दो कथनों, S1 और S2 और उनके बाद आने वाले प्रश्न पर विचार कीजिए :
- S1.p और q दोनों अभाज्य संख्याएँ हैं ।
- S2.p + q विषम पूर्णांक है ।
- प्रश्न: क्या pq विषम पूर्णांक है ?
निम्नलिखित में से कौन-सा एक सही है ?
Read this question in English
Consider two statements S1 and S2 followed by a question:
S1. p and q both are prime numbers.
S2. p + q is an odd integer.
Question. Is pq an odd integer?
Which one of the following is correct?
(a) S1 alone is sufficient to answer the question · (b) S2 alone is sufficient to answer the question · (c) Both S1 and S2 taken together are not sufficient to answer the question · (d) Both S1 and S2 are necessary to answer the question
उत्तर और व्याख्या · explanation in English
Answer: (b) इस प्रश्न का उत्तर देने के लिए अकेले S2 पर्याप्त है
Two whole numbers have an odd sum only when one is even and the other odd, and then their product is even. So S2 alone gives a definite 'No'. S1 alone fails: 3 × 5 = 15 is odd but 2 × 3 = 6 is even.
- S1 alone: p = 3, q = 5 gives pq = 15 (odd); p = 2, q = 3 gives pq = 6 (even) — not sufficient.
- S2 alone: for whole numbers, an odd sum means one number is even and the other odd.
- Then pq has an even factor, so pq is even — a definite 'No'. S2 is sufficient.
- Since S2 works alone, S1 is not needed, so (c) and (d) fail.
- Like the question itself, this reading takes p and q to be whole numbers.
Remember · In data sufficiency a definite 'No' is an answer; odd + even = odd, and an even factor makes a product even.
Question and answer: UPSC's official GS Paper II (2019, Series A) — paper ↗ · answer key ↗. Explanation: Minimalist IAS, checked 30 Sept 2026 (how we verify). ·