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?
Answer & explanation
Answer: (d) The Question can be answered even without using any of the Statements.
Dividing both sides by 11 gives P × PQ = 100R + S, which must be at least 100. With P ≤ 3 and Q ≤ 4, only 33 × 34 = 1122 works, so Q = 4 without using either statement.
- PP = 11 × P and RRSS = 1100R + 11S = 11 × (100R + S). So P × PQ = 100R + S.
- R is non-zero, so P × PQ must be at least 100. P = 1 gives at most 1 × 14 = 14; P = 2 gives at most 2 × 24 = 48. Too small.
- P = 3: 3 × (30 + Q) = 90 + 3Q reaches 100 only for Q = 4, giving 102, so R = 1 and S = 2.
- Check: 33 × 34 = 1122, and the digits 3, 4, 1, 2 are distinct.
- Q = 4 follows from the question alone; neither statement is needed.
- ✗ Statement I Not needed: R = 1 already follows from the question itself.
- ✗ Statement II Not needed: S = 2 also follows from the question itself.
Remember · PP and RRSS are multiples of 11 — divide it out first. Digit limits often settle the question on their own.
Question and answer: UPSC's official GS Paper II (2025, Series A) — paper ↗ · answer key ↗. Explanation: Minimalist IAS, checked 30 Sept 2026 (how we verify). ·