Question: Is (p + q − r) greater than (p − q + r), where p, q and r are integers?
- Statement-1: (p − q) is positive.
- Statement-2: (p − r) is negative.
Which one of the following is correct in respect of the above Question and the Statements?
Answer & explanation
Answer: (c) The Question can be answered by using both the Statements together, but cannot be answered using either Statement alone.
(p + q − r) > (p − q + r) simplifies to q > r. Statement 1 gives q < p and Statement 2 gives p < r; neither alone compares q with r, but together q < p < r, so q < r and the answer is a definite 'no'.
- (p + q − r) − (p − q + r) = 2q − 2r, so the Question is simply: is q > r?
- Statement 1: p − q > 0, i.e. q < p. Nothing about r — not sufficient.
- Statement 2: p − r < 0, i.e. p < r. Nothing about q — not sufficient.
- Together: q < p < r, so q < r and the expression is not greater — a definite answer.
- So both Statements together are needed and are sufficient.
Remember · Simplify the question first; in data sufficiency a firm 'no' answers the question just as well as a firm 'yes'.
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). ·