UPSC Prelims 2013 · CSAT
Question 28: Basic Numeracy
There are five hobby clubs in a college viz., 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 (a).
The groups meet every 2, 3, 4, 5 and 6 days. All five meet on the same day only on days divisible by each of these, that is, multiples of the LCM: LCM(2, 3, 4, 5, 6) = 60. Within 180 days the common days are 60, 120 and 180, so all five groups meet together 3 times.
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) Right. Days 60, 120 and 180 are the common meeting days.
- (b) Wrong. 5 meetings would need a common cycle of 36 days.
- (c) Wrong. 10 meetings would need a common cycle of 18 days.
- (d) Wrong. 18 meetings would need a common cycle of 10 days.
Answer: UPSC’s key. Explanation: written by UPSC Grade, not by UPSC.
Source: UPSC, Civil Services (Preliminary) Examination 2013, General Studies Paper II (CSAT), Series A. The paper on upsc.gov.in.