Data Sufficiency MCQs for UPSC Prelims

73 practice questions on Data Sufficiency from the Data Interpretation section of the UPSC Prelims syllabus. 73 come with a written explanation and 14 are actual previous year questions. Try the sample set below - the answer stays hidden until you ask for it.

4 Easy 27 Medium 42 Hard 14 from past papers

Sample questions

Q1
Previous year question hard

A question is given followed by two Statements I and II. Consider the Question and the Statements and mark the correct option. Question: Let P, Q, R, S be distinct non-zero digits. If PP x PQ = RRSS, where P <= 3 and Q <= 4, then what is Q equal to? Statement I: R = 1. Statement II: S = 2. Which one of the following is correct in respect of the above Question and the Statements?

  1. A The Question can be answered by using one of the Statements alone, but cannot be answered using the other statement alone.
  2. B The Question can be answered by using either Statement alone.
  3. C The Question can be answered by using both the Statements together, but cannot be answered using either Statement alone.
  4. D The Question can be answered even without using any of the Statements.
Show answer and explanation

Correct answer: D - The Question can be answered even without using any of the Statements.

Write PP = 11P and RRSS = 1100R + 11S = 11(100R + S). Dividing the equation PP x PQ = RRSS by 11 gives P x (10P + Q) = 100R + S. Since R and S are non-zero digits, 100R + S is at least 101. Test the allowed values of P (P at most 3): P = 1 gives at most 1 x 14 = 14; P = 2 gives at most 2 x 24 = 48; both are too small. P = 3 gives 3 x (30 + Q) = 90 + 3Q, which reaches 101 only if Q is at least 11/3, so Q = 4 (since Q is at most 4). Check: 33 x 34 = 1122, so R = 1 and S = 2, all digits distinct. Q = 4 is forced by the conditions in the question itself, so neither statement is required. The question can be answered even without using any of the statements. The official UPSC key confirms option (d).

Q2
Previous year question medium

A Question is given followed by two Statements I and II. Consider the Question and the Statements. A person buys three articles p, q and r for Rs. 50. The price of the article q is Rs. 16 which is the least. Question : What is the price of the article p? Statement-I : The cost of p is not more than that of r. Statement-II : The cost of r is not more than that of p. Which one of the following is correct in respect of the above Question and the Statements?

  1. A The Question can be answered by using one of the Statements alone, but cannot be answered using the other Statement alone
  2. B The Question can be answered by using either Statement alone
  3. C The Question can be answered by using both the Statements together, but cannot be answered using either Statement alone
  4. D The Question cannot be answered even by using both the Statements together
Show answer and explanation

Correct answer: C - The Question can be answered by using both the Statements together, but cannot be answered using either Statement alone

Given p + q + r = 50 and q = 16 is the least price, p + r = 34 with p > 16 and r > 16, so each of p and r lies strictly between 16 and 18. Statement I alone: p <= r with p + r = 34 gives 16 < p <= 17, not a unique value. Statement II alone: r <= p gives 17 <= p < 18, again not unique. Together: p <= r and r <= p force p = r, so p = r = 17. The price of p is Rs. 17, determined only by using both statements together.

Q3
Previous year question hard

A Question is given followed by two Statements I and II. Consider the Question and the Statements. There are three distinct prime numbers whose sum is a prime number. Question : What are those three numbers? Statement-I : Their sum is less than 23. Statement-II : One of the numbers is 5. Which one of the following is correct in respect of the above Question and the Statements?

  1. A The Question can be answered by using one of the Statements alone, but cannot be answered using the other Statement alone
  2. B The Question can be answered by using either Statement alone
  3. C The Question can be answered by using both the Statements together, but cannot be answered using either Statement alone
  4. D The Question cannot be answered even by using both the Statements together
Show answer and explanation

Correct answer: A - The Question can be answered by using one of the Statements alone, but cannot be answered using the other Statement alone

The sum of the three distinct primes is itself a prime greater than 2, hence odd. If 2 were among them, the sum would be even (2 + odd + odd) and could not be an odd prime, so all three primes are odd. Statement I alone: odd prime triples with sum less than 23 are 3 + 5 + 7 = 15 (not prime), 3 + 5 + 11 = 19 (prime), 3 + 5 + 13 = 21 (not prime), 3 + 7 + 11 = 21 (not prime); every other triple sums to 23 or more. So {3, 5, 11} is the unique answer and Statement I alone suffices. Statement II alone: triples containing 5 include {3, 5, 11} with sum 19 and {3, 5, 23} with sum 31, both prime, so it is not unique. Hence the question can be answered by one statement alone but not by the other, which is option (a), as per the official UPSC key.

Q4
Previous year question hard

A Question is given followed by two Statements I and II. Consider the Question and the Statements. P, Q, R and S appeared in a test. Question : Has P scored more marks than Q? Statement-I : The sum of the marks scored by P and Q is equal to the sum of the marks scored by R and S. Statement-II : The sum of the marks scored by P and S is more than the sum of the marks scored by Q and R. Which one of the following is correct in respect of the above Question and the Statements?

  1. A The Question can be answered by using one of the Statements alone, but cannot be answered using the other Statement alone
  2. B The Question can be answered by using either Statement alone
  3. C The Question can be answered by using both the Statements together, but cannot be answered using either Statement alone
  4. D The Question cannot be answered even by using both the Statements together
Show answer and explanation

Correct answer: D - The Question cannot be answered even by using both the Statements together

Statement I (P + Q = R + S) relates P and Q only through R and S, so it alone says nothing about P versus Q. Statement II (P + S > Q + R) alone is also insufficient. Combining them: subtracting the equation from the inequality yields S > Q, and adding suitably yields P > R, but the comparison between P and Q is still not fixed. Counterexamples: P = 6, Q = 5, R = 1, S = 10 satisfies both (11 = 11 and 16 > 6) with P > Q; while P = 5, Q = 5, R = 0, S = 10 also satisfies both (10 = 10 and 15 > 5) with P not greater than Q. Since both outcomes are possible, the question cannot be answered even using both statements together. The official UPSC key confirms (d).

Q5
Previous year question medium

A Question is given followed by two Statements I and II. Consider the Question and the Statements. A certain amount was distributed among X, Y and Z. Question : Who received the least amount? Statement-I : X received 4/5 of what Y and Z together received. Statement-II : Y received 2/7 of what X and Z together received. Which one of the following is correct in respect of the above Question and the Statements?

  1. A The Question can be answered by using one of the Statements alone, but cannot be answered using the other Statement alone
  2. B The Question can be answered by using either Statement alone
  3. C The Question can be answered by using both the Statements together, but cannot be answered using either Statement alone
  4. D The Question cannot be answered even by using both the Statements together
Show answer and explanation

Correct answer: C - The Question can be answered by using both the Statements together, but cannot be answered using either Statement alone

Let the total be T. Statement I: X = (4/5)(Y + Z) gives X = (4/9)T and Y + Z = (5/9)T. The smaller of Y and Z is at most (5/18)T, which is less than X, so X is not the least, but we cannot tell whether Y or Z is least. Insufficient. Statement II: Y = (2/7)(X + Z) gives Y = (2/9)T and X + Z = (7/9)T; X or Z could individually be smaller or larger than Y. Insufficient. Together: X = (4/9)T = 4T/9, Y = 2T/9, and Z = T - 4T/9 - 2T/9 = 3T/9. Since 2T/9 < 3T/9 < 4T/9, Y received the least. Both statements together are required.

Q6
Previous year question medium

A Question is given followed by two Statements I and II. Consider the Question and the Statements. Question : If the average marks in a class are 60, then what is the number of students in the class? Statement-I : The highest marks in the class are 70 and the lowest marks are 50. Statement-II : Exclusion of highest and lowest marks from the class does not change the average. Which one of the following is correct in respect of the above Question and the Statements?

  1. A The Question can be answered by using one of the Statements alone, but cannot be answered using the other Statement alone
  2. B The Question can be answered by using either Statement alone
  3. C The Question can be answered by using both the Statements together, but cannot be answered using either Statement alone
  4. D The Question cannot be answered even by using both the Statements together
Show answer and explanation

Correct answer: D - The Question cannot be answered even by using both the Statements together

Neither statement gives any handle on the number of students. Statement I only bounds the marks between 50 and 70. Statement II says removing the highest and lowest marks leaves the average at 60, which only tells us the highest and lowest average to 60 (70 + 50 = 120 = 2 x 60); it is automatically consistent with Statement I for any class size. For example, marks (70, 60, 50) for 3 students and (70, 60, 60, 50) for 4 students both have average 60 and satisfy both statements. Since multiple class sizes fit all the conditions, the question cannot be answered even using both statements together.

Q7
Previous year question medium

Year-wise variation of the price of a certain commodity is shown in the following graph. The vertical axis shows the price in Rupees (with marked levels of 10, 20, 30, 40, 50) and the horizontal axis shows the years 1980, 1990, 2000 and 2010. The plotted line covers the period from 1990 onward. The price of the commodity in the year 1980: (a) Must have been Rs. 10/-. (b) Must have been Rs. 12/-. (c) Must have been anywhere between Rs. 10/- and Rs. 20/-. (d) is higher than that in the year 1991.

  1. A Must have been Rs. 10/-.
  2. B Must have been Rs. 12/-.
  3. C Must have been anywhere between Rs. 10/- and Rs. 20/-.
  4. D is higher than that in the year 1991.
Show answer and explanation

Correct answer: C - Must have been anywhere between Rs. 10/- and Rs. 20/-.

The graph plots prices only from 1990 onwards, where the value sits between Rs. 10 and Rs. 20. The year 1980 lies before the plotted line, so no exact reading exists for it. We cannot fix it at exactly Rs. 10 or Rs. 12, and we have no data to claim it is higher than the 1991 price. The only defensible inference, extending the visible trend in that band, is that the 1980 price would lie somewhere between Rs. 10 and Rs. 20. So option (c) is correct.

Q8
Previous year question medium

A 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?

  1. A The Question can be answered by using one of the Statements alone, but cannot be answered using the other statement alone.
  2. B The Question can be answered by using either Statement alone.
  3. C The Question can be answered by using both the Statements together, but cannot be answered using either Statement alone.
  4. D The Question can be answered even without using any of the Statements.
Show answer and explanation

Correct answer: D - The Question can be answered even without using any of the Statements.

First answer the embedded question on its own. Count the factors of each 1-digit number: 1 has 1; 2, 3, 5, 7 have 2; 4 and 9 have 3; 6 has 4 (1, 2, 3, 6); 8 has 4 (1, 2, 4, 8). The numbers with exactly 4 distinct factors are 6 and 8, and the smallest is 6. The question has a unique answer with no extra information, so neither statement is needed. Hence the question can be answered even without using any of the statements. The official UPSC key confirms option (d).

Practice all 73 Data Sufficiency questions free

Timed practice, instant scoring, and explanations for every question. Free forever - no card, no catch.

Start practicing I am a teacher - create a test

More Data Interpretation topics

Caselets & Mixed Data 96 Tables 96 Line Graphs 88 Pie Charts 85 Bar Graphs 82