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# In a certain orchestra, each musician plays only one instrument and th

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Math Expert
Joined: 02 Sep 2009
Posts: 56302
In a certain orchestra, each musician plays only one instrument and th  [#permalink]

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19 Aug 2018, 09:28
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Difficulty:

15% (low)

Question Stats:

83% (01:15) correct 17% (01:23) wrong based on 25 sessions

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In a certain orchestra, each musician plays only one instrument and the ratio of musicians who play either the violin or the viola to musicians who play neither instrument is 5 to 9. If 7 members of the orchestra play the viola and four times as many play the violin, how many play neither?

(A) 14
(B) 28
(C) 35
(D) 63
(E) 72

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Re: In a certain orchestra, each musician plays only one instrument and th  [#permalink]

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19 Aug 2018, 10:19
Bunuel wrote:
In a certain orchestra, each musician plays only one instrument and the ratio of musicians who play either the violin or the viola to musicians who play neither instrument is 5 to 9. If 7 members of the orchestra play the viola and four times as many play the violin, how many play neither?

(A) 14
(B) 28
(C) 35
(D) 63
(E) 72

Given, 7 members of the orchestra play the viola and four times as many play the violin. Therefore #member who play violin=7*4=28
So, # member who play either viola or violin=28+7=35

Given, the ratio of musicians who play either the violin or the viola to musicians who play neither instrument is 5 to 9 or 5x:9x
So, 5x=35 or, x=7
So, #member who play neither=9x=9*7=63

Ans. (D)
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Re: In a certain orchestra, each musician plays only one instrument and th   [#permalink] 19 Aug 2018, 10:19
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