If p, q, r and s are distinct single digit positive numbers, then what is the greatest value of (p + q)(r + s)?
Answer & explanation
Answer: (b) 225
Use the four largest digits 9, 8, 7 and 6, which add up to 30. For a fixed total, the product of two parts is greatest when the parts are equal, so split 30 as 15 and 15: (9 + 6)(8 + 7) = 225.
- To make the product large, use the four largest distinct digits: 9, 8, 7, 6 (total 30).
- Split 30 into two sums as equal as possible: 9 + 6 = 15 and 8 + 7 = 15.
- Greatest value = 15 × 15 = 225.
- Check: the other splits give 17 × 13 = 221 and 16 × 14 = 224, both smaller.
Remember · With a fixed total, a product of parts is largest when the parts are as equal as possible.
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). ·