Joseph visits the club on every 5th day, Harsh visits on every 24th day, while Sumit visits on every 9th day. If all three of them met at the club on a Sunday, then on which day will all three of them meet again ?
- (a) Monday
- (b) Wednesday ✓ UPSC's answer
- (c) Thursday
- (d) Sunday
Why the answer is (b)
• Calculate the Least Common Multiple (LCM) of the visit intervals: 5, 24, and 9.
• The prime factorization of 5 is 5, of 24 is 2³ × 3, and of 9 is 3².
• The LCM is 2³ × 3² × 5 = 8 × 9 × 5 = 360 days.
• Determine the number of weeks in 360 days by dividing by 7: 360 ÷ 7 = 51 weeks and 3 days remainder.
• Since they met on a Sunday, adding 3 days to Sunday results in Wednesday.
• Therefore, the next meeting day is Wednesday.
Why the other options are wrong
- (a) Monday
- Monday would require a remainder of 1 day when dividing the LCM by 7, but the remainder is 3.
- (c) Thursday
- Thursday would require a remainder of 4 days when dividing the LCM by 7, but the remainder is 3.
- (d) Sunday
- Sunday would require the LCM to be a multiple of 7, but 360 is not divisible by 7.
Asked in the CSAT Paper II of the UPSC Civil Services Preliminary Examination 2021, held on 10 October 2021. Question and answer key: Union Public Service Commission. Explanation: UPSC Answer Check.