UPSC Prelims 2013·CSAT·Quantitative Aptitude·Number System

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?

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Last updated 23 May 2026, 3:31 pm IST
  1. A3Correct
  2. B5
  3. C10
  4. D18

Explanation

To determine when all five groups meet on the same day, we need to find the Least Common Multiple (LCM) of their meeting frequencies. The meeting frequencies are: Gardening: every 2nd day Electronics: every 3rd day Chess: every 4th day Yachting: every 5th day Photography: every 6th day LCM of (2, 3, 4, 5, 6): Prime factorization: 2 = 2 3 = 3 4 = 2 x 2 = 2^2 5 = 5 6 = 2 x 3 To find the LCM, we take the highest power of each prime factor present: LCM = 2^2 x 3 x 5 = 4 x 3 x 5 = 60. This means all five groups meet on the same day every 60 days. Now, we need to find how many times they meet within 180 days. Number of times = Total days / LCM Number of times = 180 / 60 = 3. The groups will meet together on day 60, day 120, and day 180. Therefore, they meet 3 times within 180 days. The final answer is A
Quantitative Aptitude: There are five hobby clubs in a college viz, photography, yachting, chess, electronics and gardening. The gardening grou
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