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 Paper
Explanation:
32^5 + 2^27
1) 32^5:
32 = 2^5
So, 32^5 = (2^5)^5 = 2^25
2) Now our expression is 2^25 + 2^27
3) We can factor out 2^25:
2^25 * (1 + 2^2) = 2^25 * (1 + 4) = 2^25 * 5
4) Now, let’s consider the divisibility:
c) 10: 2^25 * 5 is clearly divisible by 10, and since 2^25 * 5 = 2^24*10
The answer remains c) 10.