दो संख्याओं के संबंध में दो कथन S1 और S2 नीचे दिए गए हैं और उनके उपरांत एक प्रश्न दिया गया है :
- S1.उनका गुणनफल 21 है।
- S2.उनका योग 10 है।
- प्रश्न: वे दो संख्याएँ क्या हैं?
निम्नलिखित में से कौन-सा उपर्युक्त कथनों और प्रश्न के लिए सही है?
Read this question in English
Two Statements S1 and S2 are given below with regard to two numbers followed by a Question:
S1. Their product is 21.
S2. Their sum is 10.
Question. What are the two numbers?
Which one of the following is correct in respect of the above Statements and the Question?
(a) S1 alone is sufficient to answer the Question. · (b) S2 alone is sufficient to answer the Question. · (c) S1 and S2 together are sufficient to answer the Question, but neither S1 alone nor S2 alone is sufficient to answer the Question. · (d) S1 and S2 together are not sufficient to answer the Question.
उत्तर और व्याख्या · explanation in English
Answer: (c) दोनों कथन S1 और S2 एकसाथ प्रश्न का उत्तर देने के लिए पर्याप्त हैं किन्तु न तो अकेला S1 और न ही अकेला S2 प्रश्न का उत्तर देने के लिए पर्याप्त है।
A product of 21 alone allows 3 and 7, 1 and 21 and many other pairs, and a sum of 10 alone allows endless pairs. Together, the numbers are the roots of t² − 10t + 21 = 0, which are exactly 3 and 7.
- S1 alone: 3 × 7, 1 × 21, 2 × 10·5 … — not unique.
- S2 alone: 3 + 7, 4 + 6, 5 + 5 … — not unique.
- Together: the numbers satisfy t² − 10t + 21 = 0, i.e. (t − 3)(t − 7) = 0, so they are 3 and 7.
Remember · Two numbers are fixed by their sum and product together: they are the roots of t² − (sum)t + (product) = 0.
Question and answer: UPSC's official GS Paper II (2020, Series A) — paper ↗ · answer key ↗. Explanation: Minimalist IAS, checked 30 Sept 2026 (how we verify). ·