2023 CSAT, all questions
UPSC Prelims 2023 · CSAT
Question 28: Basic Numeracy
Each digit of a 9-digit number is 1. It is multiplied by itself. What is the sum of the digits of the resulting number ?
a64
b80
c81
d100
AnswerUPSC’s answer is (c).
The square of 111111111 (nine 1s) is 12345678987654321. Its digit sum is (1 + 2 + ... + 9) + (8 + 7 + ... + 1) = 45 + 36 = 81. In general a repunit of n ones (n up to 9) squares to a palindrome that rises to n and falls back, with digit sum n^2, here 9^2 = 81.
Why each option is right or wrong
- (a) Wrong: 64 would be the case for eight 1s.
- (b) Wrong: the digit sum is 81.
- (c) Right: 45 + 36 = 81.
- (d) Wrong: the digit sum is 81.
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.