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?
Answer & explanation
Answer: (c) S1 and S2 together are sufficient to answer the Question, but neither S1 alone nor S2 alone is sufficient to answer the Question.
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). ·