2023 CSAT, all questions
UPSC Prelims 2023 · CSAT
Question 10: Basic Numeracy
D is a 3-digit number such that the ratio of the number to the sum of its digits is least. What is the difference between the digit at the hundred's place and the digit at the unit's place of D ?
a0
b7
c8
d9
AnswerUPSC’s answer is (c).
For N = 100a + 10b + c, N / (a + b + c) = 1 + (99a + 9b) / (a + b + c). To make it smallest, keep a small (a = 1) and make the digit sum large, so b = c = 9. D = 199: 199 / 19 is about 10.47, below 189 / 18 = 10.5 and 198 / 18 = 11. Difference of the hundred's and unit's digits = 9 - 1 = 8.
Why each option is right or wrong
- (a) Wrong: the digits of 199 are 1 and 9, which differ.
- (b) Wrong: 9 - 1 = 8, not 7.
- (c) Right: D = 199 and 9 - 1 = 8.
- (d) Wrong: 9 is a digit of D, not the difference.
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.