2023 CSAT, all questions
UPSC Prelims 2023 · CSAT
Question 8: Basic Numeracy
What is the unit digit in the expansion of (57242)^(9×7×5×3×1) ?
a2
b4
c6
d8
AnswerUPSC’s answer is (a).
Only the unit digit of the base, 2, matters. The exponent is 9 x 7 x 5 x 3 x 1 = 945. Powers of 2 end in 2, 4, 8, 6 and then repeat, a cycle of length 4. Divide the exponent by 4: 945 = 4 x 236 + 1, remainder 1, so the unit digit is the first in the cycle, which is 2.
Why each option is right or wrong
- (a) Right: remainder 1 on dividing 945 by 4 gives the first digit of the cycle, 2.
- (b) Wrong: 4 would need an exponent leaving remainder 2.
- (c) Wrong: 6 would need an exponent that is a multiple of 4.
- (d) Wrong: 8 would need an exponent leaving remainder 3.
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.