32⁵ + 2²⁷ is divisible by

Answer: (c) 10

32⁵ = (2⁵)⁵ = 2²⁵, so the sum is 2²⁵ + 2²⁷ = 2²⁵ × (1 + 4) = 5 × 2²⁵. It has the factors 2 and 5, so it is divisible by 10.

1. 32 = 2⁵, so 32⁵ = 2²⁵.
2. 32⁵ + 2²⁷ = 2²⁵ + 2²⁷ = 2²⁵ × (1 + 2²) = 5 × 2²⁵.
3. This contains 2 × 5 = 10, so it is divisible by 10.
4. Its only prime factors are 2 and 5, so it is not divisible by 3, 7 or 11.

Remember · Write every term with the same base, take out the common power, and read off the factors.

Question and answer: UPSC's official GS Paper II (2024, Series A) — paper ↗ · answer key ↗. Explanation: Minimalist IAS, checked 30 Sept 2026 (how we verify). · Report an error