If x is greater than or equal to 25 and y is less than or equal to 40, then which one of the following is always correct?
Answer & explanation
Answer: (c) (y − x) is less than or equal to 15
y − x is largest when y is as big as allowed (40) and x as small as allowed (25), giving 15. So y − x can never exceed 15; the other options fail for suitable values.
- Maximum of y − x = 40 − 25 = 15, so y − x ≤ 15 always.
- (a) fails: x = 25, y = 40 gives x < y.
- (b) fails: y − x never goes above 15.
- (d) fails: x = 25, y = 10 gives x + y = 35.
Remember · For 'always correct' with bounds, test the extreme values; a single counter-example removes an option.
Question and answer: UPSC's official GS Paper II (2019, Series A) — paper ↗ · answer key ↗. Explanation: Minimalist IAS, checked 30 Sept 2026 (how we verify). ·