UPSC CSE 2024 · PYQ · Number System / Divisibility · medium
32⁵ + 2²⁷ is divisible by
- A.3
- B.7
- C.10✓ Correct
- D.11
32⁵ = (2⁵)⁵ = 2²⁵. So 32⁵ + 2²⁷ = 2²⁵ + 2²⁷ = 2²⁵(1 + 2²) = 2²⁵ × 5. This equals 2²⁵ × 5 = 2²⁴ × 10. Hence it is divisible by 10. Check others: divisible by 3? 2²⁵ × 5 — neither factor divisible by 3, so no. Divisible by 7? No. Divisible by 11? No. The answer is 10.
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