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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]

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26 Aug 2012, 03:16
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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]

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31 Aug 2012, 03:01
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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.

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Re: If 90 students auditioned for the school musical, how many [#permalink]

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31 Aug 2012, 03:53
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]

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18 Nov 2013, 16:42
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Re: If 90 students auditioned for the school musical, how many [#permalink]

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02 May 2015, 04:40
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Re: If 90 students auditioned for the school musical, how many [#permalink]

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16 Jul 2016, 01:07
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Re: If 90 students auditioned for the school musical, how many [#permalink]

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09 Aug 2016, 13:35
Quote:
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.

We are given that 90 students auditioned for a musical, and we need to determine how many were accepted.

Statement One Alone:

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

With statement one, we can set up two equations in which b = the number of the boys who auditioned and g = the number of girls who auditioned:

b + g = 90

(2/3)b + (1/3)g = total accepted

We see we do not have enough information to determine how many students were accepted. Statement one is not sufficient to answer the question. We can eliminate answer choices A and D.

Statement Two Alone:

26 of the boys who auditioned were accepted.

Without knowing how many girls were accepted, we do not have enough information to determine how many total students were accepted. Statement two is not sufficient to answer the question. We can eliminate answer choice B.

Statements One and Two Together:

From statements one and two we know the following:

b + g = 90

(2/3)b + (1/3)g = total accepted

We also know that 26 boys who auditioned were accepted. Thus we can say:

(2/3)b = 26

b = 26 x 3/2

b = 39

Since there are 39 boys and 90 total students, we know there are 90 – 39 = 51 total girls. We also know that 1/3 of the girls who auditioned were accepted. Thus, we know that 51 x 1/3 = 17, is the total number of girls who were accepted. So finally we can say:

A total of 39 boys + 17 girls = 56 students who auditioned were accepted.

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Re: If 90 students auditioned for the school musical, how many   [#permalink] 09 Aug 2016, 13:35
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