The age of Mr. X last year was the square of a number and it would be the cube of a number next year. What is the least number of years he must wait for his age to become the cube of a number again?
Answer & explanation
Answer: (b) 38
Next year's age is 2 more than last year's, so we need a square that is 2 less than a cube: 25 + 2 = 27. Mr. X was 25, is 26 now and turns 27 next year. The next cube is 64, which is 38 years away from his present age.
- If last year's age is n² and next year's is m³, then m³ − n² = 2.
- Try cubes: 8 − 2 = 6 (not a square), 27 − 2 = 25 = 5² ✓, 64 − 2 = 62, 125 − 2 = 123, 216 − 2 = 214 — only 27 works for a human age.
- So he was 25 last year, is 26 now and will be 27 next year.
- After 27, the next cube is 4³ = 64.
- Years to wait from his present age: 64 − 26 = 38.
Remember · 'Square last year, cube next year' means the two numbers differ by 2 — list squares and cubes side by side.
Question and answer: UPSC's official GS Paper II (2017, Series A) — paper ↗ · answer key ↗. Explanation: Minimalist IAS, checked 30 Sept 2026 (how we verify). ·