2024 CSAT, all questions
UPSC Prelims 2024 · CSAT
Question 17: Basic Numeracy
What is the rightmost digit preceding the zeros in the value of 30^30?
a1
b3
c7
d9
AnswerUPSC’s answer is (d).
30^30 = 3^30 × 10^30, so the digit just before the zeros is the last digit of 3^30. Powers of 3 end in 3, 9, 7, 1 and then repeat every 4 powers. Since 30 = 4 × 7 + 2, 3^30 ends like 3^2, which is 9. Therefore the rightmost non-zero digit is 9. Remember: the last digit of a power depends only on the exponent's remainder on division by the cycle length.
Why each option is right or wrong
- (a) Wrong. A power of 3 ends in 1 when the exponent is a multiple of 4; 30 is not.
- (b) Wrong. 3 is the last digit when the exponent leaves remainder 1 on division by 4; here the remainder is 2.
- (c) Wrong. 7 comes at remainder 3; the remainder here is 2.
- (d) Right. Remainder 2 corresponds to 3^2 = 9.
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.