UPSC Prelims 2016 · CSAT
Question 13: Basic Numeracy
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 ?
AnswerUPSC’s answer is (d).
Each group meets together again at the LCM of 2, 3, 4, 5 and 6, which is 60 (2 x 2 x 3 x 5). So all five meet on days 60, 120 and 180 within 180 days: 180 / 60 = 3 times. Remember: 'meet together' means LCM; count its multiples within the period.
How you could have got this
No shortcut here: in a “how many” question, ruling out options doesn’t help. Every statement has to be judged.
Which options go is worked out from UPSC’s key and the options, not by a model.
Why each option is right or wrong
- (a) Would need a 36-day cycle, but the LCM is 60.
- (b) Would need a 10-day cycle, but the LCM is 60.
- (c) Would need an 18-day cycle, but the LCM is 60.
- (d) Right: days 60, 120 and 180.
Answer: UPSC’s key. Explanation: written by UPSC Grade, not by UPSC.
Source: UPSC, Civil Services (Preliminary) Examination 2016, General Studies Paper II (CSAT), Series A. The paper on upsc.gov.in.