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If 90 students auditioned for the school musical, how many

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If 90 students auditioned for the school musical, how many [#permalink] New post 26 Aug 2012, 02:16
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If 90 students auditioned for the school musical, how many were accepted?

(1) 2/3 of the boys and 1/3 of the girls who auditioned were accepted.
(2) 26 of the boys who auditioned were accepted.

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Re: If 90 students auditioned for the school musical, how many [#permalink] New post 31 Aug 2012, 02:01
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SOLUTION:

If 90 students auditioned for the school musical, how many were accepted?

(1) 2/3 of the boys and 1/3 of the girls who auditioned were accepted --> \frac{2}{3}*B+\frac{1}{3}(90-B) students were accepted: if there were 30 boys and 60 girls (90-30), then 40 students were accepted but if there were 60 boys and 30 girls, then 50 students were accepted. Not sufficient.

(2) 26 of the boys who auditioned were accepted. Clearly insufficient.

(1)+(2) From (2) we have that \frac{2}{3}*B=26 --> B=39, so \frac{2}{3}*39+\frac{1}{3}*51=43 students were accepted. Sufficient.

Answer: C.
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Re: If 90 students auditioned for the school musical, how many [#permalink] New post 31 Aug 2012, 02:53
The answer is C.
The only way to solve this question is to use both information offered.
1) Insufficient. We don't know the ratio of boys to girls, so we cannot calculate the solution.
2)Insufficient. We don't know how many girls were accepted.

Combination of these information enables us to solve the problem.
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Re: If 90 students auditioned for the school musical, how many [#permalink] New post 18 Nov 2013, 15:42
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Re: If 90 students auditioned for the school musical, how many   [#permalink] 18 Nov 2013, 15:42
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