If 4 ≤ x ≤ 8 and 2 ≤ y ≤ 7, then what is the ratio of maximum value of (x + y) to minimum value of (x − y)?
Answer & explanation
Answer: (d) None of the above
The largest x + y is 8 + 7 = 15 and the smallest x − y is 4 − 7 = −3, so the ratio is −5. None of the listed values matches; 15/2 comes from wrongly taking the smallest x − y as 4 − 2.
- Maximum of (x + y): take both at their largest, 8 + 7 = 15.
- Minimum of (x − y): take the smallest x and the largest y, 4 − 7 = −3.
- Ratio = 15 ÷ (−3) = −5.
- −5 is not 6, 15/2 or −15/2, so the answer is 'None of the above'.
- Check: the trap 15/2 uses 4 − 2 = 2, but y = 7 makes x − y smaller.
Remember · To minimise a difference, take the smallest first term and the largest second term — and keep track of the sign.
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). ·