CSAT Paper II of the 2023 Preliminary examination, held on 28 May 2023. 80 questions · 200 marks · qualifying at 33%. The questions broke down as Comprehension 27, Basic Numeracy 20, Mental Ability 19, Logical Reasoning 7, Data Interpretation 5.
The answer under each question is UPSC's official key. The note beside it is the first line of our explanation; the full reasoning, option by option, is one click away.
Which one of the following statements best reflects the most rational, practical and immediate action required to ensure fair and equitable allocation of water to different stakeholders ?
UPSC's answer: (a) — The passage explicitly states that water is a State subject under the Constitution, except for the regulation of inter-State rivers, which necessitates a unified legal and policy framework to manage these exceptions effectively.
Which one of the following statements best reflects what is implied by the passage ?
UPSC's answer: (d) — The passage highlights that anaemia and tuberculosis cause significant lost productivity among working-age Indians, with women and men being 5–15% less productive due to these health issues.
Which one of the following statements best reflects the most logical and rational message conveyed by the author of the passage ?
UPSC's answer: (c) — The passage states that while perception is a necessary pre-requisite for adaptation, it is not always sufficient on its own.
Raj has ten pairs of red, nine pairs of white and eight pairs of black shoes in a box. If he randomly picks shoes one by one (without replacement) from the box to get a red pair of shoes to wear, what is the maximum number of attempts he has to make ?
UPSC's answer: (d) — Total shoes: 10 red pairs = 20 red shoes, 9 white pairs = 18 white shoes, 8 black pairs = 16 black shoes, so 54 shoes. To delay a red pair as long as possible, Raj can first pick all 34 non-red shoes (18 white + 16 black).
In how many ways can a batsman score exactly 25 runs by scoring single runs, fours and sixes only, irrespective of the sequence of scoring shots ?
UPSC's answer: (b) — Let s, f and x be the numbers of singles, fours and sixes, so s + 4f + 6x = 25 with each at least 0; singles fill whatever is left, so every valid pair (f, x) gives exactly one way. x = 0: 4f ≤ 25, so f = 0 to 6 — 7 ways. x = 1: 4f ≤ 19, so f = 0 to 4 — 5 ways.
There are four letters and four envelopes and exactly one letter is to be put in exactly one envelope with the correct address. If the letters are randomly inserted into the envelopes, then consider the following statements : 1. It is possible that exactly one letter goes into an incorrect envelope. 2. There are only six ways in which only two letters can go into the correct envelopes. Which of the statements given above is/are correct ?
UPSC's answer: (b) — Statement 1 is wrong: if three letters are in their correct envelopes, the only envelope left is the fourth letter's own, so exactly one letter can never be misplaced.
What is the remainder when 85 × 87 × 89 × 91 × 95 × 96 is divided by 100 ?
UPSC's answer: (a) — The remainder on division by 100 is the last two digits of the product. 85 = 5 × 17 and 95 = 5 × 19 supply two factors of 5, and 96 = 2⁵ × 3 supplies more than two factors of 2. So 5² × 2² = 100 divides the product. Hence the remainder is 0, option (a).
What is the unit digit in the expansion of (57242)⁹ˣ⁷ˣ⁵ˣ³ˣ¹ ?
UPSC's answer: (a) — The exponent is 9 × 7 × 5 × 3 × 1 = 945, and the unit digit of the base 57242 is 2. Unit digits of powers of 2 repeat in the cycle 2, 4, 8, 6 (period 4). 945 = 4 × 236 + 1, so the exponent leaves remainder 1 on division by 4. The unit digit is therefore the first in the cycle, 2 — option (a).
If ABC and DEF are both 3-digit numbers such that A, B, C, D, E and F are distinct non-zero digits such that ABC + DEF = 1111, then what is the value of A + B + C + D + E + F ?
UPSC's answer: (d) — Since ABC and DEF are 3-digit numbers summing to 1111, the sum of their digits must account for the carries generated in each column. In the units column, C + F must equal 11 (to produce a digit 1 and carry 1 to the tens place), so C + F = 11.
D is a 3-digit number such that the ratio of the number to the sum of its digits is least. What is the difference between the digit at the hundred's place and the digit at the unit's place of D ?
UPSC's answer: (c) — For D = 100a + 10b + c, the ratio D ÷ (a + b + c) is smallest when the hundreds digit is small and the other two digits are large. With hundreds digit 1, the number 199 gives 199 ÷ 19 ≈ 10.47; neighbours give more — 189 ÷ 18 = 10.5, 198 ÷ 18 = 11, 188 ÷ 17 ≈ 11.06.
Which one of the following statements best reflects the crucial message conveyed by the author of the passage ?
UPSC's answer: (c) — The passage states that current emissions will affect the climate from the middle of the century onwards, creating immediate long-term consequences. It highlights that technological change is uncertain; it might make the transition away from fossil fuels cheap, or it might not.
Which one of the following statements best implies the most rational assumption that can be made from the passage ?
UPSC's answer: (a) — The passage states that substantial lifestyle changes to reduce environmental or health problems are 'almost impossible to adopt' due to collective lethargy and perceived negligible individual impact.
Which one of the following statements best reflects the crux of the passage ?
UPSC's answer: (b) — The passage highlights that poor dietary choices and limited access to nutritious food are increasing non-communicable diseases and burdening health-care systems. It argues that this burden threatens economic progress, which is essential for poverty alleviation.
Three of the five positive integers p, q, r, s, t are even and two of them are odd (not necessarily in order). Consider the following : 1. p + q + r - s - t is definitely even. 2. 2p + q + 2r - 2s + t is definitely odd. Which of the above statements is/are correct ?
UPSC's answer: (a) — There are exactly three even and two odd integers among p, q, r, s, t. In statement 1, subtraction does not change parity, so p + q + r - s - t has the same parity as p + q + r + s + t. The sum of three even numbers and two odd numbers is even, so statement 1 is definitely even.
Consider the following in respect of prime number p and composite number c. 1. (p + c)/(p - c) can be even. 2. 2p + c can be odd. 3. pc can be odd. Which of the statements given above are correct ?
UPSC's answer: (d) — Each statement says 'can be', so a single valid example proves it. Statement 1: p = 5, c = 15 gives (p + c)/(p − c) = 20/(−10) = −2, which is even. Statement 2: p = 2, c = 9 gives 2p + c = 13, which is odd (any odd composite c works). Statement 3: p = 3, c = 9 gives pc = 27, which is odd.
A 3-digit number ABC, on multiplication with D gives 37DD where A, B, C and D are different non-zero digits. What is the value of A + B + C ?
UPSC's answer: (a) — ABC × D = 37DD means ABC × D = 3700 + 11D, so ABC = (3700 + 11D) ÷ D must be a whole 3-digit number. D = 1, 2 or 3 makes ABC too large (over 999); so try D = 4 to 9. D = 4: 3744 ÷ 4 = 936 — digits 9, 3, 6 and 4 are all different and non-zero, so it works.
For any choices of values of X, Y and Z, the 6-digit number of the form XYZXYZ is divisible by :
UPSC's answer: (d) — XYZXYZ = XYZ × 1000 + XYZ = XYZ × 1001. 1001 = 7 × 11 × 13. So every number of this form is divisible by 7, 11 and 13, whatever the digits X, Y and Z. Hence option (d).
125 identical cubes are arranged in the form of a cubical block. How many cubes are surrounded by other cubes from each side ?
UPSC's answer: (a) — 125 = 5 × 5 × 5, so the block is 5 cubes along each edge. A cube is surrounded on every side only if it does not lie on any outer face. Removing the outer layer on each side leaves an inner block of (5 − 2) × (5 − 2) × (5 − 2) = 3 × 3 × 3. That inner block has 27 cubes, option (a).
How many distinct 8-digit numbers can be formed by rearranging the digits of the number 11223344 such that odd digits occupy odd positions and even digits occupy even positions ?
UPSC's answer: (c) — The number 11223344 contains two 1s, two 2s, two 3s, and two 4s. Odd digits are 1, 1, 3, 3 (four digits) and even digits are 2, 2, 4, 4 (four digits). There are 4 odd positions (1st, 3rd, 5th, 7th) and 4 even positions (2nd, 4th, 6th, 8th).
A, B, C working independently can do a piece of work in 8, 16 and 12 days respectively. A alone works on Monday, B alone works on Tuesday, C alone works on Wednesday; A alone, again works on Thursday and so on. Consider the following statements : 1. The work will be finished on Thursday. 2. The work will be finished in 10 days. Which of the above statements is/are correct ?
UPSC's answer: (a) — The total work is taken as the LCM of 8, 16, and 12, which is 48 units, so A completes 6 units per day, B completes 3 units per day, and C completes 4 units per day.
Which one of the following statements best reflects the most logical and rational implication conveyed by the passage ?
UPSC's answer: (b) — The passage argues that drastic, arbitrary measures like odd-even schemes or banning specific vehicle types are ineffective because they do not address the root causes of pollution.
Which of the following statements best reflects the logical inference from the passage given above ?
UPSC's answer: (b) — The passage states that effective corporate governance enhances access to external financing by firms. It further explains that investors place funds where standards of disclosure, timely and accurate financial reporting, and equal treatment are met.
Which one of the following statements best reflects the most logical and rational inference that can be drawn from the passage ?
UPSC's answer: (b) — The passage describes elephants as 'landscape architects' who create clearings, prevent overgrowth, and allow regeneration of other plant species.
If 7 ⊕ 9 ⊕ 10 = 8, 9 ⊕ 11 ⊕ 30 = 5, 11 ⊕ 17 ⊕ 21 = 13, what is the value of 23 ⊕ 4 ⊕ 15 ?
UPSC's answer: (a) — Add the three numbers in each expression: 7+9+10=26, 9+11+30=50, 11+17+21=49. Add the digits of that sum: 2+6=8, 5+0=5, 4+9=13. Apply the same rule to 23+4+15=42. Add the digits: 4+2=6, so option (a) follows.
Let x be a positive integer such that 7x + 96 is divisible by x. How many values of x are possible ?
UPSC's answer: (c) — (7x + 96) ÷ x = 7 + 96 ÷ x, so x must divide 96 exactly. 96 = 2⁵ × 3, so the number of positive divisors is (5 + 1) × (1 + 1) = 12. They are 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48 and 96. Hence 12 values, option (c).
If p, q, r and s are distinct single digit positive numbers, then what is the greatest value of (p + q)(r + s) ?
UPSC's answer: (b) — Let A = p + q and B = r + s; then A + B is the sum of four distinct digits from 1 to 9, so A + B ≤ 9 + 8 + 7 + 6 = 30. For any positive A and B with fixed sum T, the product AB is maximized when A and B are as close as possible, so AB ≤ (T/2)². Since T ≤ 30, AB ≤ (30/2)² = 225.
A number N is formed by writing 9 for 99 times. What is the remainder if N is divided by 13 ?
UPSC's answer: (a) — N (ninety-nine 9s) = 10⁹⁹ − 1. Remainders of powers of 10 on division by 13: 10 → 10, 10² → 9, 10³ → 12 (that is, −1), so 10⁶ leaves 1 and the pattern repeats every 6. 99 = 6 × 16 + 3, so 10⁹⁹ leaves the same remainder as 10³, i.e. 12. N = 10⁹⁹ − 1 therefore leaves 12 − 1 = 11, option (a).
Each digit of a 9-digit number is 1. It is multiplied by itself. What is the sum of the digits of the resulting number ?
UPSC's answer: (c) — The number is 111111111 (nine 1s). 111111111 × 111111111 = 12345678987654321. Its digits rise 1 to 9 and fall back to 1, so the digit sum is 2 × (1 + 2 + … + 8) + 9 = 2 × 36 + 9 = 81. Hence option (c).
What is the sum of all digits which appear in all the integers from 10 to 100 ?
UPSC's answer: (b) — The integers from 10 to 100 consist of 91 numbers: 90 two-digit numbers (10-99) and one three-digit number (100). For the number 100, the sum of digits is 1 + 0 + 0 = 1.
ABCD is a square. One point on each of AB and CD; and two distinct points on each of BC and DA are chosen. How many distinct triangles can be drawn using any three points as vertices out of these six points ?
UPSC's answer: (c) — There are 6 points in all: one on AB, one on CD, two on BC and two on DA. Any 3 of the 6 can be chosen in 6C3 = 20 ways. Three points fail to make a triangle only if they lie on one straight line; points on different sides of a square are never collinear, and no side holds three points.
Based on the above passage, the following assumptions have been made : 1. Collection, processing and segregation of municipal waste should be with government agencies. 2. Resource recovery and recycling require technological inputs that can be best handled by private sector enterprises. Which of the assumptions given above is/are correct ?
UPSC's answer: (d) — Assumption 1 is not supported: the passage describes where the municipal budget goes (collection and transport) but never says that collection, processing and segregation should be with government agencies.
Which one of the following statements best reflects the crux of the passage ?
UPSC's answer: (c) — The passage explicitly states that waste-to-energy ideally fits in the chain 'after segregation' and 'before getting to the landfill'. It highlights that segregation at source is currently rare in India, implying it is a critical missing link.
Based on the above passage, the following assumptions have been made : 1. Organic farming is inherently unsafe for both farmers and consumers. 2. Farmers and consumers need to be educated about eco-friendly food. Which of the assumptions given above is/are correct ?
UPSC's answer: (b) — The passage opens by reporting a claim that organic farming is inherently safer and healthier, and then questions it: in India the sector is young and poorly regulated.
Which one of the following statements best reflects the most logical, rational and practical message conveyed by the author of the passage ?
UPSC's answer: (c) — The passage highlights that the organic farming industry in India is young and lacks proper regulation, leading to confusion among farmers and consumers.
Based on the above passage, the following assumptions have been made : 1. To implement the Sustainable Development Goals and to achieve zero-hunger goal, monoculture agriculture practices are inevitable even if they do not address malnutrition. 2. Dependence on a few crops has negative consequences for human health and the ecosystem. 3. Government policies regarding food planning need to incorporate nutritional security. 4. For the present monoculture agriculture practices, farmers receive subsidies in various ways and government offers remunerative prices for grains and therefore they do not tend to consider crop diversity. Which of the above assumptions are valid ?
UPSC's answer: (b) — Assumption 1 is invalid because the passage explicitly states that monoculture practices perpetuate food and nutrition security problems, contradicting the idea that they are inevitable for achieving zero-hunger.
A box contains 14 black balls, 20 blue balls, 26 green balls, 28 yellow balls, 38 red balls and 54 white balls. Consider the following statements : 1. The smallest number n such that any n balls drawn from the box randomly must contain one full group of at least one colour is 175. 2. The smallest number m such that any m balls drawn from the box randomly must contain at least one ball of each colour is 167. Which of the above statements is/are correct ?
UPSC's answer: (c) — To find the smallest n that guarantees a full group of at least one colour, we first find the maximum number of balls that can be drawn while still missing at least one ball of every colour: 13 black, 19 blue, 25 green, 27 yellow, 37 red, and 53 white, giving 13 + 19 + 25 + 27 + 37 + 53 = 174.
If 'ZERO' is written as 'CHUR', then how is 'PLAYER' written ?
UPSC's answer: (d) — In 'ZERO', each letter is shifted forward by 3 places in the alphabet: Z to C, E to H, R to U, O to R. Apply the same +3 shift to P, L, A, Y, E, R in 'PLAYER'. P+3=S, L+3=O, A+3=D, Y+3=B, E+3=H, R+3=U. Therefore 'PLAYER' is written as SODBHU, which is option (d).
Consider the following statements : 1. A is older than B. 2. C and D are of the same age. 3. E is the youngest. 4. F is younger than D. 5. F is older than A. How many statements given above are required to determine the oldest person/persons ?
UPSC's answer: (d) — Statement 3 establishes that E is the youngest, but this does not identify the oldest person among the others. Statement 2 states C and D are the same age, but without knowing their position relative to others, their age is undetermined.
Consider the following including the Question and the Statements : There are 5 members A, B, C, D, E in a family. Question : What is the relation of E to B ? Statement-1 : A and B are a married couple. Statement-2 : D is the father of C. Statement-3 : E is D's son. Statement-4 : A and C are sisters. Which one of the following is correct in respect of the above Question and Statements ?
UPSC's answer: (c) — Statement-4 makes A and C sisters, so A is female and A and C have the same father. Statement-2 says D is the father of C, so D is the father of A. Statement-3 says E is D's son, so E is A's brother.
Choose the group which is different from the others :
UPSC's answer: (d) — Option (a) contains 17, 37, 47, and 97, all of which are prime numbers. Option (b) contains 31, 41, 53, and 67, all of which are prime numbers. Option (c) contains 71, 73, 79, and 83, all of which are prime numbers.
With reference to the above passage, the following assumptions have been made : 1. Global warming is causing spring to come early and for longer durations. 2. Early spring and longer period of spring is not good for bird populations. Which of the above assumptions is/are correct ?
UPSC's answer: (a) — The passage states that warmer winters with less snow result in a 'longer lag time' and a 'more protracted vernal window,' which supports the assumption that global warming is causing spring to last for longer durations.
Which one of the following statements best reflects the most logical, rational and crucial message implied by the passage ?
UPSC's answer: (a) — The passage highlights that the global average nitrogen use efficiency is only 0.4, meaning 60% of added nitrogen is lost to the environment as pollution.
Which one of the following statements best reflects the most logical, rational and crucial message conveyed by the passage ?
UPSC's answer: (a) — The passage identifies climate justice as a significant principle that has 'eluded consensus' in past climate change summits and compacts. It defines the scope of climate justice to include mitigation, adaptation support, and compensation for loss and damage, not just mitigation.
A principal P becomes Q in 1 year when compounded half-yearly with R% annual rate of interest. If the same principal P becomes Q in 1 year when compounded annually with S% annual rate of interest, then which one of the following is correct ?
UPSC's answer: (c) — Half-yearly compounding at R% a year for one year: Q = P × (1 + R/200) × (1 + R/200). Annual compounding at S%: Q = P × (1 + S/100). Equating: 1 + S/100 = 1 + R/100 + R²/40000, so S = R + R²/400. For any positive rate R²/400 > 0, so S is strictly greater than R — option (c), R < S.
How many natural numbers are there which give a remainder of 31 when 1186 is divided by these natural numbers ?
UPSC's answer: (d) — If 1186 leaves remainder 31 on division by n, then n divides 1186 − 31 = 1155, and n must be greater than 31. 1155 = 3 × 5 × 7 × 11, which has 2 × 2 × 2 × 2 = 16 divisors. The divisors up to 31 are 1, 3, 5, 7, 11, 15 and 21 — seven of them.
Let pp, qq and rr be 2-digit numbers where p < q < r. If pp + qq + rr = tt0, where tt0 is a 3-digit number ending with zero, consider the following statements : 1. The number of possible values of p is 5. 2. The number of possible values of q is 6. Which of the above statements is/are correct ?
UPSC's answer: (c) — pp, qq, rr are repdigits, so pp=11p, qq=11q, rr=11r, and tt0=110t. Equation gives 11(p+q+r)=110t, hence p+q+r=10t. Since p,q,r are distinct digits 1 to 9 with p<q<r, their sum can only be 10 or 20.
What is the sum of all 4-digit numbers less than 2000 formed by the digits 1, 2, 3 and 4, where none of the digits is repeated ?
UPSC's answer: (a) — The 4-digit numbers must be less than 2000, so the thousands digit must be 1. The remaining three digits (2, 3, 4) can be arranged in the hundreds, tens, and units places in 3! = 6 ways. The sum of the digits in the thousands place is 1 × 6 = 6.
What is the number of selections of 10 consecutive things out of 12 things in a circle taken in the clockwise direction ?
UPSC's answer: (c) — In a circle of 12 things, a block of 10 consecutive things taken clockwise is fixed completely by its starting point. Any of the 12 things can be the starting point, and each start gives a different block (because 10 is less than 12).
If today is Sunday, then which day is it exactly on 10¹⁰ th day ?
UPSC's answer: (a) — The key treats today (Sunday) as day 1, so the 10¹⁰th day falls 10¹⁰ − 1 days after today. Remainders of 10ⁿ on division by 7 repeat every 6 (10 → 3, 10² → 2, 10³ → 6, 10⁴ → 4, 10⁵ → 5, 10⁶ → 1); since 10 = 6 + 4, 10¹⁰ leaves the same remainder as 10⁴, which is 4.
There are three traffic signals. Each signal changes colour from green to red and then from red to green. The first signal takes 25 seconds, the second signal takes 39 seconds and the third signal takes 60 seconds to change the colour from green to red. The durations for green and red colours are same. At 2:00 p.m, they together turn green. At what time will they change to green next, simultaneously ?
UPSC's answer: (b) — Each signal's full cycle (green to red and back to green) is twice the given green-to-red duration: Signal 1 = 50s, Signal 2 = 78s, Signal 3 = 120s. The signals turn green simultaneously again after the Least Common Multiple (LCM) of their cycle durations.
Which one of the following statements best reflects the most logical and rational message conveyed by the author of the passage ?
UPSC's answer: (d) — The passage explicitly states that sourcing food from non-agricultural lands (like forests and wetlands) 'in addition to' agricultural lands enables a systemic approach to food consumption.
Which one of the following statements best reflects the most logical and practical message conveyed by the passage ?
UPSC's answer: (a) — The passage explicitly identifies the 'environmental impact of antibiotics-manufacturing companies not treating their waste' as the primary, under-discussed issue. It establishes a direct causal link between this untreated waste and the rise of drug-resistant infections around pharma plants.
Which one of the following statements best reflects the crux of the passage ?
UPSC's answer: (a) — The passage argues that the benefits of good quality school education are realized only when students acquire foundational 'gateway skills' before moving to advanced levels.
40 children are standing in a circle and one of them (say child-1) has a ring. The ring is passed clockwise. Child-1 passes on to child-2, child-2 passes on to child-4, child-4 passes on to child-7 and so on. After how many such changes (including child-1) will the ring be in the hands of child-1 again ?
UPSC's answer: (b) — The ring moves 1, then 2, then 3 places, and so on, so after n passes it has moved 1 + 2 + … + n = n(n + 1)/2 places. It is back with child-1 when this total is a multiple of 40. n = 14 gives 105 (child 26 — not a multiple of 40); n = 15 gives 120 = 3 × 40.
What is the middle term of the sequence Z, Z, Y, Y, Y, X, X, X, X, W, W, W, W, W, ..., A ?
UPSC's answer: (b) — Z appears 2 times, Y 3 times, X 4 times and so on, so the k-th letter from Z appears k + 1 times, down to A (the 26th) appearing 27 times. Total terms = 2 + 3 + … + 27 = 377, so the middle term is the 189th.
Question : Is p greater than q ? Statement-1 : p × q is greater than zero. Statement-2 : p² is greater than q². Which one of the following is correct in respect of the above Question and the Statements ?
UPSC's answer: (d) — Statement 1 states that p × q > 0, which implies that p and q have the same sign (both positive or both negative), but it does not determine their relative magnitudes.
Question : Is (p + q - r) greater than (p - q + r), where p, q and r are integers ? Statement-1 : (p - q) is positive. Statement-2 : (p - r) is negative. Which one of the following is correct in respect of the above Question and the Statements ?
UPSC's answer: (c) — The question asks if (p + q - r) > (p - q + r), which simplifies to 2q > 2r, or q > r. Statement 1 states (p - q) > 0, implying p > q. This does not provide any information about the relationship between q and r, so it is insufficient alone. Statement 2 states (p - r) < 0, implying p < r.
In a party, 75 persons took tea, 60 persons took coffee and 15 persons took both tea and coffee. No one taking milk takes tea. Each person takes at least one drink. Question : How many persons attended the party ? Statement-1 : 50 persons took milk. Statement-2 : Number of persons who attended the party is five times the number of persons who took milk only. Which one of the following is correct in respect of the above Question and the Statements ?
UPSC's answer: (a) — From the given data, tea drinkers = 75, coffee drinkers = 60, and tea ∩ coffee = 15, so the number of people who take tea or coffee (or both) is 75 + 60 − 15 = 120.
Consider a 3-digit number. Question : What is the number ? Statement-1 : The sum of the digits of the number is equal to the product of the digits. Statement-2 : The number is divisible by the sum of the digits of the number. Which one of the following is correct in respect of the above Question and the Statements ?
UPSC's answer: (d) — Let the 3-digit number have digits a, b, c (a from 1 to 9, b and c from 0 to 9). Statement 1 requires a + b + c = a × b × c. If any digit is 0 the product is 0 while the sum is at least 1, so all digits are at least 1. Setting one digit to 1 and the other two to p and q gives 1 + p + q = pq, i.e.
For five children with ages a < b < c < d < e; any two successive ages differ by 2 years. Question : What is the age of the youngest child ? Statement-1 : The age of the eldest is 3 times the youngest. Statement-2 : The average age of the children is 8 years. Which one of the following is correct in respect of the above Question and the Statements ?
UPSC's answer: (b) — Let the ages of the five children be a, a+2, a+4, a+6, and a+8, where 'a' is the age of the youngest child. Using Statement-1: The eldest child's age is a+8. The statement says a+8 = 3a, which simplifies to 2a = 8, giving a = 4. This uniquely determines the youngest child's age.
Which one of the following statements best reflects the most logical message implied by the above passage ?
UPSC's answer: (d) — The passage introduces the 'paradox of choice' using the story of Buridan's ass, which starves because it cannot choose between two equally appealing options. It states that modern technology and constant connectivity exacerbate the 'glut of choices,' making decisions more difficult.
Regarding the financialization of household savings, which of the following statements best reflect the solutions that are implied by the passage ? 1. A flexible environment is needed to develop solutions. 2. Households need customised solutions. 3. Innovations in financial technology are required. Select the correct answer using the code given below :
UPSC's answer: (d) — The passage identifies 'onerous bureaucracy' as a hurdle, implying that a 'flexible environment' is needed to develop solutions, supporting statement 1.
Based on the above passage, the following assumptions have been made : 1. Patent protection given to patentees puts a huge burden on public's purchasing power in accessing patented medicines. 2. Dependence on other countries for pharmaceutical products is a huge burden for developing and poor countries. 3. Providing medicines to the public at affordable prices is a key goal during the public health policy design in many countries. 4. Governments need to find an appropriate balance between the rights of patentees and the requirements of the patients. Which of the above assumptions are valid ?
UPSC's answer: (b) — Assumption 1 is valid because the passage explicitly states that patentees determine prices which 'could be unaffordable to the public,' implying a burden on purchasing power.
Based on the above passage, the following assumptions have been made : 1. Protection of privacy is not just a right, but it has value to the economy. 2. There is a fundamental link between privacy and innovation. Which of the above assumptions is/are valid ?
UPSC's answer: (c) — The passage explicitly states that India must ensure digital economy growth while keeping personal data secure, directly linking privacy protection to economic value, which validates Assumption 1.
In an examination, the maximum marks for each of the four papers namely P, Q, R and S are 100. Marks scored by the students are in integers. A student can score 99% in n different ways. What is the value of n ?
UPSC's answer: (d) — The total maximum marks for the four papers P, Q, R, and S is 400. Scoring 99% means the student must obtain exactly 396 marks (0.99 * 400). This is equivalent to losing exactly 4 marks from the maximum possible score (400 - 396 = 4).
A flag has to be designed with 4 horizontal stripes using some or all of the colours red, green and yellow. What is the number of different ways in which this can be done so that no two adjacent stripes have the same colour ?
UPSC's answer: (c) — The first stripe can be any of the 3 colours. Each later stripe must differ from the one just above it, leaving 2 choices each for stripes 2, 3 and 4. Total = 3 × 2 × 2 × 2 = 24. ('Some or all' colours is automatically satisfied, since at least two colours are always used.) Hence option (c).
A rectangular floor measures 4 m in length and 2·2 m in breadth. Tiles of size 140 cm by 60 cm have to be laid such that the tiles do not overlap. A tile can be placed in any orientation so long as its edges are parallel to the edges of the floor. What is the maximum number of tiles that can be accommodated on the floor ?
UPSC's answer: (d) — Floor: 400 cm × 220 cm = 88,000 cm²; tile: 140 cm × 60 cm = 8,400 cm². Area alone would allow at most 10 tiles, but the shapes do not allow that many. Simple layouts give only 8, e.g. six tiles laid lengthwise in a 280 × 180 block plus two upright tiles in the remaining 120 cm strip.
There are five persons P, Q, R, S and T each one of whom has to be assigned one task. Neither P nor Q can be assigned Task-1. Task-2 must be assigned to either R or S. In how many ways can the assignment be done ?
UPSC's answer: (d) — Five people take five tasks with one task each, so an assignment is a one-to-one matching of the five people to the five tasks. Task-2 must go to R or S, which splits the count into two cases. Take Task-2 = R.
Consider the following : I. A + B means A is neither smaller nor equal to B. II. A - B means A is not greater than B. III. A × B means A is not smaller than B. IV. A ÷ B means A is neither greater nor equal to B. V. A ± B means A is neither smaller nor greater than B. Statement : P × Q, P - T, T ÷ R, R ± S Conclusion-1 : Q ± T Conclusion-2 : S + Q Which one of the following is correct in respect of the above Statement and the Conclusions ?
UPSC's answer: (b) — Translate the codes: '×' means ≥, '-' means ≤, '÷' means <, '±' means =, and '+' means >. The statement P × Q, P - T, T ÷ R, R ± S translates to P ≥ Q, P ≤ T, T < R, and R = S. Combining these gives the chain: Q ≤ P ≤ T < R = S, which simplifies to Q < S. Conclusion-1 states Q ± T (Q = T).
Which one of the following statements most likely reflects as to what the author of the passage intends to say ?
UPSC's answer: (b) — The passage states that the standard unemployment rate is an inaccurate measure of economic performance in India due to rising school and college enrolment.
Which one of the following statements best reflects the most rational, logical and practical message conveyed by the passage ?
UPSC's answer: (b) — The passage argues that both science and government require an external guiding force (philosophy/statesmanship) to coordinate their efforts and set correct goals, preventing them from becoming superficial or destructive.
Based on the above passage, which one of the following terms best expresses the ultimate goal of the state ?
UPSC's answer: (d) — The passage explicitly states that the end of the state is to 'free each man from fear' so he may live with 'full security'. It further clarifies that the goal is to enable bodies and minds to function safely, not to restrain or dominate.
What is the remainder if 2¹⁹² is divided by 6 ?
UPSC's answer: (d) — Powers of 2 on division by 6 leave remainders 2, 4, 2, 4, … : 2¹ → 2, 2² → 4, 2³ = 8 → 2, 2⁴ = 16 → 4. Odd powers leave 2 and even powers leave 4. 192 is even, so 2¹⁹² leaves remainder 4. Hence option (d).
Consider the sequence ABC_ _ ABC_ DABBCD_ ABCD that follows a certain pattern. Which one of the following completes the sequence ?
UPSC's answer: (d) — The sequence is composed of four 4-letter blocks: 'ABC_', '_ABC', '_DAB', 'BCD_'. Analyzing the first block 'ABC_', the missing letter must be 'D' to form the set {A, B, C, D}, making it 'ABCD'.
AB and CD are 2-digit numbers. Multiplying AB with CD results in a 3-digit number DEF. Adding DEF to another 3-digit number GHI results in 975. Further A, B, C, D, E, F, G, H, I are distinct digits. If E = 0, F = 8, then what is A + B + C equal to ?
UPSC's answer: (a) — Since E = 0 and F = 8, the product DEF is D08, which is a 3-digit number ending in 8. The sum DEF + GHI = 975 implies D08 + GHI = 975, so GHI = 975 - D08.
Consider the following statements in respect of five candidates P, Q, R, S and T. Two statements are true and one statement is false. True Statement : One of P and Q was selected for the job. False Statement : At least one of R and S was selected for the job. True Statement : At most two of R, S and T were selected for the job. Which of the following conclusions can be drawn ? 1. At least four were selected for the job. 2. S was selected for the job. Select the correct answer using the code given below :
UPSC's answer: (d) — The false statement 'At least one of R and S was selected' implies that neither R nor S was selected for the job. Since R and S are not selected, the condition 'At most two of R, S and T were selected' is automatically satisfied regardless of T's status, as the count of selected candidates among…
Let P, Q, R, S and T be five statements such that : I. If P is true, then both Q and S are true. II. If R and S are true, then T is false. Which of the following can be concluded ? 1. If T is true, then at least one of P and R must be false. 2. If Q is true, then P is true. Select the correct answer using the code given below :
UPSC's answer: (a) — Statement I is P → (Q and S), so P true forces S true. Statement II is (R and S) → not T, so if T is true, R and S cannot both be true. If T is true and both P and R were true, P true would make S true, so R and S would both be true.
A cuboid of dimensions 7 cm × 5 cm × 3 cm is painted red, green and blue colour on each pair of opposite faces of dimensions 7 cm × 5 cm, 5 cm × 3 cm, 7 cm × 3 cm respectively. Then the cuboid is cut and separated into various cubes each of side length 1 cm. Which of the following statements is/are correct ? 1. There are exactly 15 small cubes with no paint on any face. 2. There are exactly 6 small cubes with exactly two faces, one painted with blue and the other with green. Select the correct answer using the code given below :
UPSC's answer: (a) — The cuboid dimensions are 7 cm × 5 cm × 3 cm, so the number of unpainted cubes (interior) is (7-2) × (5-2) × (3-2) = 5 × 3 × 1 = 15, making statement 1 correct. The faces are painted as follows: 7×5 faces are Red, 5×3 faces are Green, and 7×3 faces are Blue.
Question paper and answer key: Union Public Service Commission. Explanations: UPSC Answer Check. Practise this paper with a timer →
Practise Prelims PYQs and the daily 21 free
Score the daily set, see your rank, and let Guru explain what you missed.
Already have an account? Log in