2024 CSAT, all questions
UPSC Prelims 2024 · CSAT
Question 54: Basic Numeracy
32^5 + 2^27 is divisible by
a3
b7
c10
d11
AnswerUPSC’s answer is (c).
32^5 = (2^5)^5 = 2^25, so the expression is 2^25 + 2^27 = 2^25 (1 + 4) = 5 × 2^25. Its only prime factors are 2 and 5, so it is divisible by 10 = 2 × 5. It is not divisible by 3, 7 or 11, since none of these is a factor. Remember: take out the common power first and read off the prime factors.
Why each option is right or wrong
- (a) Wrong. 3 is not a factor; the number is 5 × 2^25.
- (b) Wrong. 7 is not a factor of 5 × 2^25.
- (c) Right. Both 2 and 5 are factors, so 10 divides it.
- (d) Wrong. 11 is not a factor of 5 × 2^25.
Answer: UPSC’s key. Explanation: written by UPSC Grade, not by UPSC.
Source: UPSC, Civil Services (Preliminary) Examination 2024, General Studies Paper II (CSAT), Series A. The paper on upsc.gov.in.