# Q. 32^5 + 2^27 is divisible by

a) 3

b) 7

c) 10

d) 11

Correct answer: c) 10

#### Question from UPSC Prelims 2024 CSAT

**Explanation : **

## 32^5 + 2^27

To determine which of the given options divides 32^5 + 2^27, let’s simplify and analyze the expression step-by-step.

Simplify the Expression First, express everything in terms of powers of 2: 32 = 2^5 implies 32^5 = (2^5)^5 = 2^25

2^27 remains as is.

So, the expression becomes: 32^5 + 2^27 = 2^25 + 2^27 = 2^25(1 + 2^2) = 2^25 × 5

This shows that the expression is divisible by 2^25 and 5, and consequently by 2 × 5 = 10.