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# In a certain 120-person orchestra, each musician plays one or more....

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Joined: 11 Feb 2015
Posts: 714
In a certain 120-person orchestra, each musician plays one or more....  [#permalink]

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09 Sep 2018, 07:30
1
2
00:00

Difficulty:

15% (low)

Question Stats:

82% (01:25) correct 18% (03:00) wrong based on 22 sessions

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In a certain 120-person orchestra, each musician plays one or more of the following musical instruments: the piano, the violin, or the tuba. A total of 50 musicians play the violin, 70 musicians play the piano, and 60 musicians play the tuba. If 30 musicians play exactly two of the instruments, how many musicians play exactly all three of the instruments?

A) 10
B) 13
C) 14
D) 15
E) 17

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Re: In a certain 120-person orchestra, each musician plays one or more....  [#permalink]

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09 Sep 2018, 07:40
1
CAMANISHPARMAR wrote:
In a certain 120-person orchestra, each musician plays one or more of the following musical instruments: the piano, the violin, or the tuba. A total of 50 musicians play the violin, 70 musicians play the piano, and 60 musicians play the tuba. If 30 musicians play exactly two of the instruments, how many musicians play exactly all three of the instruments?

A) 10
B) 13
C) 14
D) 15
E) 17

Formula for overlapping sets with exactly 2 groups:
Total=A+B+C−(sum of EXACTLY 2group overlaps)−2∗(all three)+Neither
120=50+70+60-30-2*all three+0
120=180-30-2*all three
Musicians who play All three=30/2=15
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Re: In a certain 120-person orchestra, each musician plays one or more....   [#permalink] 09 Sep 2018, 07:40
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