UPSC 2021 CSAT PYQs with Answers

15. If 7/8 of the job takes 21 days, the full original job would take 21 x 8/7 = 24 days. The total work is increased by 50%, so total required work = 3/2 of the original job. Work already done = 7/8. Remaining work = 3/2 - 7/8 = 12/8 - 7/8 = 5/8. Time for 5/8 job = 24 x 5/8 = 15 days.

15873. We need the smallest number N such that 7N is made only of digit 1. Test repunits: 1, 11, 111, 1111 and 11111 are not divisible by 7 in a way that gives the options. 111111 is divisible by 7, and 111111/7 = 15873. Hence the smallest such number is 15873.

Decrease by 20% multiplies the price by 0.8; the subsequent increase by 25% multiplies it by 1.25. Net multiplier = 0.8 x 1.25 = 1, so the net change in the price is 0%.

2 only. Let Y's present age be y. At Y's birth, X was 42 - y, and the question says this equalled twice Y's present age, so 42 - y = 2y and y = 14. Eight years ago, X = 34 and Y = 6, not a five-times relation. After 14 years, X = 56 and Y = 28, so X will be twice Y. Only statement 2 is correct.

Let the digits be x and y. The difference between the number and its reverse is (10x + y) − (10y + x) = 9(x − y) = 54, giving x − y = 6. Thus the difference between the two digits can definitely be determined — statement 2 is correct. Statement 1 is not correct: the difference alone does not fix the sum (possible pairs (6,0), (7,1), (8,2), (9,3) give sums 6, 8, 10 and 12), and the claim that the sum can be determined only if the product is known is unsupported. Hence only statement 2 is correct.

Joseph comes every 5th day, Harsh every 24th day and Sumit every 9th day. They meet together every LCM(5, 24, 9) = 360 days. Since 360 = 3 (mod 7), a Sunday plus 3 days is Wednesday. Hence they meet again on Wednesday.

108. Proteins are 16% and water is 70%, so other dry elements are 100 - 16 - 70 = 14%. Proteins plus other dry elements = 16 + 14 = 30%. Central angle for 30% of a circle = 30/100 x 360 = 108 degrees.

The passage says even the most truthful people tell semantic lies - their use of words contains some measure of falsehood, more or less deliberate. So the habit found more often in good people is the intentional mixing up of truth with the false (semantic lies), not outright falsification of facts or complete concealment of truth.

The first part of the passage records general agreement that deliberate lying is wrong, except in special situations where telling the truth would do more harm. What is really in question in that exception is the harm caused by telling the truth - so the idea is disagreement about the harm in telling the truth.

The passage says medieval merchants braved the Silk Road and Portuguese caravels sailed beyond the known world searching less for knowledge than for gold and spices - the driver for opening frontiers has always been the search for resources, with science and curiosity weaker drivers. The message is that human beings are motivated to explore new frontiers principally by economic considerations.

1 only. Shares are proportional to p, q and r. If p > q+r, then p is certainly greater than q and greater than r, so A gets the maximum share. But r < p+q does not imply r is smaller than both p and q; for example p=2, q=3, r=4 satisfies r<p+q but r is not minimum. Hence only statement 1 is correct.

4. Choose 3 persons from positions 1 to 6 with no two consecutive. The possible position sets are (1,3,5), (1,3,6), (1,4,6), and (2,4,6). Hence there are 4 combinations.

1000000. A cube of side 1 m has volume 1 cubic metre. 1 cubic metre = 1000 litres, and 1 litre = 1000 millilitres. Therefore water contained = 1000 x 1000 = 1,000,000 millilitres.

Both 1 and 2. Sum of 5 consecutive integers centred at n is 5n, so it can be 100 when n=20. For statement 2, 1 x 2 x 3 = 6 and 1+2+3=6, so the product of three consecutive natural numbers can equal their sum. Both statements are correct.

6. To be greater than 30000, the first digit must be 3. Fix one 3 in the first place. The remaining digits are 2, 2, 3, 3. Number of distinct arrangements = 4!/(2!2!) = 6.

The series is formed by repeating the pair ab followed by the closing block aab. Filling the six blanks with a, b, a, b, a, b completes the periodic arrangement ab ab ab ab ab ab aab, while the other options break the pattern. Hence the missing letters are ababab.

6. On a chessboard, consider the two main diagonals, each having 8 squares. Along one 8-square diagonal, a block of 6 consecutive squares can start at square 1, 2 or 3, giving 3 choices. There are two main diagonals, so total choices = 3 x 2 = 6.

2. If the points are ordered P-Q-R, then PR = PQ + QR and PQ:PR = 3:(3+5)=3:8. If the order is Q-P-R, then QR = QP + PR and PQ:QR = 3:5 gives PR = 2 parts, so PQ:PR = 3:2. These are two possible values. Other placements do not give a new positive ratio.

The passage argues that schools teach academic subjects but not caste divide, famine, gender sensitivity, atheism as a choice, or how to ask questions. The inference is that to be a better citizen, the present world order demands societal and life-coping skills in addition to academic content.

Assumption 3 is valid: the passage says markets reward initiative and skill but some people are too poor or handicapped to develop skills, implying government programmes are needed for those left behind. Assumptions 1 and 2 are not supported - the passage does not say democracies rely on markets to be welfare states, nor that markets ensure sufficient growth.

Writing the multiplication in place-value form: (10P + Q) × 3 = 100R + 11Q, which simplifies to 30P + 3Q = 100R + 11Q, i.e. 15P = 50R + 4Q. Testing R = 1, 2, 3 in turn, only R = 2 works: 15P = 100 + 4Q, and with Q = 5 we get P = 8, so that 85 × 3 = 255 = RQQ. Thus P = 8, Q = 5, R = 2, and (P + R) ÷ Q = 10 ÷ 5 = 2.

202. Write the sum in terms of digit P: 3P + 4P + PP + PP = (30+P)+(40+P)+(11P)+(11P) = 70 + 24P. The result must be a three-digit number ending in 2. Testing digits gives P=3, sum=142, and P=8, sum=262. The arithmetic mean of possible sums = (142+262)/2 = 202.

9. Let incorrect responses be w. Correct responses = 90 - w. Score = 5(90-w) - 2w = 450 - 7w. Given score = 387, so 450 - 7w = 387. Thus 7w = 63 and w = 9.

Between 7:05 hours and 7:10 hours. At 7:00, the hour hand is at 210 degrees and the minute hand is at 0 degrees, so the angle is 150 degrees. To make 180 degrees, the minute hand must gain 30 degrees relative to the hour hand. Relative speed = 6 - 0.5 = 5.5 degrees per minute. Time = 30/5.5 = 5.45 minutes, i.e. between 7:05 and 7:10.

MATHEMATICS is coded as LBSIDNZUHDR by alternately subtracting 1 and adding 1: M-1=L, A+1=B, T-1=S, H+1=I, E-1=D, M+1=N, A-1=Z, T+1=U, I-1=H, C+1=D, S-1=R. Applying the same alternation to CHEMISTRY gives B-I-D-N-H-T-S-S-X, i.e., BIDNHTSSX.

From the second condition, if Z gives Rs. 40 to X, all three have equal amounts: X + 40 = Y = Z - 40. From the first condition, if Y gives Rs. 40 to X, Y has half of Z: Y - 40 = Z/2. Combining, Y = X + 40 and Z = X + 80; then X = (X + 80)/2 gives X = 80, so Y = 120 and Z = 160. Total = 80 + 120 + 160 = Rs. 360.

Let P's marks be p. Q scored 10% less than P, so p - q = 0.10p = 40, giving p = 400. Hence Q scored 400 - 40 = 360.

Equal spending means 3 pens + 5 pencils = 2 pens + 7 pencils, so 1 pen = 2 pencils. Hence the price of a pen is two times the price of a pencil.

The passage says cities are vulnerable to climate change because of dense populations and poor infrastructure, with no systems to address climate impacts despite contributing 65 per cent of GDP. The message is that to maintain and develop our cities we need to adopt sustainability-related interventions.

The passage describes how top universities put lectures online free for the world and encourage other institutions to integrate them into their pedagogy. The central idea is that the availability of higher education can be made easier and cheaper without diluting the content.

607. The pattern is multiply by 3 and add 1: 2 x 3 + 1 = 7, 7 x 3 + 1 = 22, 22 x 3 + 1 = 67, 67 x 3 + 1 = 202. Therefore X = 202 x 3 + 1 = 607; and 607 x 3 + 1 = 1822 confirms the next term.

Some greens are blues and some blues are blacks, but no link is established between greens and blacks. None of the four conclusions - some greens are blacks, no green is black, all greens are blacks, all blacks are greens - necessarily follows.

1 January 2027 is a Friday (2026 has 365 days and begins on a Thursday). 10 October 2027 is day 283 of the year, i.e., 282 days after 1 January; 282 = 2 (mod 7), so 10 October 2027 is a Sunday.

Statement-2 alone is sufficient to answer the Question. Statement 2 says the third Saturday was the 17th. Therefore the 14th was Wednesday, so Statement 2 alone answers the question. Statement 1 says only that the last day of the month was Wednesday; without knowing the number of days in the month, it does not uniquely fix the 14th. Hence Statement 2 alone is sufficient.

Some villagers under 25 years of age are literate. Four-fifth of villagers are under 25 and one-third are literate. Since 4/5 + 1/3 = 17/15, the two groups must overlap by at least 2/15 of the village. So some villagers under 25 years of age are definitely literate. The other options make claims not forced by the fractions.

B. Compare total runs per ball over both innings. A: 75 runs in 175 balls. B: 55 runs in 97 balls. C: 35 runs in 125 balls. D: 25 runs in 105 balls. B has the highest scoring rate, so B is the fastest run scorer.

The passage says no one wing of macroeconomic policy - monetary or fiscal - can work independently without the active support of the other, in the pursuit of economic welfare. The corollary is that the central bank cannot work independently of the Government.

The passage says bad-debt resolution and recapitalisation are only part of the solution, and that without systemic reforms addressing unsustainable lending, future credit cycles will continue to stress the banking system. The practical suggestion is that the Indian banking system requires structural reforms as a long-term solution for the bad-loans problem.

The passage shows new technologies blurring borders - a driverless car, a driver in California and a programmer in Hyderabad bound by different jurisdictions - implying modern technologies blur economic borders (2), innovation and capital impinge on the domain of the State (3), and geopolitics will have to reconcile to many ambiguities and uncertainties (5). Too much globalization and supply-chain policies are not implied.

The passage argues that in a natural state every man consults only his own advantage and determines good or bad by his own fancy, so sin and right or wrong cannot be conceived in a natural state. The inference is that the conceptions of what is right or wrong exist due to the formation of a state.

Rewrite the alphabet in blocks of four reversed: DCBA HGFE LKJI PONM TSRQ XWVU ZY. The 13th letter is P. The fourth letter to the right of P is T.

There are 40 students. Statement 1: Priya is 31st from the bottom, i.e., 10th from the top; she is 4 ranks below Seema, so Seema is 6th from the top. Statement 2: Ena is 37th from the bottom, i.e., 4th from the top; she is 2 ranks above Seema, so Seema is again 6th from the top. Hence either statement alone is sufficient.

1 only. Class B scores range from 22 to 30. The four students shifted from Class A have scores between 17 and 21, so adding them to Class B must reduce Class B's average. But removing four students from Class A need not definitely increase Class A's average; it depends whether the removed students were above or below Class A's previous average. Hence only statement 1 is correct.

Both 1 and 2. The only non-zero digits that are multiples of 3 are 3, 6 and 9. The six 3-digit numbers without repetition are 369, 396, 639, 693, 936 and 963. Their sum is 3996. Since 3996 is divisible by 74 and by 9, both statements are correct.

30 or more. Total persons = 120, Indians = 80, so foreigners = 40. English speakers = 70. To minimise Indians who speak English, maximise foreign English speakers; at most all 40 foreigners can speak English. Therefore minimum Indian English speakers = 70 - 40 = 30. The number can be 30 or more.

The passage shows aristocratic, oligarchic and democratic governments each ruining themselves by pushing their own basic principle to excess. Hence the message is that any form of government tends to deteriorate by excess of its basic principle.

Assumption 1 is valid: equality as a default principle lets persons participate in society's transactions from a position of confidence. Assumption 4 is valid: the passage treats equality as a basic democratic norm that belongs in our day-to-day political vocabulary. Assumption 2 overstates - the passage does not say inequality is detrimental to the survival of democracy - and assumption 3 contradicts the passage's framing.

The passage says seditions, wars and contempt of law are due not to the wickedness of subjects but to the bad state of a dominion, because men are not born fit for citizenship but must be made so. The inference is that the best dominion is the one which pursues the aim of unity and has laws for good citizenship.

The passage argues that if each person judges only his own religion, no religion is wrong, but if everyone judges others' religions, none is right - the whole world is either right or wrong in the matter of religion. The most logical assumption behind this is that religious denominations tend to ignore the unity of man.

3. Let each paper have maximum marks M. The student's marks are in the ratio 5:6:7:8:9:10, whose sum is 45 parts. Overall score is 60%, so total marks = 6 x 0.60M = 3.6M. Therefore 45 parts = 3.6M and one part = 0.08M. Paper scores are 40%, 48%, 56%, 64%, 72% and 80% of M. Three papers are below 60%.

X's constant speed is 1.5 km/h and Y's hourly speeds are 1, 1.25, 1.5, 1.75 and 2 km/h. In 5 hours X covers 7.5 km and Y covers 7.5 km, so they meet in 5 hours exactly midway. Statements 1 and 2 are correct.

The pattern multiplies by 0.5, 1.5, 2.5, 3.5, 4.5 successively: 8 x 0.5 = 4, 4 x 1.5 = 6, 6 x 2.5 = 15, 15 x 3.5 = 52.5, 52.5 x 4.5 = 236.25. Applying the same to Sequence-II: A = 5 x 0.5 = 2.5, B = 2.5 x 1.5 = 3.75, and C = 3.75 x 2.5 = 9.375.

In each row the third entry equals the second number minus the first: 10 - 7 = 3, 9 - 3 = 6, and 13 - 10 = 3. The letters in each row follow the cycle B, A, C, so the third row ends with B. Hence the missing entry is 3B.

The odd terms 3, 7, 13, 21, 31, 43 have differences 4, 6, 8, 10, 12, each increasing by 2. The even terms 2, 4, 10, 18, 28, 40 have differences 2, 6, 8, 10, 12 - to follow the same pattern the first difference must be 4, so the first even term 2 should be replaced by 0. Hence the correct term is 0.

Blue-covered books are Q, R and T. Old books are all except S and U. Gazetteers are all except P, R and S. Combining these, the old Gazetteers with blue covers are Q and T (R is a law report).

Assumption 1 is not valid: the passage does not say rising GDP is essential for a country to be developed. Assumption 2 is not valid: it says GDP growth enables setting aside funds, but nowhere guarantees a reasonable distribution of income to all households. Hence neither is valid.

Assumption 1 is not valid: the passage blames high fuel prices, not oil-producing countries as such. Assumption 2 is not valid: it says mass consumption in emerging economies could create a global food crisis, not that any future crisis will be located in the emerging economies. Hence neither is valid.

The passage shows that using antibiotics as growth promoters creates drug-resistant superbugs that can pass to humans, and that countries like Denmark have banned such use. The rational implication is that antibiotics should only be used to treat diseases, not as growth promoters.

The passage lists a wide web of energy problems - sputtering fossil-fuel access, limited electricity and cooking fuel for the poor, rising imports, pricing and governance challenges, and climate policy. The inference is that India's energy decision-making process is ever more complex and interconnected.

An angle less than 45 North of East. Net north-south displacement = 12 km north - 6 km south = 6 km north. Eastward displacement = 8 km. The direction is therefore north of east. Since tan(theta)=6/8=0.75, theta is less than 45 degrees. Hence the position is less than 45 degrees north of east.

9. Count numbers from 700 to 999 whose digit sum is 10; 1000 has digit sum 1 and is excluded. The valid numbers are 703, 712, 721, 730, 802, 811, 820, 901 and 910. Therefore there are 9 such integers.

25 km. Track displacement using coordinates. Start at (0,0). Drive 10 km south: (0,-10). Turn left from south, i.e. east, and drive 20 km: (20,-10). Turn left, north 40 km: (20,30). Turn right from north, east 5 km: (25,30). Turn right from east, south 30 km: (25,0). Shortest distance from home = 25 km.

Capitals with vertical mirror symmetry are A, H, I, M, O, T, U, V, W, X, Y; among the 21 consonants these are H, M, T, V, W, X, Y (7). Hence consonants whose mirror images do not look like their originals = 21 - 7 = 14.

5. Initial height = 1.5 m = 150 cm. Bounce heights are 4/5 of the previous height: after 1st hit 120 cm, after 2nd hit 96 cm, after 3rd hit 76.8 cm, after 4th hit 61.44 cm, after 5th hit 49.152 cm. Since after the 5th hit the bounce height becomes less than 50 cm, the ball does not bounce further. It hits the ground 5 times before stopping.

Conclusion I follows: some almirahs are chairs and all chairs are tables, so some almirahs are tables. Conclusion II follows: the statement says only some cats are almirahs, so some cats may not be chairs. Both conclusions follow.

Assumption 4 is valid: personal cleanliness alone cannot control infections when the environment is unhygienic - scientific, micro-level interventions are insufficient (4). Assumption 5 is valid: real effectiveness comes from community hygiene implemented through public health measures. Assumptions 1, 2 and 3 are not supported by the passage.

The passage shows computers now control cars, aeroplanes, prosthetics and insulin pumps, so their failure can threaten human life and safety. The logical inference is simply that computers are not completely safe.

The passage says agroecosystems should mimic natural ecosystems - recycling nutrients, using natural processes for pest control and building soil fertility through intercropping. Compatible practices are cover crops (1), mixed farming (4) and polyculture (5). Fertigation, hydroponics and vertical farming are industrial, external-input methods not implied by the passage.

The passage says fig trees support a high density and diversity of frugivores when other resources are scarce (1 - keystone role), that sacred fig trees in disturbed landscapes promote abundance and thus aid biodiversity conservation (3), and that seedlings of other tree species grow around fig trees thanks to frugivores (4 - seed dispersal). Assumption 2 is not stated.

Some radios are mobiles and all mobiles are computers, so some radios are computers, but no link is forced between radios and watches or mobiles and watches. Neither conclusion necessarily follows.

20%. Take total students as 100. Indians = 60 and foreigners = 40. Girls overall = 50. Indian girls = 30% of 60 = 18. Therefore foreign girls = 50 - 18 = 32. Foreign boys = 40 - 32 = 8. As a percentage of foreign students, foreign boys = 8/40 x 100 = 20%.

Doubling every 12 years means the population after n years is 50 multiplied by 2 raised to the number of doublings n/12. Hence the correct equation is P = 50(2)^(n/12).

Petrol rises 0.1 rupee per day for 100 days to reach 80 + 10 = Rs. 90 and stays constant thereafter. Diesel rises 0.15 rupee per day: 69 + 0.15n = 90 gives n = 140. The 140th day of 2021 (31 + 28 + 31 + 30 + 20) is 20th May.

6. Test divisibility by 7 for the possible digit P. The number is 3798125P369. Substituting P=6 gives 37981256369, which is exactly divisible by 7. The other options do not satisfy divisibility by 7. Hence P = 6.

7. The intended expression is 3^2019. Powers of 3 modulo 10 repeat in a cycle: 3, 9, 7, 1. Since 2019 leaves remainder 3 when divided by 4, 3^2019 has the same units digit as the third term of the cycle, which is 7. Therefore the remainder on division by 10 is 7.

The passage says BPA toxicity was detected during the differentiation of embryonic stem cells, which implies BPA may alter embryonic development in vivo (1) and that embryonic stem cells can serve as a model to evaluate the physiological effects of environmental pollutants (3). The passage describes assays as tools for detection, not for finding treatments (2). Hence 1 and 3 only.

Assumption 3 is valid: the passage says effective pollination requires refuges of pristine natural vegetation, so pollinators become scarce in cultivated areas devoid of natural vegetation. Assumption 4 is valid: pollination rests on intricate plant-animal relationships, so diversity in insects induces diversity of plants. Assumption 1 overstates - cereal grains are largely wind-pollinated, and the passage does not make this claim for India - and assumption 2 is not stated.

Assumption 3 is valid: the passage says effective pollination requires refuges of pristine natural vegetation, so pollinators become scarce in cultivated areas devoid of natural vegetation. Assumption 4 is valid: pollination rests on intricate plant-animal relationships, so diversity in insects induces diversity of plants. Assumption 1 overstates - cereal grains are largely wind-pollinated, and the passage does not make this claim for India - and assumption 2 is not stated.

The experiment showed that low-intensity amber street lighting inhibited flowering in a wild plant - a concrete, lasting ecological change caused by artificial light. The inference is that light pollution can have a permanent adverse impact on an ecosystem.