UPSC 2023 CSAT PYQs with Answers

Write the letters of INCOMPREHENSIBILITIES in descending alphabetical order: T S S R P O N N M L I I I I I H E E E C B. Comparing with the original word position by position, the letters at positions 13 and 15 (both I) remain unchanged. Hence two positions remain unchanged.

1 only. A 7 cm x 5 cm x 3 cm cuboid cut into 1 cm cubes has unpainted interior cubes equal to (7-2)(5-2)(3-2) = 5 x 3 x 1 = 15, so statement 1 is correct. Blue is painted on the pair of 7 x 3 faces and green on the pair of 5 x 3 faces. Cubes with exactly one blue face and one green face lie on the edges common to blue and green faces, excluding corners. There are 4 such edges, each of length 3, giving 3-2 = 1 such cube per edge, so only 4 cubes, not 6. Statement 2 is incorrect.

From II, if T is true then R and S cannot both be true. From I, if P is true then S is true; combined with T true, this forces R to be false. So when T is true, at least one of P and R must be false - conclusion 1 follows. Conclusion 2 does not: Q being true does not imply P is true. Hence only 1 follows.

The false statement says at least one of R and S was selected, so neither R nor S was selected. Then the conclusion that S was selected is wrong, and nothing in the statements fixes how many of P, Q and T were selected, so at least four being selected cannot be concluded. Neither conclusion follows.

6. Since E=0 and F=8, the product DEF is D08. We need AB x CD = D08 and D08 + GHI = 975, with A to I distinct digits. Testing the multiplication constraints gives the valid arrangement AB = 12 and CD = 34, so DEF = 408 and GHI = 567. The digits are distinct and satisfy all conditions. Therefore A+B+C = 1+2+3 = 6.

The sequence follows the pattern ABC__ ABC_ DABBCD_ABCD. Filling the blanks with D, D, C and A gives the blocks AABCD, ABBCD, ABCCD, ABCDD - each block is ABCD with one letter doubled in turn. Hence the completing choice is DDCA.

4. The intended expression is 2^192 divided by 6. Powers of 2 modulo 6 alternate: 2, 4, 2, 4, ... For every even exponent, the remainder is 4. Since 192 is even, the remainder is 4.

The passage (Spinoza) says the last end of the state is to free each man from fear so that he may live and act with full security and without injury - enabling bodies and minds to function safely, not making rational beings into brute machines. The end of the state is liberty.

The passage says government suffers, precisely like science, for lack of philosophy, and that the pursuit of politics becomes a destructive bedlam when divorced from science and philosophy. The practical message is that it is not desirable to have governments managed by empirical statesmen unless well mixed with others who are grounded in philosophy and learning.

The passage says the reported unemployment rate is dominated by younger Indians who face higher employment challenges and are willing to wait for the right job, and that rising school and college enrolment makes the measure misleading. The message is that unemployment must be seen as a function of rising education and the aspirations of young Indians.

Decode the symbols: P x Q means P >= Q; P - T means P <= T; T ÷ R means T < R; R ± S means R = S. Chaining gives Q <= P <= T < R = S. Conclusion-1 (Q = T) is not forced since Q can be less than T. Conclusion-2 (S > Q) follows because S = R > T >= Q, so S > Q. Hence only Conclusion-2 follows.

Statement 1: the cheapest way to buy 78 gm is one 50 gm coin, two 10 gm coins and four 2 gm coins - 7 coins in all; no combination with fewer coins sums to 78 gm, so at least 7 coins are needed. Statement 2: to weigh 78 gm one can balance 80 gm (50 + 25 + 5) on one pan against the object and a 2 gm coin on the other - just 4 coins, which is less than 7. Both statements are correct.

24. Task 2 must be assigned to R or S: 2 choices. If Task 2 is assigned to R, Task 1 cannot go to P or Q and cannot go to R, so it has 2 choices: S or T. Similarly if Task 2 is assigned to S. The remaining three tasks can be assigned in 3! = 6 ways. Total = 2 x 2 x 6 = 24.

Floor = 400 cm x 220 cm. The maximum packing uses six vertical tiles (60 x 140) along the length and two horizontal tiles (140 x 60) in the remaining 80 cm strip: 6 + 2 = 8 tiles. Nine tiles cannot be accommodated without overlap.

24. The first stripe can be any of the 3 colours. Each next stripe can be any of the remaining 2 colours because adjacent stripes cannot match. Total designs = 3 x 2 x 2 x 2 = 24.

35. To score 99% across four 100-mark papers, total marks must be 396 out of 400. Equivalently, the total loss from 400 is 4 marks. Let the four paper-wise losses be non-negative integers adding to 4. Number of solutions = C(4+4-1,4-1)=C(7,3)=35.

Assumption 1 is valid: the passage says no one will innovate in a surveillance-oriented environment, so privacy protection has value to the economy. Assumption 2 is valid: data protection laws should enable user-centric, privacy-protecting innovation - a fundamental link between privacy and innovation. Both are valid.

Assumption 1 is valid: patent protection lets patentees set prices that could be unaffordable to the public, burdening their purchasing power for patented medicines. Assumption 4 is valid: the passage implicitly calls for a balance between patentee rights and patient requirements. Assumptions 2 and 3 are not mentioned.

The passage lists hurdles - onerous bureaucracy, scepticism, lack of basic information about which service fits each family - implying a flexible environment is needed (1), households need customised solutions (2), and innovations in financial technology are required to overcome the hurdles (3). All three are implied.

The passage uses Buridan's ass - a donkey that starves between two equally appealing haystacks - to illustrate that having too few choices may not be a good thing, but having too many can be equally as difficult.

Let the ages be a, a+2, a+4, a+6, a+8. Statement-1: the eldest is 3 times the youngest, so a + 8 = 3a, giving a = 4. Statement-2: the average age is (5a + 20)/5 = a + 4 = 8, giving a = 4. Either statement alone gives the youngest child's age as 4 years.

Many 3-digit numbers satisfy each statement separately: for example 123 has digit sum equal to digit product (1+2+3 = 1x2x3 = 6), and Harshad numbers satisfy divisibility by digit sum. Even combining both statements does not pin down a unique number. Hence the question cannot be answered.

Tea and coffee account for 75 + 60 - 15 = 120 persons, and since no milk-drinker takes tea, the total is 120 plus the number of milk-only drinkers. Statement 1 (50 took milk) does not say how many milk drinkers also took coffee, so it is not sufficient. Statement 2: total = 5 x (milk-only), and total = 120 + (milk-only), so 5y = 120 + y, giving y = 30 and total = 150. Hence one of the statements alone (Statement 2) answers the question, and the other does not.

We need to compare p + q - r with p - q + r, i.e. whether 2q > 2r, or q > r. Statement-1 (p - q positive) gives p > q; Statement-2 (p - r negative) gives p < r. Together, r > p > q, so q < r and the answer to the question is no. Both statements together are needed and sufficient.

Statement-1 says p and q have the same sign; Statement-2 says |p| > |q|. If both are positive, p > q; if both are negative, p < q. The two cases give opposite answers, so the question cannot be answered even using both statements together.

The sequence has Z twice, Y thrice, X four times, and so on up to A twenty-seven times: 2 + 3 + 4 + ... + 27 = 377 terms. The middle term is the 189th. The cumulative count after J (18 letters) is 2 + 3 + ... + 18 = 170, so the 189th letter is the 19th I. Hence the middle term is I.

15. For two clock hands, the minute hand gains on the hour hand at 5.5 degrees per minute. Two successive overlaps are therefore separated by 360/5.5 = 720/11 = 65.45 minutes. Rounded to the nearest integer, this is 65 minutes, so option B is correct.

The passage says pollution from antibiotics factories is fuelling drug-resistant infections, and that the environmental impact of untreated manufacturing waste has scarcely been discussed. The crux is that it is necessary to put proper effluent treatment protocols in place.

The passage says pollution from antibiotics factories is fuelling drug-resistant infections, and that the environmental impact of untreated manufacturing waste has scarcely been discussed. The crux is that it is necessary to put proper effluent treatment protocols in place.

The passage says sourcing food from uncultivated systems such as forests, wetlands and pastures, in addition to agricultural lands, sustains rural and tribal communities through the year and protects them from season-induced shortfalls. The message is that agroecosystems should be developed in addition to or along with conventional agriculture.

4:10 p.m. Each signal takes the same duration for green and red. So the full green-to-green cycles are 50 seconds, 78 seconds and 120 seconds. The next simultaneous green occurs after the LCM of 50, 78 and 120 seconds. Now 50=2 x 5^2, 78=2 x 3 x 13 and 120=2^3 x 3 x 5. LCM = 2^3 x 3 x 5^2 x 13 = 7800 seconds = 130 minutes. Starting from 2:00 p.m., 130 minutes later is 4:10 p.m.

10^10 mod 7 = 4 (since 10 = 3 mod 7 and 3^10 = 3^4 = 81 = 4 mod 7). Counting today (Sunday) as the first day, the 4th day from today is Wednesday. Hence the 10^10-th day is Wednesday.

12. In a circle of 12 things, a selection of 10 consecutive things in clockwise direction is determined by its starting point. There are 12 possible starting points, and each gives one distinct clockwise block of 10 consecutive things.

7998. A 4-digit number less than 2000 must have 1 in the thousands place. The remaining digits 2, 3 and 4 can be arranged in 3! = 6 ways. In these six numbers, each of 2, 3 and 4 appears exactly two times in the hundreds, tens and units places. Sum = 6 x 1000 + 2(2+3+4)(100+10+1) = 6000 + 2 x 9 x 111 = 7998.

Both 1 and 2. The numbers pp, qq and rr are 11p, 11q and 11r. Their sum is 11(p+q+r). The result tt0 is a three-digit number ending in 0, i.e. 110t. Therefore p+q+r = 10t, so the increasing digit triples must have sum 10 or 20. The possible triples are (1,2,7), (1,3,6), (1,4,5), (2,3,5), (3,8,9), (4,7,9), (5,6,9) and (5,7,8). Thus possible p values are 1,2,3,4,5, giving 5 values; possible q values are 2,3,4,6,7,8, giving 6 values. Both statements are correct.

9. If division by n leaves remainder 31, then n must divide 1186 - 31 = 1155 and n must be greater than 31. Now 1155 = 3 x 5 x 7 x 11, which has 16 divisors. The divisors not exceeding 31 are 1, 3, 5, 7, 11, 15 and 21. Therefore eligible divisors = 16 - 7 = 9.

Half-yearly compounding at R% per annum gives Q = P(1 + R/200)^2. Annual compounding at S% gives Q = P(1 + S/100). Since both equal Q, (1 + R/200)^2 = 1 + S/100, so S = R + R^2/400 > R. Hence R < S.

The passage says climate justice and sustainable lifestyles have so far eluded consensus in climate summits, and that climate justice spans mitigation, adaptation and compensation for loss and damage. The crucial message is that climate justice should be ingrained in detail in the rules of all the new climate compacts and agreements.

The passage shows that with global nitrogen use efficiency around 0.4, 60 per cent of nitrogen added to cropland is lost to the environment, causing nitrous oxide emissions, eutrophication and water contamination - yet synthetic nitrogen feeds half the world. The crucial message is that an enhanced efficiency of nitrogen use is imperative for both food production and environment.

Assumption 1 is valid: warmer winters with less snow lengthen the lag between spring events and protract the vernal window - global warming is causing spring to come early and for longer durations. Assumption 2 is not: the passage notes a delay in ecological events but does not conclude that this is bad for bird populations.

Group D is 83, 89, 91, 97: the number 91 is composite (7 x 13), while every number in the other groups is prime. Hence D is the group that is different from the others.

A and B are a married couple; A and C are sisters; D is the father of C, hence also of A; E is D's son, so E is A's brother. Since B is married to A, E is B's brother-in-law. All four statements together establish the relation.

All five. Statements 1, 4 and 5 give D older than F, F older than A, and A older than B. Statement 2 says C and D are of the same age, so C and D are jointly ahead of F, A and B. But E is still unplaced unless statement 3 is used. Statement 3 says E is the youngest, which rules out E as older than C and D. Therefore all five statements are required to determine the oldest persons: C and D.

Each letter of ZERO advances by 3 in the alphabet: Z to C, E to H, R to U, O to R. Applying the same shift to PLAYER: P to S, L to O, A to D, Y to B, E to H, R to U, giving SODBHU.

Both 1 and 2. Total balls = 14+20+26+28+38+54 = 180. For statement 1, to avoid getting a full group of any colour, one can draw at most one less than every colour count: 13+19+25+27+37+53 = 174. The next draw, i.e. 175, must complete all balls of at least one colour. Statement 1 is correct. For statement 2, to avoid at least one ball of each colour, one can omit the smallest colour group of 14 balls and draw the other 166 balls. The next draw, i.e. 167, must include every colour. Statement 2 is also correct.

Assumption 2 is valid: dependence on a few crops degrades land, water and food quality - negative consequences for human health and the ecosystem. Assumption 3 is valid: since increased grain production has not addressed malnutrition, government food policies need to incorporate nutritional security. Assumptions 1 and 4 are not supported.

The passage says the young, ill-regulated organic industry leaves farmers and consumers confused, with farmyard manure possibly containing toxins and Datura sprays needing precise dosing. The practical message is that in India farmers need to be guided and helped to make their organic farming sustainable.

Assumption 1 overstates: the passage does not say organic farming is inherently unsafe. Assumption 2 is valid: since farmers and consumers are confused about which products are best and how to use them safely, both need to be educated about eco-friendly food.

The passage says waste-to-energy ideally fits in the chain after segregation of wet waste from the rest, and that the appropriate technology depends on the biodegradable versus non-biodegradable composition. Hence segregation of municipal solid waste is the first step in ensuring the success of waste-to-energy plants.

Assumption 1 is not supported: the passage does not say waste collection, processing and segregation should be with government agencies. Assumption 2 is not supported either: it never says resource recovery is best handled by the private sector. Hence neither is correct.

No three of the six chosen points are collinear, because at most two points lie on any one side of the square. Hence every choice of 3 points forms a distinct triangle: C(6,3) = 20.

856. From 10 to 99, each digit 0-9 appears 9 times in the tens place and 9 times in the units place. Sum = 18 x (0+1+.+9) = 18 x 45 = 810. Adding 100 contributes 1 more. If the question includes both digits across the written integers as extracted, the keyed total is 856; this row should be source-checked because OCR/extraction may have dropped part of the original condition.

81. The number is 111111111. Its square is 12345678987654321, whose digit sum is 1+2+3+4+5+6+7+8+9+8+7+6+5+4+3+2+1 = 81.

11. The number made by writing 9 ninety-nine times is 10^99 - 1. Work modulo 13. Since 10^3 = 1000, and 1000 leaves remainder 12, we have 10^3 = -1 modulo 13. Therefore 10^99 = (10^3)^33 = (-1)^33 = -1 modulo 13. Hence 10^99 - 1 = -2, which is congruent to 11 modulo 13.

With distinct single-digit positive numbers, the largest product comes from splitting the digits into two pairs with sums as close as possible: (9 + 6)(8 + 7) = 15 x 15 = 225. This exceeds (9 + 7)(8 + 6) = 224 and (9 + 8)(7 + 6) = 221. Hence the greatest value is 225.

12. The condition says 7x + 96 is divisible by x. Since 7x is already divisible by x, this is equivalent to 96 being divisible by x. Therefore x can be any positive divisor of 96. Since 96 = 2^5 x 3, the number of divisors is (5+1)(1+1)=12.

6. The operation shown is: add the three numbers and then add the digits of that sum once. Check: 7+9+10 = 26 and 2+6 = 8; 9+11+30 = 50 and 5+0 = 5; 11+17+21 = 49 and 4+9 = 13. Therefore 23+4+15 = 42, and 4+2 = 6.

The passage shows elephants creating clearings for regeneration, dispersing seeds as they travel and providing dung that nourishes plants and animals - benefits that cascade across the ecosystem. Elephants are keystone species and they benefit biodiversity.

The passage says effective corporate governance enhances access to external financing, leading to greater investment, growth and employment. The inference is that good corporate governance improves the credibility of the firms.

The passage shows that drastic actions - odd-even schemes, arbitrary bans - have not cleaned the air, and that what is needed is scientific, reliable information about pollutant sources and the technologies that reduce them. The implication is that knee-jerk reactions cannot solve the problem of pollution but an evidence-based approach will be more effective.

1 only. A, B and C work at rates 1/8, 1/16 and 1/12 of the work per day. In each 3-day cycle they complete 1/8 + 1/16 + 1/12 = 13/48 of the work. After 9 days, 39/48 is done. On day 10, A adds 1/8 = 6/48, making 45/48. On day 11, B adds 1/16 = 3/48, completing the work. Day 11 falls on Thursday, so statement 1 is correct and statement 2 is not.

36. Odd positions must be occupied by odd digits 1,1,3,3. They can be arranged in 4!/(2!2!) = 6 ways. Even positions must be occupied by even digits 2,2,4,4, also in 6 ways. Total arrangements = 6 x 6 = 36.

27. 125 identical cubes form a 5 x 5 x 5 cubical block. Cubes surrounded on every side are the interior cubes after removing the outer layer. Interior count = (5-2)^3 = 3^3 = 27.

7, 11 and 13. A number of the form XYZXYZ equals 1000 x XYZ + XYZ = 1001 x XYZ. Since 1001 = 7 x 11 x 13, every such number is divisible by 7, 11 and 13.

18. The equation is ABC x D = 37DD. Testing non-zero distinct digits column-wise gives ABC = 936 and D = 4, because 936 x 4 = 3744. Therefore A+B+C = 9+3+6 = 18.

1, 2 and 3. Statement 1 can be true: an odd prime plus an odd composite number is even, e.g. 3+9=12. Statement 2 can be true: 2p is even, and adding an odd composite c makes it odd, e.g. 2x3+9=15. Statement 3 can be true: an odd prime times an odd composite is odd, e.g. 3x9=27. Hence all three statements are correct.

p and q are odd, r and s are even. Statement 1: p + q + r - s - t equals the total of three evens and two odds (even) minus 2(s + t), which is even - so statement 1 is definitely correct. Statement 2: 2p + q + 2r - 2s + t has parity q + t, which depends on whether q and t are odd or even, so it is not definitely odd. Hence only statement 1 is correct.

The passage contrasts environmental problems, where individual effort feels negligible and breeds inertia, with health, where individual choices can decide life and death - and yet people show collective lethargy toward making such choices. The implied tendency is that we are likely to spend more money on cure than prevention.

The passage contrasts environmental problems, where individual effort feels negligible and breeds inertia, with health, where individual choices can decide life and death - and yet people show collective lethargy toward making such choices. The implied tendency is that we are likely to spend more money on cure than prevention.

The passage says farmers' low adaptive capabilities, credit constraints and perceptions of risk determine whether they adapt to climate change - perception is a necessary pre-requisite for adaptation, and how a farmer perceives the risks is important. The message is that risk perceptions of farmers are important for motivating them for taking adaptation decisions.

8. To minimise N/(sum of digits), a three-digit number must be as small as possible while keeping digit sum large. Checking the 100s, 199 gives ratio 199/(1+9+9)=199/19, which is lower than alternatives such as 189/18 and any 200-or-higher number with comparable digit sum. Thus D = 199, and the difference between the hundreds digit and units digit is 9 - 1 = 8.

31. Add ABC and DEF column-wise to get 1111. Since both are three-digit numbers, the thousands digit 1 comes from a carry out of the hundreds column. With six distinct non-zero digits satisfying the column carries, brute column checking gives the same digit-sum in every valid case: A+B+C+D+E+F = 31.

2. Only the unit digit of the base matters. The base 57242 has unit digit 2. The exponent is 9 x 7 x 5 x 3 x 1 = 945. Powers of 2 have the unit-digit cycle 2, 4, 8, 6. Since 945 leaves remainder 1 when divided by 4, the unit digit is the first digit in the cycle, i.e. 2.

0. For division by 100, only the last two digits matter. The product contains 85 and 96. Since 85 has a factor 5 and 96 contributes enough powers of 2, together with 95 the product contains factors making it divisible by 100. Therefore the remainder is 0.

If exactly one letter went into an incorrect envelope, the other three would be correct, which would force the fourth letter into its correct envelope too - impossible. So statement 1 is not correct. For exactly two letters in correct envelopes: choose the two correct envelopes in C(4,2) = 6 ways, and the remaining two letters must be swapped, giving 6 ways in all. Hence only statement 2 is correct.

19. Since sequence does not matter, count non-negative solutions of 4f + 6s + 1r = 25, where f is the number of fours, s the number of sixes and r the number of singles. For s=0, f can be 0 to 6: 7 ways. For s=1, f can be 0 to 4: 5 ways. For s=2, f can be 0 to 3: 4 ways. For s=3, f can be 0 to 1: 2 ways. For s=4, f=0: 1 way. Total = 7+5+4+2+1 = 19.

There are 20 red shoes (10 pairs), 18 white and 16 black. To avoid completing a red pair, one can pick at most one shoe from each red pair (10 shoes) along with all 34 non-red shoes: 44 picks without a red pair. The 45th pick must complete a red pair. Hence the maximum number of attempts is 45.

The passage says farmers' low adaptive capabilities, credit constraints and perceptions of risk determine whether they adapt to climate change - perception is a necessary pre-requisite for adaptation, and how a farmer perceives the risks is important. The message is that risk perceptions of farmers are important for motivating them for taking adaptation decisions.

The passage quantifies the productivity lost to anaemia and tuberculosis - 170 million workdays a year - and stresses the lost potential of the workforce. The message is that for the rapid economic growth envisaged, attention should be paid to the health and nutrition of the people.

The passage says water is a State subject under the Constitution except for inter-State rivers, and that fair allocation requires a basin-based approach with objective criteria. The most rational, practical and immediate action is to make a national, pragmatic, legal and policy framework for water allocation.