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 ?
- (a) 45
- (b) 44 ✓ UPSC's answer
- (c) 38
- (d) 30
Why the answer is (b)
• 5% of 120 musicians can play all three instruments, so all-three = 6.
• Musicians who can play exactly two instruments = 30.
• Musicians who can play guitar alone = 40.
• The remaining musicians must be those who can play violin alone or flute alone, since the categories are mutually exclusive and cover the 120 musicians.
• Therefore violin alone + flute alone = 120 - 6 - 30 - 40 = 44, so option (b) follows.
Why the other options are wrong
- (a) 45
- 45 would require the remaining count to be 45, but 120 - 40 - 30 - 6 equals 44.
- (c) 38
- 38 would require subtracting 82 from 120, but the given exactly-two and all-three counts total 36 and guitar alone is 40, leaving 44.
- (d) 30
- 30 is the number who can play exactly two instruments, not the number who can play violin alone or flute alone.
Asked in the CSAT Paper II of the UPSC Civil Services Preliminary Examination 2014, held on 24 August 2014. Question and answer key: Union Public Service Commission. Explanation: UPSC Answer Check.