UPSC Prelims 2021 · CSAT
Question 75: Basic Numeracy
Joseph visits the club on every 5^th day, Harsh visits on every 24^th day, while Sumit visits on every 9^th day. If all three of them met at the club on a Sunday, then on which day will all three of them meet again ?
AnswerUPSC’s answer is (b).
They next all meet after the least common multiple of 5, 24 and 9 days. 5 is prime, 24 = 2³ × 3 and 9 = 3², so the LCM is 2³ × 3² × 5 = 360 days. 360 ÷ 7 leaves remainder 3, since 357 is a multiple of 7, so the day moves three days forward from Sunday, to Wednesday. Remember: for meeting-again questions use the LCM, then reduce the days modulo 7 to get the weekday.
Why each option is right or wrong
- (a) Monday needs a remainder of 1 on dividing 360 by 7; it is 3.
- (b) Right: 360 days is 51 weeks and 3 days, so Sunday plus 3 is Wednesday.
- (c) Thursday needs a remainder of 4; it is 3.
- (d) Sunday would need 360 to be a multiple of 7; it is not.
Answer: UPSC’s key. Explanation: written by UPSC Grade, not by UPSC.
Source: UPSC, Civil Services (Preliminary) Examination 2021, General Studies Paper II (CSAT), Series A. The paper on upsc.gov.in.