UPSC Prelims 2014 · CSAT
Question 6: Basic Numeracy
Five persons fire bullets at a target at an interval of 6, 7, 8, 9 and 12 seconds respectively. The number of times they would fire the bullets together at the target in an hour is
AnswerUPSC’s answer is (b) or (c).
Find the least common multiple of the intervals: 6 = 2x3, 7, 8 = 2x2x2, 9 = 3x3, 12 = 2x2x3, so LCM = 8 x 9 x 7 = 504 seconds. In an hour (3600 s) all five fire together at 504, 1008, and so on up to 7 x 504 = 3528 s, since 8 x 504 = 4032 is beyond 3600. That gives 7 times; if the common first shot at the start is also counted, it is 8.
Why each option is right or wrong
- (a) Six undercounts; seven multiples of 504 s fit within 3600 s.
- (b) Fits if only the repeats after the opening shot are counted: 7 x 504 = 3528 s.
- (c) Also keyed: it includes the simultaneous shot at time zero, giving 7 + 1 = 8.
- (d) Nine would need 9 x 504 = 4536 s, more than an hour.
Worth knowing: UPSC accepted both (b) and (c), because the question does not say whether the opening simultaneous shot counts.
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.