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Data Sufficiency — UPSC CSAT Paper II Quantitative Aptitude previous year questions
20 free solved previous year questions on Data Sufficiency, papers from 2020 to 2026, drawn from UPSC CSAT, covering questions of the kind UPSC asks in CSAT Paper II. Every answer key has been checked again against published sources and solved independently, and each explanation is written fresh.
Read all 20 questions with answers
- #1UPSC CSAT 2026X receives three coins of different denominations out of 1, 2, 5, 10 and 20. If the total amount received by X is m, does X receive a coin of denomination 5?Statement I: m is not a prime number.Statement II: The sum of the digits of m is greater than 5.
- AThe question can be answered using one of the statements alone, but cannot be answered using the other statement.
- BThe question can be answered using either statement alone.
- CThe question can be answered using both the statements together, but cannot be answered using either statement alone.
- DThe question cannot be answered even using both the statements together.
Answer: (A) The question can be answered using one of the statements alone, but cannot be answered using the other statement.Explanation
List all 10 ways of picking 3 different coins from 1, 2, 5, 10, 20.
Sums with a 5-coin: 8, 16, 26, 17, 27, 35.
Sums without a 5-coin: 13, 23, 31, 32.
Statement I: non-prime sums are 8, 16, 26, 27, 35 and also 32. 32 has no 5-coin, so I alone cannot answer.
Statement II: the digit sum is above 5 for every sum with a 5-coin (8, 16, 26, 17, 27, 35). It is 5 or less for 13, 23, 31, 32.
So II alone settles the question; I does not.
Answer: (a).Source: UPSC CSAT 2026 Paper II (Set A); answer key checked by independent computation and against UPSC's provisional key
- #2UPSC CSAT 2026For two distinct real numbers x and y, which of them is bigger?Statement I: x² < y < 1Statement II: y < √x < 1
- AThe question can be answered using one of the statements alone, but cannot be answered using the other statement.
- BThe question can be answered using either statement alone.
- CThe question can be answered using both the statements together, but cannot be answered using either statement alone.
- DThe question cannot be answered even using both the statements together.
Answer: (D) The question cannot be answered even using both the statements together.Explanation
Statement I: take x = 0.5, y = 0.3. Then 0.25 < 0.3 < 1, so x is bigger.
Now take x = 0.1, y = 0.5. Then 0.01 < 0.5 < 1, so y is bigger. I alone fails.
Statement II: take x = 0.25, y = 0.1. Then 0.1 < 0.5 < 1, so x is bigger.
Now take x = 0.25, y = 0.4. Then 0.4 < 0.5 < 1, so y is bigger. II alone fails.
Both together: x = 0.25 needs 0.0625 < y < 0.5. Both y = 0.1 and y = 0.4 fit.
So even together they cannot decide. Answer: (d).Source: UPSC CSAT 2026 Paper II (Set A); answer key checked by independent computation and against UPSC's provisional key
- #3UPSC CSAT 2026If x and y are integers, then is x even?Statement I: x²y² is even.Statement II: 1 + x² + y² is odd.
- AThe question can be answered using one of the statements alone, but cannot be answered using the other statement.
- BThe question can be answered using either statement alone.
- CThe question can be answered using both the statements together, but cannot be answered using either statement alone.
- DThe question cannot be answered even using both the statements together.
Answer: (C) The question can be answered using both the statements together, but cannot be answered using either statement alone.Explanation
Statement I: x²y² is even when at least one of x, y is even. The even one could be y, so x may be odd. I alone fails.
Statement II: 1 + x² + y² is odd, so x² + y² is even.
This means x and y have the same parity (both odd or both even). II alone fails.
Together: at least one is even and both have the same parity.
So both are even, and x is even.
Both statements are needed. Answer: (c).Source: UPSC CSAT 2026 Paper II (Set A); answer key checked by independent computation and against UPSC's provisional key
- #4UPSC CSAT 2026X is a collection of certain odd numbers whereas Y is a collection of certain even numbers. T consists of numbers all of which are either from X or from Y. Is every number of T from Y?Statement I: The sum of any two numbers belonging to T is even.Statement II: If both p and q are picked from T, then (p – 1)q is even.
- AThe question can be answered using one of the statements alone, but cannot be answered using the other statement.
- BThe question can be answered using either statement alone.
- CThe question can be answered using both the statements together, but cannot be answered using either statement alone.
- DThe question cannot be answered even using both the statements together.
Answer: (D) The question cannot be answered even using both the statements together.Explanation
Statement I: a sum of two numbers is even only if both are odd or both even. So T is all odd or all even. We cannot tell which. I alone fails.
Statement II: (p – 1)q is odd only when p is even and q is odd. It must never be odd, so T cannot hold both an even and an odd number.
Again T is all odd or all even. II alone fails.
Both statements give the same information, so together they still cannot decide.
Answer: (d).Source: UPSC CSAT 2026 Paper II (Set A); answer key checked by independent computation and against UPSC's provisional key
- #5UPSC CSAT 2026If x, y and z are integers, each greater than 1, then is x a prime number?Statement I: xy² = 116Statement II: xz = 261
- AThe question can be answered using one of the statements alone, but cannot be answered using the other statement.
- BThe question can be answered using either statement alone.
- CThe question can be answered using both the statements together, but cannot be answered using either statement alone.
- DThe question cannot be answered even using both the statements together.
Answer: (A) The question can be answered using one of the statements alone, but cannot be answered using the other statement.Explanation
Statement I: 116 = 2² × 29. Since y > 1, y² must divide 116, so y = 2.
Then x = 116 ÷ 4 = 29, which is prime. I alone answers.
Statement II: 261 = 3² × 29. Since x > 1 and z > 1, x can be 3, 9, 29 or 87.
3 and 29 are prime, but 9 and 87 are not. II alone fails.
So only Statement I is enough. Answer: (a).Source: UPSC CSAT 2026 Paper II (Set A); answer key checked by independent computation and against UPSC's provisional key
- #6UPSC CSAT 2025A question is given followed by two Statements I and II. Consider the Question and the Statements and mark the correct option.Question: What is the smallest 1-digit number having exactly 4 distinct factors?Statement I: 2 is one of the factors.Statement II: 3 is one of the factors.Which one of the following is correct in respect of the above Question and the Statements?
- AThe Question can be answered by using one of the Statements alone, but cannot be answered using the other statement alone.
- BThe Question can be answered by using either Statement alone.
- CThe Question can be answered by using both the Statements together, but cannot be answered using either Statement alone.
- DThe Question can be answered even without using any of the Statements.
Answer: (D) The Question can be answered even without using any of the Statements.Explanation
Among 1-digit numbers, 6 (1,2,3,6) and 8 (1,2,4,8) have exactly four factors; the smallest is 6.
The answer is found without either statement.
Answer: option (d).Source: UPSC CSAT 2025 question; answer key checked by independent computation
- #7UPSC CSAT 2025A question is given followed by two Statements I and II. Consider the Question and the Statements and mark the correct option.Question: Is (p + q)^2 - 4pq, where p, q are natural numbers, positive?Statement I: p < q.Statement II: p > q.Which one of the following is correct in respect of the above Question and the Statements?
- AThe Question can be answered by using one of the Statements alone, but cannot be answered using the other statement alone.
- BThe Question can be answered by using either Statement alone.
- CThe Question can be answered by using both the Statements together, but cannot be answered using either Statement alone.
- DThe Question can be answered even without using any of the Statements.
Answer: (B) The Question can be answered by using either Statement alone.Explanation
(p + q)^2 - 4pq = (p - q)^2, which is positive exactly when p is not equal to q.
Statement I (p < q) and Statement II (p > q) each guarantee p is not equal to q.
Either statement alone is enough.
Answer: option (b).Source: UPSC CSAT 2025 question; answer key checked by independent computation
- #8UPSC CSAT 2024A Question is given followed by two Statements I and II. Consider the Question and the Statements.Question: What are the values of m and n, where m and n are natural numbers?Statement-I: m+n > mn and m > n.Statement-II: The product of m and n is 24.Which one of the following is correct in respect of the above Question and the Statements?
- AThe Question can be answered by using one of the Statements alone, but cannot be answered using the other Statement alone
- BThe Question can be answered by using either Statement alone
- CThe Question can be answered by using both the Statements together, but cannot be answered using either Statement alone
- DThe Question cannot be answered even by using both the Statements together
Answer: (C) The Question can be answered by using both the Statements together, but cannot be answered using either Statement aloneExplanation
I: m + n > mn means (m-1)(n-1) < 1, so with m > n we get n = 1 and m is any number; not unique.
II: mn = 24 has several pairs; not unique.
Together n = 1 and m = 24, a unique answer. Answer: option (c).Source: UPSC CSAT 2024 question; answer key checked by independent computation
- #9UPSC CSAT 2024A Question is given followed by two Statements I and II. Consider the Question and the Statements.Question: What is the time required to download the software?Statement-I: The size of the software is 12 megabytes.Statement-II: The transfer rate is 2.4 kilobytes per second.Which one of the following is correct in respect of the above Question and the Statements?
- AThe Question can be answered by using one of the Statements alone, but cannot be answered using the other Statement alone
- BThe Question can be answered by using either Statement alone
- CThe Question can be answered by using both the Statements together, but cannot be answered using either Statement alone
- DThe Question cannot be answered even by using both the Statements together
Answer: (C) The Question can be answered by using both the Statements together, but cannot be answered using either Statement aloneExplanation
Time = size / rate, so both quantities are needed.
Size alone gives no time, and rate alone gives no time.
Together the time can be found, so both statements are needed. Answer: option (c).Source: UPSC CSAT 2024 question; answer key checked by independent computation
- #10UPSC CSAT 2024A Question is given followed by two Statements I and II. Consider the Question and the Statements.Question: What are the unique values of x and y, where x, y are distinct natural numbers?Statement-I: x / y is odd.Statement-II: xy = 12Which one of the following is correct in respect of the above Question and the Statements?
- AThe Question can be answered by using one of the Statements alone, but cannot be answered using the other Statement alone.
- BThe Question can be answered by using either Statement alone.
- CThe Question can be answered by using both the Statements together, but cannot be answered using either Statement alone.
- DThe Question cannot be answered even by using both the Statements together.
Answer: (C) The Question can be answered by using both the Statements together, but cannot be answered using either Statement alone.Explanation
I alone: many pairs such as (3,1), (6,2), (15,3) have an odd quotient.
II alone: (1,12), (2,6), (3,4) and reverses are all possible.
With xy = 12 and an odd integer quotient, only (6,2) works, so both together are needed. Answer: option (c).Source: UPSC CSAT 2024 question; answer key checked by independent computation
- #11UPSC CSAT 2023Question: Is p greater than q?Statement-1: p x q is greater than zero.Statement-2: p^2 is greater than q^2.Which one of the following is correct in respect of the above Question and the Statements?
- AThe Question can be answered by using one of the Statements alone, but cannot be answered using the other Statement alone.
- BThe Question can be answered by using either Statement alone.
- CThe Question can be answered by using both the Statements together, but cannot be answered using either Statement alone.
- DThe Question cannot be answered even by using both the Statements together.
Answer: (D) The Question cannot be answered even by using both the Statements together.Explanation
Statement 1 only says p and q have the same sign.
Statement 2 only says |p| > |q|.
Together: p = 2, q = 1 satisfies both and gives yes; p = -2, q = -1 also satisfies both and gives no.
So even together the question cannot be answered.
Answer: option (d).Source: UPSC CSAT 2023 question; answer key checked by independent computation
- #12UPSC CSAT 2023Question: 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?
- AThe Question can be answered by using one of the Statements alone, but cannot be answered using the other Statement alone.
- BThe Question can be answered by using either Statement alone.
- CThe Question can be answered by using both the Statements together, but cannot be answered using either Statement alone.
- DThe Question cannot be answered even by using both the Statements together.
Answer: (C) The Question can be answered by using both the Statements together, but cannot be answered using either Statement alone.Explanation
(p+q-r) > (p-q+r) simplifies to q > r.
Statement 1 gives p > q only; statement 2 gives p < r only; neither fixes q against r alone.
Together q < p < r, so q < r and the answer to the question is definitely 'No'.
Answer: option (c).Source: UPSC CSAT 2023 question; answer key checked by independent computation
- #13UPSC CSAT 2023In 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?
- AThe Question can be answered by using one of the Statements alone, but cannot be answered using the other Statement alone.
- BThe Question can be answered by using either Statement alone.
- CThe Question can be answered by using both the Statements together, but cannot be answered using either Statement alone.
- DThe Question cannot be answered even by using both the Statements together.
Answer: (A) The Question can be answered by using one of the Statements alone, but cannot be answered using the other Statement alone.Explanation
Tea drinkers are 75 (60 tea only + 15 both); coffee only = 60 - 15 = 45.
Let x be milk-only persons; milk drinkers may also take coffee, which is already counted, so total = 75 + 45 + x = 120 + x.
Statement 1 gives x + (milk with coffee) = 50, which does not fix x.
Statement 2: 120 + x = 5x gives x = 30 and total 150, so it alone suffices.
Answer: option (a).Source: UPSC CSAT 2023 question; answer key checked by independent computation
- #14UPSC CSAT 2023Consider 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?
- AThe Question can be answered by using one of the Statements alone, but cannot be answered using the other Statement alone.
- BThe Question can be answered by using either Statement alone.
- CThe Question can be answered by using both the Statements together, but cannot be answered using either Statement alone.
- DThe Question cannot be answered even by using both the Statements together.
Answer: (D) The Question cannot be answered even by using both the Statements together.Explanation
Statement 1 holds only for the digits 1, 2, 3, so the number is one of 123, 132, 213, 231, 312, 321.
Statement 2 alone allows many numbers.
Together: the digit sum is 6, and both 132 and 312 are divisible by 6.
Two numbers fit, so the number is not unique.
Answer: option (d).Source: UPSC CSAT 2023 question; answer key checked by independent computation
- #15UPSC CSAT 2022Consider the Question and two Statements given below:Question: Is x an integer?Statement-1: x/3 is not an integer.Statement-2: 3x is an integer.Which one of the following is correct in respect of the Question and the Statements?
- AStatement-1 alone is sufficient to answer the Question
- BStatement-2 alone is sufficient to answer the Question
- CBoth Statement-1 and Statement-2 are sufficient to answer the Question
- DBoth Statement-1 and Statement-2 are not sufficient to answer the Question
Answer: (D) Both Statement-1 and Statement-2 are not sufficient to answer the QuestionExplanation
Statement-1: x = 1 gives x/3 non-integer and x is an integer; x = 1/2 also works and x is not an integer.
Statement-2: x = 1 and x = 1/3 both make 3x an integer, with different answers.
Together, x = 1 and x = 1/2 satisfy both, so still no unique answer.
Answer: option (d).Source: UPSC CSAT 2022 question; answer key checked by independent computation
- #16UPSC CSAT 2022Consider the Question and two Statements given below in respect three cities P, Q and R in a State:Question: How far is city P from city Q?Statement-1: City Q is 18 km from city R.Statement-2: City P is 43 km from city R.Which one of the following is correct in respect of the Question and the Statements?
- AStatement-1 alone is sufficient to answer the Question
- BStatement-2 alone is sufficient to answer the Question
- CBoth Statement-1 and Statement-2 are sufficient to answer the Question
- DBoth Statement-1 and Statement-2 are not sufficient to answer the Question
Answer: (D) Both Statement-1 and Statement-2 are not sufficient to answer the QuestionExplanation
The layout of the cities is not given. P, Q and R need not lie on one straight line.
With both statements, PQ can be anything from 25 km to 61 km depending on the angle at R.
So the data are not sufficient.
Answer: option (d).Source: UPSC CSAT 2022 question; answer key checked by independent computation
- #17UPSC CSAT 2022Consider the Question and two Statements given below:Question: What is the age of Manisha?Statement-1: Manisha is 24 years younger than her mother.Statement-2: 5 years later, the ages of Manisha and her mother will be in the ratio 3:5.Which one of the following is correct in respect of the Question and the Statements?
- AStatement-1 alone is sufficient to answer the Question
- BStatement-2 alone is sufficient to answer the Question
- CBoth Statement-1 and Statement-2 are sufficient to answer the Question
- DBoth Statement-1 and Statement-2 are not sufficient to answer the Question
Answer: (C) Both Statement-1 and Statement-2 are sufficient to answer the QuestionExplanation
Statement-1 gives only the difference of 24 years; Statement-2 gives only a ratio, so neither alone fixes the age.
Together: (M+5)/(M+29) = 3/5 gives 5M + 25 = 3M + 87, so M = 31.
Both statements are needed.
Answer: option (c).Source: UPSC CSAT 2022 question; answer key checked by independent computation
- #18UPSC CSAT 2021Consider two Statements and a Question:Statement-1: Priya is 4 ranks below Seema and is 31st from the bottom.Statement-2: Ena is 2 ranks above Seema and is 37th from the bottom.Question: What is Seema's rank from the top in the class of 40 students?Which one of the following is correct in respect of the Statements and the Question?
- AStatement-1 alone is not sufficient to answer the Question
- BStatement-2 alone is not sufficient to answer the Question
- CEither Statement-1 alone or Statement-2 alone is sufficient to answer the Question
- DBoth Statement-1 and Statement-2 are required to answer the Question
Answer: (C) Either Statement-1 alone or Statement-2 alone is sufficient to answer the QuestionExplanation
Statement-1: Priya is 31st from bottom and Seema is 4 ranks above her, so Seema is 35th from bottom.
Statement-2: Ena is 37th from bottom and Seema is 2 ranks below her, so Seema is again 35th from bottom.
Either gives rank from top = 40 - 35 + 1 = 6.
Answer: option (c).Source: UPSC CSAT 2021 question; answer key checked by independent computation
- #19UPSC CSAT 2020Two Statements S1 and S2 are given below with regard to four numbers P, Q, R and S followed by a Question:S1: R is greater than P as well as Q.S2: S is not the largest one.Question: Among four numbers P, Q, R and S which one is the largest?Which one of the following is correct in respect of the above Statements and the Question?
- AS1 alone is sufficient to answer the Question.
- BS2 alone is sufficient to answer the Question.
- CS1 and S2 together are sufficient to answer the Question, but neither S1 alone nor S2 alone is sufficient to answer the Question.
- DS1 and S2 together are not sufficient to answer the Question.
Answer: (C) S1 and S2 together are sufficient to answer the Question, but neither S1 alone nor S2 alone is sufficient to answer the Question.Explanation
S1 alone leaves S and R both possible as the largest. S2 alone leaves P, Q or R possible.
Together: R beats P and Q, and S is not the largest, so R is the largest.
Answer: option (c).Source: UPSC CSAT 2020 question; answer key checked by independent computation
- #20UPSC CSAT 2020Two Statements S1 and S2 are given below followed by a Question:S1: n is a prime number.S2: n leaves a remainder of 1 when divided by 4.Question: If n is a unique natural number between 10 and 20, then what is n?Which one of the following is correct in respect of the above Statements and the Question?
- AS1 alone is sufficient to answer the Question.
- BS2 alone is sufficient to answer the Question.
- CS1 and S2 together are sufficient to answer the Question, but neither S1 alone nor S2 alone is sufficient to answer the Question.
- DS1 and S2 together are not sufficient to answer the Question.
Answer: (D) S1 and S2 together are not sufficient to answer the Question.Explanation
S1: n can be 11, 13, 17 or 19. S2: n can be 13 or 17.
Both together still leave 13 and 17, so n is not unique.
Answer: option (d).Source: UPSC CSAT 2020 question; answer key checked by independent computation
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