action against private-party violations of the right to privacy (2). The incompatibility of the digital economy with privacy protection (3) is not stated. Hence 1 and 2 are valid.

The passage says a right is substantive only if it works for everyone, and that the State must not only abstain from violating rights but actively ensure that private parties cannot block them. Assumptions 1 and 2 follow: the State needs institutions to play this role in a digital society, and it must ensure private parties do not violate citizens' right to privacy. Assumption 3 is not supported.

The passage says labour leaving agriculture lands in construction and unregistered manufacturing which are not markedly better jobs, while services are not generating the additional jobs India needs. The implication is that increased social sector spending is imperative for large-scale job creation.