2022 CSAT, all questions
UPSC Prelims 2022 · CSAT
Question 65: Basic Numeracy
What is the smallest number greater than 1000 that when divided by any one of the numbers 6, 9, 12, 15, 18 leaves a remainder of 3?
a1063
b1073
c1083
d1183
AnswerUPSC’s answer is (c).
A number leaving remainder 3 when divided by 6, 9, 12, 15 and 18 has the form Lk + 3, where L is the LCM of those divisors. LCM = 180 (2² × 3² × 5). The numbers are 183, 363, 543, 723, 903, 1083, and so on. The first above 1000 is 180 × 6 + 3 = 1083, since 180 × 5 + 3 = 903 is still below 1000.
Why each option is right or wrong
- (a) 1063 − 3 = 1060 is not a multiple of 180.
- (b) 1073 − 3 = 1070 is not a multiple of 180.
- (c) Correct: 1083 − 3 = 1080 = 180 × 6.
- (d) 1183 − 3 = 1180 is not a multiple of 180.
Answer: UPSC’s key. Explanation: written by UPSC Grade, not by UPSC.
Source: UPSC, Civil Services (Preliminary) Examination 2022, General Studies Paper II (CSAT), Series A. The paper on upsc.gov.in.