2023 CSAT, all questions
UPSC Prelims 2023 · CSAT
Question 74: Basic Numeracy
What is the remainder if 2^192 is divided by 6 ?
a0
b1
c2
d4
AnswerUPSC’s answer is (d).
Powers of 2 mod 6 alternate: 2^1 = 2, 2^2 = 4, 2^3 = 8 leaves 2, 2^4 = 16 leaves 4, and so on. Odd powers leave 2 and even powers leave 4. 192 is even, so the remainder is 4. Check: 2^192 is even and leaves 1 mod 3 (as (-1)^192 = 1), which gives 4 mod 6.
Why each option is right or wrong
- (a) Wrong: 2^192 is not divisible by 3, so not by 6.
- (b) Wrong: the number is even, so the remainder on division by 6 cannot be 1.
- (c) Wrong: only odd powers of 2 leave 2.
- (d) Right: even powers of 2 leave 4 mod 6.
Answer: UPSC’s key. Explanation: written by UPSC Grade, not by UPSC.
Source: UPSC, Civil Services (Preliminary) Examination 2023, General Studies Paper II (CSAT), Series A. The paper on upsc.gov.in.