श्री X की आयु एक वर्ष पूर्व किसी संख्या का वर्ग थी तथा अगले वर्ष यह किसी संख्या का घन हो जाएगी। उसे अपनी आयु के पुनः किसी संख्या का घन होने के लिए न्यूनतम कितने वर्ष प्रतीक्षा करनी पड़ेगी?
Read this question in English
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?
(a) 42 · (b) 38 · (c) 25 · (d) 16
उत्तर और व्याख्या · explanation in English
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). ·