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 × 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 ?
- (a) The Question can be answered by using one of the Statements alone, but cannot be answered using the other statement alone.
- (b) The Question can be answered by using either Statement alone.
- (c) The Question can be answered by using both the Statements together, but cannot be answered using either Statement alone.
- (d) The Question can be answered even without using any of the Statements. ✓ UPSC's answer
Why the answer is (d)
• PP = 11P and RRSS = 1100R + 11S = 11(100R + S), so PP × PQ = RRSS reduces to P × (10P + Q) = 100R + S.
• P = 1: the left side is at most 1 × 14 = 14, too small since R ≥ 1. P = 2: at most 2 × 24 = 48, also too small.
• So P = 3, and 3 × (30 + Q) = 90 + 3Q must be at least 100 (R ≥ 1) while Q ≤ 4 caps it at 102. Only Q = 4 works: 3 × 34 = 102, giving R = 1 and S = 2.
• Check: 33 × 34 = 1122, and the digits 3, 4, 1, 2 are distinct and non-zero.
• Q = 4 is fixed by the question alone, without either statement — option (d).
Why the other options are wrong
- (a) The Question can be answered by using one of the Statements alone, but cannot be answered…
- The question can be answered without any statements, so it is not dependent on one statement alone.
- (b) The Question can be answered by using either Statement alone.
- The question can be answered without any statements, so it is not dependent on either statement alone.
- (c) The Question can be answered by using both the Statements together, but cannot be…
- The question can be answered without any statements, so it does not require both statements together.
Asked in the CSAT Paper II of the UPSC Civil Services Preliminary Examination 2025, held on 25 May 2025. Question and answer key: Union Public Service Commission. Explanation: UPSC Answer Check.