प्रश्न : क्या (p + q − r) बड़ा है (p − q + r) से, जहाँ p, q और r पूर्णांक हैं ?
- कथन-1: (p − q) धनात्मक है ।
- कथन-2: (p − r) ऋणात्मक है ।
उपर्युक्त प्रश्न और कथनों के बारे में निम्नलिखित में से कौन-सा एक सही है ?
Read this question in English
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?
(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 cannot be answered even by using both the Statements together.
उत्तर और व्याख्या · explanation in English
Answer: (c) इस प्रश्न का उत्तर, दोनों कथनों का एक साथ उपयोग कर दिया जा सकता है, किन्तु दोनों में से किसी एक कथन का अकेले उपयोग कर नहीं दिया जा सकता ।
(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). ·