X and Y are natural numbers other than 1, and Y is greater than X. Which of the following represents the largest number?
Answer & explanation
Answer: (a) XY
With X at least 2, the product XY is at least 2Y, while Y/X is at most Y/2, X/Y is below 1 and (X + Y)/XY is below 1. XY is always the largest.
- Try the smallest values X = 2, Y = 3: XY = 6, X/Y ≈ 0.67, Y/X = 1.5, (X + Y)/XY = 5/6.
- In general X ≥ 2, so XY ≥ 2Y > Y > Y/X.
- X/Y < 1 because Y > X, and (X + Y)/XY = 1/X + 1/Y ≤ 1/2 + 1/3 < 1.
- So XY is the largest.
Remember · For 'which is largest' under conditions, test the smallest allowed values first, then confirm with a general inequality.
Question and answer: UPSC's official GS Paper II (2018, Series A) — paper ↗ · answer key ↗. Explanation: Minimalist IAS, checked 30 Sept 2026 (how we verify). ·