Question: Is p greater than q?
- Statement-1: p × q is greater than zero.
- Statement-2: p² is greater than q².
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.
Statement 1 says p and q have the same sign; Statement 2 says p is larger than q in size. Even together, p = 3, q = 1 gives 'yes' while p = −3, q = −1 gives 'no', so the Question cannot be answered.
- Statement 1 alone: p × q > 0 means p and q have the same sign. p = 3, q = 1 (yes) and p = 1, q = 3 (no) — not sufficient.
- Statement 2 alone: p² > q² means p is larger in size than q. p = 3, q = 1 (yes) and p = −3, q = 1 (no) — not sufficient.
- Both together: same sign and larger size. p = 3, q = 1 gives p > q, but p = −3, q = −1 gives p < q.
- So the Question cannot be answered even with both Statements.
Remember · In inequality data sufficiency, always test negative numbers; products and squares hide signs.
Question and answer: UPSC's official GS Paper II (2023, Series A) — paper ↗ · answer key ↗. Explanation: Minimalist IAS, checked 30 Sept 2026 (how we verify). ·