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?
Answer & explanation
Answer: (d) The Question cannot be answered even by using both the Statements together
Combining the statements gives only P > R and S > Q; nothing compares P with Q directly. Examples with P above Q and with P below Q both satisfy the data.
- Statement I alone: P + Q = R + S says nothing about P versus Q.
- Statement II alone: P + S > Q + R also depends on S and R, so it is not sufficient.
- Together: putting R = P + Q − S into Statement II gives 2S > 2Q, i.e. S > Q; similarly P > R. Neither compares P with Q.
- Example: P = 5, Q = 1, R = 4, S = 2 (P > Q) and P = 5, Q = 6, R = 4, S = 7 (P < Q) both satisfy I and II. So the question cannot be answered.
Remember · Combine the equations to see what they really fix, then build two examples that give opposite answers.
Question and answer: UPSC's official GS Paper II (2024, Series A) — paper ↗ · answer key ↗. Explanation: Minimalist IAS, checked 30 Sept 2026 (how we verify). ·