प्रश्न : क्या p बड़ा है q से ?
- कथन-1: p × q बड़ा है शून्य से ।
- कथन-2: p² बड़ा है q² से ।
उपर्युक्त प्रश्न और कथनों के बारे में निम्नलिखित में से कौन-सा एक सही है ?
Read this question in English
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?
(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: (d) इस प्रश्न का उत्तर, दोनों कथनों का एक साथ उपयोग करके भी नहीं दिया जा सकता ।
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). ·