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# Every student at the Performing Arts Academy (PAA) must take

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Every student at the Performing Arts Academy (PAA) must take [#permalink]  26 Aug 2011, 02:35
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Every student at the Performing Arts Academy (PAA) must take at least one of the two drama courses offered, Classical Theater or Improvisation. If 15% of the students who take Classical Theater also take Improvisation, how many students take both Classical Theater and Improvisation?

1) Ten percent of the students who take Improvisation also take Classical Theater

2) The PAA has a total of 450 students
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Re: Performing Arts Academy [#permalink]  02 Sep 2011, 03:33
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The answer is (E).

0.15 x = 0.10 y

x + y - 0.15x = 450

Solving these two equations, we get 0.15x and 0.10y as decimals.

(E) it is.
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Last edited by GyanOne on 20 Sep 2011, 14:54, edited 1 time in total.
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Re: Performing Arts Academy [#permalink]  18 Sep 2011, 00:24
To me answer should be C

total number of students took Classical Theater = x
total number of students took Improvisation = y
given .15x also took Improvisation.

statement 1 -> .1 y also took Classical Theater i.e .1y=.15x
statement 2 -> x+y - .15x = 450 (subtracted .15x because we need to remove intersection area between two once)
two equations can be solved to get x and y
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Re: Performing Arts Academy [#permalink]  01 Nov 2011, 16:07
parulbhatnagar wrote:
To me answer should be C

total number of students took Classical Theater = x
total number of students took Improvisation = y
given .15x also took Improvisation.

statement 1 -> .1 y also took Classical Theater i.e .1y=.15x
statement 2 -> x+y - .15x = 450 (subtracted .15x because we need to remove intersection area between two once)
two equations can be solved to get x and y

Unless I made a mistake, I'm getting y=187.5. So sincere there's no half students I'd say E, too.
Re: Performing Arts Academy   [#permalink] 01 Nov 2011, 16:07
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