2024 CSAT, all questions
UPSC Prelims 2024 · CSAT
Question 15: Basic Numeracy
222^333 + 333^222 is divisible by which of the following numbers?
a2 and 3 but not 37
b3 and 37 but not 2
c2 and 37 but not 3
d2, 3 and 37
AnswerUPSC’s answer is (b).
Check each divisor. 222 = 6 × 37 and 333 = 9 × 37, so both bases are multiples of 3 and of 37, and so is every power of them: the sum is divisible by 3 and 37. For 2: 222^333 is even but 333^222 is odd, so the sum is odd and not divisible by 2. Answer: divisible by 3 and 37 but not by 2. Remember to test each divisor term by term.
Why each option is right or wrong
- (a) Wrong. The sum is odd, so it is not divisible by 2, and it is divisible by 37.
- (b) Right. Both terms are multiples of 3 and 37, while the sum is odd.
- (c) Wrong. It is not divisible by 2 (even + odd = odd), and it is divisible by 3.
- (d) Wrong. The sum is odd, so 2 is excluded.
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.