32⁵ + 2²⁷ is divisible by
- (a) 3
- (b) 7
- (c) 10 ✓ UPSC's answer
- (d) 11
Why the answer is (c)
• 32⁵ = (2⁵)⁵ = 2²⁵.
• 2²⁵ + 2²⁷ = 2²⁵(1 + 2²) = 5 × 2²⁵.
• The number has both 2 and 5 as factors, so it is divisible by 10 — option (c).
Why the other options are wrong
- (a) 3
- 5 × 2²⁵ has only the prime factors 2 and 5, so it is not divisible by 3 (it leaves remainder 1).
- (b) 7
- 5 × 2²⁵ has only the prime factors 2 and 5, so it is not divisible by 7 (it leaves remainder 3).
- (d) 11
- 5 × 2²⁵ has only the prime factors 2 and 5, so it is not divisible by 11 (it leaves remainder 6).
Asked in the CSAT Paper II of the UPSC Civil Services Preliminary Examination 2024, held on 16 June 2024. Question and answer key: Union Public Service Commission. Explanation: UPSC Answer Check.