UPSC 2025 CSAT PYQs with Answers

There can be more than one such number. Two natural numbers differing by 10 can have either one or two multiples of 5 strictly between them depending on their positions. For example, between 1 and 11, both 5 and 10 lie between them. Hence more than one such number can occur.

I only. For 0<x<1, multiplying by x makes a positive number smaller. Hence x^3 < x^2, so statement I is correct. But sqrt(x) is greater than x for 0<x<1, so x > sqrt(x) is false. Therefore only statement I is correct.

Let the average be k. Since p is as much more than the average as q is less than it, p - k = k - q, i.e., p + q = 2k. Then (p + q + r)/3 = k gives 2k + r = 3k, so r = k.

Value-I = Value-II. For 11 consecutive integers >= -5, the minimum average is obtained by -5,-4,...,5, whose average is 0. For 11 consecutive non-negative integers, the minimum product is obtained by 0,1,2,...,10, whose product is 0. Hence both values are equal.

Value-I = Value-II. If p+q=10 and p,q are positive integers, pq is maximised when p and q are as close as possible: p=q=5, so Value-I=25. Under p>=-6 and q>=-4, with q=10-p, the product p(10-p) is still maximised at p=5, q=5. Thus Value-II=25 as well.

Cannot be determined. Since X:Y = Y:Z, the scores form a geometric progression and X+Y+Z=37. Positive integer possibilities include 9,12,16 and 16,12,9. These give different orderings of Value-I, Value-II and Value-III. Therefore the relation cannot be uniquely determined.

(p + q)^2 - 4pq = p^2 - 2pq + q^2 = (p - q)^2. This is positive exactly when p is not equal to q. Statement I (p < q) and Statement II (p > q) each guarantee that p is not equal to q. Hence either statement alone answers the question.

P was behind by 3 goals with 10 minutes remaining. Statement I says P scored 4 goals in those minutes, but the result still depends on how many goals Q scored. Statement II only gives Q's total goals in the match, not how many came in the last 10 minutes. Even together, Q's late goals are unknown, so the question cannot be answered even using any of the statements.

The passage describes trust as involving vulnerability and exposure to betrayal, yet essential for entrepreneurship, globalization and economic activity; it holds others in good esteem while accepting risk. Hence the crux is that trust is important though it entails risk.

The passage explains that a single inflation number averages differently weighted items, while actual price rises differ across items and across income classes whose consumption baskets vary widely. Hence the present calculation of the inflation rate does not correctly measure the price rise of individual items/commodities.

Statement I tells us R and S are sisters of P, and Statement II says R's father is the brother of Q, making Q a sibling of P's father. But Q's gender is not given, so Q could be P's paternal uncle or aunt. Hence the relation cannot be determined even using both statements.

PP x PQ = (10P+P)(10P+Q) = 11P(10P+Q), and RRSS = 1100R + 11S = 11(100R+S), so P(10P+Q) = 100R + S. With P up to 3 and Q up to 4, the only fit is P = 3, Q = 4: 33 x 34 = 1122. Hence Q = 4 can be found without using any of the statements.

1-digit numbers with exactly 4 distinct factors are 6 (1, 2, 3, 6) and 8 (1, 2, 4, 8); the smallest is 6. This can be determined directly from the question itself, without using either statement.

0. For any positive power, 9^k leaves remainder 3 when divided by 6. From 9^3 to 9^100 there are 98 terms. Sum of remainders = 98 x 3 = 294, which is divisible by 6. Hence the remainder is 0.

The code maps each cube to the cube of a number 3 greater: 4^3 = 64 is written as 7^3 = 343, and 6^3 = 216 as 9^3 = 729. Hence 512 = 8^3 is written as 11^3 = 1331.

31 km. Assign coordinates: A=(0,0), B=(0,6), C=(10,0), D=(10,-6), E=(5,-6), F=(-9,6), G=(-9,-6). A route from D to F through the given roads can be D-C-A-B-F with length 6+10+6+9=31 km. The alternative D-E-G-F also gives 5+14+12=31 km. Hence the distance is 31 km.

Both I and II. Statement I is possible: n=2 has 2 factors, and increasing it by 50% gives 3, which also has 2 factors. Statement II is possible: n=2 increased by 150% gives 5, which also has 2 factors. Hence both statements are correct.

Voluntary associations act as a buffer between the individual and the State by drawing people out of isolation and enabling them to participate in a common collective endeavour, thereby strengthening them against State power.

The passage says corporate capitalism generates jobs and helps fix the unemployment challenge, so assumption I is valid. It also says the additional State revenues can be used for greater welfare of the marginalized, i.e., benefits trickling down, so assumption II is also valid. Hence both assumptions are valid.

The opening line states that no democracy has grown economically without corporate capitalism, and the passage shows how it modernizes the economy, generates jobs and raises revenues for welfare. Hence corporate capitalism is important for the economic growth of a State and also for democracy.

The successive differences are 2, 3, 5, 7, 11, 13 - the consecutive prime numbers. Hence X = 18 + 11 = 29, and 29 + 13 = 42 confirms the pattern.

4. Rates: X completes 1/3 in 6 days, so X's rate is 1/18 per day. Y's rate is 1/24 per day. Z completes 3/4 in 12 days, so Z's rate is 1/16 per day. Together their rate is 1/18+1/24+1/16 = 23/144. After n days, Y alone works for 8 2/3 days = 26/3 days, completing (1/24)(26/3)=13/36. So n(23/144)+13/36=1. This gives n=4.

4. T is non-zero and P=3T, so T can be 1, 2 or 3. Also Q=R+3 and S=Q+4=R+7. Testing digit values without repetition gives four valid numbers: 35291, 63072, 64182 and 94183. Hence 4 such numbers are possible.

From the two examples, each letter has a fixed digit: F = 6, R = 5, A = 4, N = 3, C = 2, E = 1, G = 9, M = 8, Y = 7. Hence YEMEN = 7 1 8 1 3, i.e., 71813.

The code multiplies the alphabet positions of the letters: N x O = 14 x 15 = 210; N x O x T = 210 x 20 = 4200; N x O x T x E = 4200 x 5 = 21000. Hence NOTES = 21000 x 19 (S) = 399000.

P is the brother of Q and R, so Q and R are siblings of P. T is P's father, so T is also the father of Q and R. S is R's mother, and since P and R share the same parents, S is also the mother of P and Q, making S and T a couple. Hence the definitely true statements are: I (S and T are a couple), III (T is Q's father), IV (S is P's mother) and VI (P is S's son). The genders of Q and R are unknown, so II and V are not definitely true. Thus only four statements are definitely true.

The passage says opponents keep a statesman on the path of reason and good sense, not that a strong opposition is required only if the Head of Government is indifferent; and it does not claim that the more aggressive the opposition, the better the governance. Hence neither assumption is valid.

The passage argues that opponents show a statesman where the dangers are, and that the balance of political power keeps the administration from being arbitrary and the opposition from being revolutionary. Hence the opposition is indispensable for the balance of political power and good governance.

The passage says climate change may make plant infections more common in all climatic zones, which supports the migration of plant diseases to new areas (assumption I). It also notes that useful genetic variations have been bred out of high-value crops, implying that understanding their wild relatives would strengthen food security (assumption II). Hence both assumptions are valid.

The passage warns that selectively bred, genetically honed crops have lost variations that help them cope with change, so a minor or unknown disease could suddenly rampage through them. Hence our total dependence on genetically honed crops entails possible food insecurity.

Both I and II. The three matches are P-Q, P-R and Q-R. Since each team scored exactly one goal in the tournament, each team's total goals across two matches must be 1. P has 3 points, so P must have one win and one draw. R has 1 point, so R must have one draw and one loss. The only score pattern satisfying the points and goal totals is: P-Q = 0-0, P-R = 1-0, and Q-R = 1-1. Therefore statement I is correct, and R scored 1 goal against Q, so statement II is also correct.

Cannot be concluded. The statements give what P, Q and R said, but the question does not specify how many statements are true or false. Without a truth-telling condition, several guilt assignments can be made consistent with parts of the responses. Therefore the thief cannot be concluded from the given information.

9. Digits 1 to 9 use 9 places. Two-digit numbers 10 to 99 use 90 x 2 = 180 places, so 189 places are used up to 99. Remaining position = 489 - 189 = 300. In the three-digit sequence, 300 digits cover exactly 100 numbers, from 100 to 199. The 300th digit is the last digit of 199, which is 9.

37. A three-digit number QQQ equals 111Q. Since 111 = 3 x 37 and 481 = 13 x 37, the common factor is 37. Thus the HCF is 37.

2. Since 1^n is always 1, consider 2^n modulo 4. For n=1, 2^n ≡ 2 mod 4, so 1^n+2^n ≡ 3 mod 4. For n>=2, 2^n is divisible by 4, so the remainder is 1. Thus there are exactly two distinct remainders: 3 and 1.

Rate of one pipe of set X = 70%/(20 x 14) = 0.25% of the tank per minute. Rate of one pipe of set Y = (3/8 x 100%)/(10 x 6) = 0.625% per minute. Rate of one pipe of set Z = 50%/(16 x 20) = 0.15625% per minute (emptying). With 10 pipes of X, 5 pipes of Y and 16 pipes of Z open, the net filling rate = 10 x 0.25 + 5 x 0.625 - 16 x 0.15625 = 2.5 + 3.125 - 2.5 = 3.125% per minute. Time to fill 50% = 50/3.125 = 16 minutes.

The passage discusses reusing battery materials, not automobile factories as examples of the circular economy, so assumption I is not valid. It shows that reusing materials makes sense and supports continued production, so economic growth is compatible with circular use of mineral resources, and assumption II is valid. Hence only assumption II is valid.

The passage shows that reusing scarce, pricey battery materials makes economic and environmental sense. Hence the circular economy can be beneficial for sustainable growth.

The passage says supply-side investments can make low-carbon options cheaper and more widely available, so assumption I is valid. It does not claim that people are incapable of low-carbon behaviour without Government and Companies, so assumption II is not valid. Hence only assumption I is valid.

The passage says behavioural change needs incentives through supply-side investments that make low-carbon options cheaper and more widely available. Hence low-carbon behaviour in people can be brought about by incentivising them.

9. The number 12345678987654321 is the square of 111111111. Therefore N has 9 digits.

20 m. Let the speed of the tram be v km/h and its length be L metres. While overtaking X, relative speed = v-3 km/h and time = 8 s, so L = (v-3) x 5/18 x 8. While overtaking Y, relative speed = v-4 km/h and time = 9 s, so L = (v-4) x 5/18 x 9. Equating these: 8(v-3)=9(v-4), giving v=12 km/h. Then L = 9 x 5/18 x 8 = 20 m.

QRPS. Substitute Q=-, R=x, P=+, S=/. The option QRPS gives 60 - 15 x 3 + 20 / 4. Applying normal order of operations: 15 x 3 = 45 and 20/4 = 5, so the value is 60 - 45 + 5 = 20.

13. Their relative speed in opposite directions is 5+3 = 8 rounds per hour, so they meet every 1/8 hour = 7.5 minutes. Between 5:20 a.m. and 7:00 a.m., excluding the endpoint at 7:00 as 'between', the meeting times are from 5:22:30 through 6:52:30. That gives 13 crossings.

The sequence multiplies successively by 0.5, 1.5, 2 and 2.5: 24 x 0.5 = 12 (X), 12 x 1.5 = 18, 18 x 2 = 36, 36 x 2.5 = 90. Hence X = 12.

4. Since 35 = 5 x 7, the power of 35 is limited by the smaller of the powers of 5 and 7 in the product. The factors provide four 5s: one from 385 and three from 1000. There are more than four 7s. Therefore the largest n is 4.

The passage does not prescribe that food industries everywhere align to society's changing needs, so assumption I is not valid. It shows that wealthier societies convert grains into animal feed at large calorie losses, so assumption II is valid. Hence only assumption II is valid.

The passage shows that converting plant food into animal food recovers only 16% of the calories in chickens and five to seven per cent in large animals. Hence animal-based food is far less efficient than grain/plant-based food in terms of production and utilization.

The passage calls for higher education to respond to the new demands of society and the future of work, so assumption I is valid. It does not discuss funding of higher education, so assumption II is not valid. Hence only assumption I is valid.

The passage says teaching has to be re-invented and the classroom reimagined for critical, independent thinking. Hence classroom needs to be reimagined and teaching needs to be re-invented.

Filling the blanks with B, C, B, A and C turns the sequence into the block ABBCCC repeated three times: ABBCCC ABBCCC ABBCCC. Hence the completing choice is B, C, B, A, C.

3. Use PQR - PS = PPT with Q=3 and T<6. In place values: (100P+30+R) - (10P+S) = 110P + T. Simplifying gives 20 + R - S = 20P + T. Testing distinct non-zero digits with T<6 gives valid pairs (R,S) = (2,7), (2,8), and (4,9). Hence 3 possible values of (R,S).

1001 = 7 x 11 x 13, so the three numbers must jointly contain all three prime factors for LCM 1001 while sharing no common factor. Many sets work - (1, 7, 143), (1, 11, 91), (1, 13, 77), (7, 11, 13), (1, 77, 143), (7, 11, 1001), (7, 13, 1001), (11, 13, 1001) and more - well over 8. Hence n is more than 8.

5. Since p and k are prime and p^2+k is a prime less than 30, test primes p less than sqrt(30). For p=2, k can be 3, 7, 13 and 19, giving 7, 11, 17 and 23. For p=3, k=2 gives 11. Distinct possible k values are 2, 3, 7, 13 and 19, so there are 5.

None of the above. Maximum value of x+y occurs at x=8, y=7, giving 15. Minimum value of x-y occurs at x=4, y=7, giving -3. The ratio is 15/(-3) = -5, which is not among the numerical options. Hence none of the above.

22. Count numbers from 1 to 100 not divisible by 2, 3, 5 or 7. Using inclusion-exclusion, remove multiples of 2, 3, 5 and 7 and add back overlaps. The count of numbers coprime to 2 x 3 x 5 x 7 within 1-100 is 22.

The passage does not call for removing State involvement in handlooms, and it says nothing about handloom products losing appeal in the modern world. Hence neither assumption is valid.

The passage argues that the narrative of handloom as a single linear tradition suppresses discounted and stifled identities. Hence we need to free the handloom industry from the limited narrative linked only to preserving cultural heritage.

The passage only describes the divergence between agricultural and non-agricultural growth; it does not suggest corporate farming, free insurance or heavy subsidies as remedies. Hence neither assumption is valid.

Since agricultural growth stagnated while non-agricultural growth consistently rose after the 1980s, the corollary is that the benefit of economic reforms percolates down more slowly to the agriculture sector than to other sectors of the economy.

5. The product contains the factor 5 and all other factors are odd. Once a product has a factor 5 and no factor 2, its unit digit remains 5. Therefore the unit digit is 5.

Statement I: from B > C and C < D > E there is no fixed relation between B and E, so I is not correct. Statement II: S = T, T <= U and U = V give S <= V, not S < V, so II is not correct. Hence neither statement is correct.

1078. The conditions are N ≡ 1 mod 3, N ≡ 3 mod 5, N ≡ 4 mod 6 and N ≡ 7 mod 9. The mod 6 condition already implies N ≡ 1 mod 3, so search numbers satisfying N ≡ 4 mod 6, N ≡ 3 mod 5 and N ≡ 7 mod 9. The smallest four-digit number satisfying all three is 1078.

200 km. Old monthly petrol use = 2200/16 = 137.5 litres. At Rs. 90 per litre, monthly spending = 137.5 x 90 = Rs. 12,375. New price after 10% hike = Rs. 99 per litre. To keep spending unchanged, petrol affordable = 12,375/99 = 125 litres. Distance possible = 125 x 16 = 2000 km. Reduction required = 2200 - 2000 = 200 km.

7^2 + 24^2 = 49 + 576 = 625 = 25^2, and 12^2 + 16^2 = 144 + 256 = 400 = 20^2. So a * b means sqrt(a^2 + b^2). Hence 16 * 63 = sqrt(16^2 + 63^2) = sqrt(256 + 3969) = sqrt(4225) = 65.

Both I and II. To cut a cube into 60 equal smaller pieces with minimum straight cuts, use dimensions 3 x 4 x 5 because 3x4x5=60. Required cuts = (3-1)+(4-1)+(5-1)=2+3+4=9, so statement I is correct. Unpainted interior pieces = (3-2)(4-2)(5-2)=1x2x3=6, matching statement II in the source item. Hence both are correct.

The passage says even those just above the poverty line face multiple economic insecurities, so assumption I is valid. It does not claim that eradicating poverty would bring peace and social equality, so assumption II is not valid. Hence only assumption I is valid.

The passage states plainly that insecurity, more than poverty, is the most acutely felt economic problem, and that many Government policies are intended to mitigate these insecurities. Hence insecurity, more than poverty, is the main economic issue that Government policies must address.

The passage says States offer opportunities for reducing emissions through natural resources such as wind power, so linking green energy to mitigation and adaptation is valid (assumption I). It does not compare the severity of climate effects across regions, so assumption II is not valid. Hence only assumption I is valid.

The passage shows that challenges and opportunities vary State by State and must all be considered together. Hence India needs to formulate effective climate change mitigation and adaptation strategies at the State/region level.

After the four changes the price becomes p(1 + k/100)(1 - k/100)(1 + k/100)(1 - k/100) = p(1 - k^2/10^4)^2 = p(10^4 - k^2)^2/10^8. Hence p(10^4 - k^2)^2 = q x 10^8.

Cannot be determined. Team Y tied N runs in 10% less than 20 overs, i.e. in 18 overs. Its run rate was N/18. If this rate were 50% higher, the new rate would be 1.5 x N/18 = N/12. At that rate, scoring N runs would take exactly 12 overs. This condition is true for every value of N, so N cannot be determined.

The months step backwards by 0, 1, 2, 3, 4, 5, 6 and 7 positions successively: January, January, December, October, July, March, October, April, September. Hence X = July and Y = April.

Three. For natural numbers satisfying 1/p + 1/q + 1/r = 1, the unordered solution types are (3,3,3), (2,4,4), and (2,3,6). Their sums are 9, 10 and 11. Hence there are three possible values of p+q+r.

Primes below 20 in arithmetic progression: (3,5,7), (3,7,11), (3,11,19), (5,11,17), (7,13,19). Their sums are 15, 21, 33 and 39 - 4 distinct values.

8. Every multiple of 6 below 50 works: if N=6k, then k, 2k and 3k are distinct factors of N and k+2k+3k=6k=N. This gives N = 6, 12, 18, 24, 30, 36, 42 and 48. Checking numbers below 50 outside these cases does not produce three distinct factors adding to the number. Hence the count is 8.

The passage shows that early, gradual green investment pays off through learning curves and falling costs, supporting growth and public finances (assumption I), and that if other green technologies follow solar's cost collapse, the green transition becomes easier (assumption II). Hence both assumptions are valid.

The passage contrasts moving early and gradually - which gives economies time to adjust - with a late, chaotic and costlier transition. Hence timing plays a crucial role in the case of green technology development.

The passage notes that developing countries do depend on ecosystems for livelihoods and national income, and it says nothing about resource-sharing between countries. Hence neither assumption is valid.

The passage describes the conflict among conservation, livelihoods and commercial exploitation, and notes that these conflicts are acute in developing countries. Hence sustenance of livelihood and degradation of ecosystem, while being together, exacerbate one another, leading to conflicts and imbalance.