There are five hobby clubs in a college — photography, yachting, chess, electronics and gardening. The gardening group meets every second day, the electronics group meets every third day, the chess group meets every fourth day, the yachting group meets every fifth day and the photography group meets every sixth day. How many times do all the five groups meet on the same day within 180 days ?
- (a) 5
- (b) 18
- (c) 10
- (d) 3 ✓ UPSC's answer
Why the answer is (d)
• The gardening group meets every 2nd day, electronics every 3rd, chess every 4th, yachting every 5th, and photography every 6th day.
• To find when all groups meet on the same day, calculate the Least Common Multiple (LCM) of their meeting intervals: 2, 3, 4, 5, and 6.
• The LCM of 2, 3, 4, 5, and 6 is 60, meaning all five groups meet together every 60 days.
• Within a period of 180 days, the common meeting days occur on day 60, day 120, and day 180.
• Counting these instances gives a total of 3 times, which corresponds to option (d).
Why the other options are wrong
- (a) 5
- Option (a) is incorrect because 5 is not the number of common meeting days within 180 days; the correct count is 3.
- (b) 18
- Option (b) is incorrect because 18 is not the number of common meeting days within 180 days; the correct count is 3.
- (c) 10
- Option (c) is incorrect because 10 is not the number of common meeting days within 180 days; the correct count is 3.
Asked in the CSAT Paper II of the UPSC Civil Services Preliminary Examination 2016, held on 7 August 2016. Question and answer key: Union Public Service Commission. Explanation: UPSC Answer Check.