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# In a high school with 500 students, 40% of the seniors play a musical

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Manager
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Joined: 02 Nov 2018
Posts: 179
In a high school with 500 students, 40% of the seniors play a musical  [#permalink]

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26 Mar 2019, 09:08
00:00

Difficulty:

75% (hard)

Question Stats:

56% (03:52) correct 44% (02:41) wrong based on 25 sessions

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In a high school with 500 students, 40% of the seniors play a musical instrument, while 30% of the non-seniors do not play a musical instrument. In all, 46.8% of the students do not play a musical instrument. How many non-seniors play a musical instrument?

(A) 66

(B) 154

(C) 186

(D) 220

(E) 266

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Posts: 7573
Re: In a high school with 500 students, 40% of the seniors play a musical  [#permalink]

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26 Mar 2019, 09:16
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1
In a high school with 500 students, 40% of the seniors play a musical instrument, while 30% of the non-seniors do not play a musical instrument. In all, 46.8% of the students do not play a musical instrument. How many non-seniors play a musical instrument?

(A) 66

(B) 154

(C) 186

(D) 220

(E) 266

We will use weighted average method to get the ratio of seniors and non-seniors..
40% of the seniors play a musical instrument, so 60% of seniors do not play
30% of the non-seniors do not play a musical instrument.
In all, 46.8% of the students do not play a musical instrument.
By weighted average method = non-seniors = $$500*\frac{60-46.8}{60-30}=500*\frac{13.2}{30}=5*44=220$$..

Now, 70% of them play musical instruments = 220*0.7=154

B
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Re: In a high school with 500 students, 40% of the seniors play a musical  [#permalink]

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27 Mar 2019, 00:32
1
In a high school with 500 students, 40% of the seniors play a musical instrument, while 30% of the non-seniors do not play a musical instrument. In all, 46.8% of the students do not play a musical instrument. How many non-seniors play a musical instrument?

(A) 66

(B) 154

(C) 186

(D) 220

(E) 266

solve using 2x2 matrix

----Play instrument-----not play-----total
Sr---0.4x-------------0.6x---------x
Jr---0.7y--------------0.3y--------y
----266--------------234---------500

x+y=500
and we need to find value of 0.7y
so solve for
0.4x+0.7y=266
x=500-y
solve
we get y= 220
so 0.7*220 = 154
IMO B
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Re: In a high school with 500 students, 40% of the seniors play a musical   [#permalink] 27 Mar 2019, 00:32
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