Let p + q = 10, where p, q are integers.
- Value-I: Maximum value of p × q when p, q are positive integers.
- Value-II: Maximum value of p × q when p ≥ −6, q ≥ −4.
Which one of the following is correct?
Answer & explanation
Answer: (c) Value-I = Value-II
For a fixed sum of 10, the product p × q is largest when p = q = 5, giving 25. Allowing some negative values only adds negative products, so both maxima are 25 and the two values are equal.
- Value-I: with p + q = 10 and both positive, p × q = p(10 − p) is largest at p = q = 5, giving 25.
- Value-II: p ≥ −6 and q ≥ −4 allow p from −6 to 14. The product p(10 − p) still peaks at p = 5 (25).
- The extra cases give negative products, e.g. (−6) × 16 = −96 and 14 × (−4) = −56.
- So Value-II = 25 = Value-I.
Remember · For a fixed sum, the product is greatest when the two numbers are equal (or as close as possible).
Question and answer: UPSC's official GS Paper II (2025, Series A) — paper ↗ · answer key ↗. Explanation: Minimalist IAS, checked 30 Sept 2026 (how we verify). ·