UPSC Prelims 2014 · CSAT
Question 24: Basic Numeracy
Out of a total of 120 musicians in a club, 5% can play all the three instruments, guitar, violin and flute. It so happens that the number of musicians who can play any two and only two of the above instruments is 30. The number of musicians who can play the guitar alone is 40. What is the total number of those who can play violin alone or flute alone ?
AnswerUPSC’s answer is (b).
Five percent of 120 is 6 musicians who play all three. Exactly two instruments: 30. Guitar alone: 40. Taking everyone to play at least one instrument, violin-alone plus flute-alone = 120 - 40 - 30 - 6 = 44. Split the total into the non-overlapping groups (only one, exactly two, all three) and subtract the known ones from the whole.
Why each option is right or wrong
- (a) 45 is one more than the 44 left after subtracting the other groups.
- (b) Right. 120 - 40 - 30 - 6 = 44.
- (c) 38 subtracts the 6 who play all three twice.
- (d) 30 is only the exactly-two group, not violin-alone plus flute-alone.
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.