32^5 + 2^27 is divisible by

1. A. 3
2. B. 7
3. C. 10
4. D. 11

Answer: C

Explanation

The given expression is 32^5 + 2^27.
First, rewrite 32 as a power of 2: 32 = 2^5.
So, 32^5 = (2^5)^5 = 2^(5*5) = 2^25.
Now, the expression becomes 2^25 + 2^27.
Factor out the common term, which is 2^25:
2^25 + 2^27 = 2^25 + (2^25 * 2^2)
= 2^25 (1 + 2^2)
= 2^25 (1 + 4)
= 2^25 * 5.
To check for divisibility by 10, we need a factor of 10 (which is 2 * 5). We can rewrite 2^25 as 2^24 * 2:
= (2^24 * 2) * 5
= 2^24 * (2 * 5)
= 2^24 * 10.
Since the expression can be written as 2^24 * 10, it is clearly divisible by 10. This question tests basic exponent rules and divisibility properties.