UPSC CSE 2025 · PYQ · Data Sufficiency / Cryptarithm · 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 × 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.✓ Correct
Explanation
PP = 11×P and PQ = 10P+Q. Their product = 11P(10P+Q) = RRSS = 11×(100R+S)×… Actually RRSS = 1100R + 11S = 11(100R+S). So P(10P+Q) = 100R+S. Try P=3, Q=4: 3(34) = 102 → R=1, S=2 ✓. Check P=1: 1(10+Q) = 10+Q ≤ 19, can't equal 100R+S with R≥1 and digits valid (would need R=1, S=Q, but S and Q must be distinct). P=2: 2(20+Q) = 40+2Q, need = 100R+S; for R=0 not allowed (non-zero), so impossible. So only P=3, Q=4 works, giving Q=4 uniquely. The answer can be found without using any statement. Option (d) is correct.
💡 Practice unlimited UPSC CSE PYQs + AI-tracked progress on each topic. Sign up free →
Want more UPSC CSE practice?
Free daily 10-Q quiz · adaptive mocks · 4,000+ verified PYQs · AI doubt solver in Hindi + English