UPSC Prelims 2014 · CSAT
Question 46: Basic Numeracy
A bell rings every 18 minutes. A second bell rings every 24 minutes. A third bell rings every 32 minutes. If all the three bells ring at the same time at 8 o'clock in the morning, at what other time will they all ring together ?
AnswerUPSC’s answer is (b).
The bells ring together at multiples of the least common multiple of 18, 24 and 32. Since 18 = 2 x 3 x 3, 24 = 2 x 2 x 2 x 3 and 32 = 2 x 2 x 2 x 2 x 2, the LCM is 32 x 9 = 288 minutes, which is 4 hours 48 minutes. Adding that to 8:00 gives 12:48. Take the highest power of each prime to build an LCM.
Why each option is right or wrong
- (a) 12:40 is 280 minutes after 8:00, which is not a multiple of 18.
- (b) Right. 8:00 + 288 minutes = 12:48.
- (c) 12:56 is 296 minutes after 8:00, which is not a multiple of 24.
- (d) 13:04 is 304 minutes after 8:00, which is not a multiple of 18 or 24.
Answer: UPSC’s key. Explanation: written by UPSC Grade, not by UPSC.
Source: UPSC, Civil Services (Preliminary) Examination 2014, General Studies Paper II (CSAT), Series A. The paper on upsc.gov.in.