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# Every student at the Performing Arts Academy must take at

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Senior Manager
Joined: 21 Oct 2013
Posts: 435

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11 Jan 2014, 05:34
1
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3
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Difficulty:

45% (medium)

Question Stats:

57% (02:40) correct 43% (01:37) wrong based on 168 sessions

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Every student at the Performing Arts Academy 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 Performing Arts Academy has a total of 450 students.

OE
[Reveal] Spoiler:
(1): 10% of the students enrolled in Improvisation take both classes, while 90% of the students take only Improvisation. But with no actual numbers given, we cannot determine a single value for the number of students who take both classes. There may be 100 students or 1,000 students
y + 0.85x = x + 0.9y → 0.1y = 0.15x
Insufficient
(2): Without knowing how many do not take Classical Theater, we cannot calculate the value we need.
Insufficient
Combined:
x + 0.90y = 450 and 0.15x = 0.10y
we can solve for the values of both x and y
Sufficient

Hi, this question is wordy and does not look straight forward.
I want to know if we have simple solution for this question, please.
[Reveal] Spoiler: OA
Math Expert
Joined: 02 Sep 2009
Posts: 39598
Re: Every student at the Performing Arts Academy must take at [#permalink]

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11 Jan 2014, 05:44
3
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Expert's post
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Every student at the Performing Arts Academy 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?

Given:
{Total} = {Classical Theater} + {Improvisation} - {Both} (notice that we are told that every student must take at least one of the two courses, which implies that {neither}=0).
0.15{Classical Theater} = {Both} --> {Classical Theater} = {Both}/0.15.

The question asks to find the value of {Both}.

(1) Ten percent of the students who take Improvisation also take Classical Theater --> 0.1{Improvisation} = {Both} --> {Improvisation} = {Both}/0.1. Not sufficient.

(2) The Performing Arts Academy has a total of 450 students --> {Total} = 450. Not sufficient.

(1)+(2) From above: 450 = {Both}/0.15 + {Both}/0.1 - {Both} --> we can solve for {Both}. Sufficient.

Hope it's clear.
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Re: Every student at the Performing Arts Academy must take at [#permalink]

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27 Jan 2014, 11:35
1
KUDOS
Bunuel wrote:
Every student at the Performing Arts Academy 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?

Given:
{Total} = {Classical Theater} + {Improvisation} - {Both} (notice that we are told that every student must take at least one of the two courses, which implies that {neither}=0).
0.15{Classical Theater} = {Both} --> {Classical Theater} = {Both}/0.15.

The question asks to find the value of {Both}.

(1) Ten percent of the students who take Improvisation also take Classical Theater --> 0.1{Improvisation} = {Both} --> {Improvisation} = {Both}/0.1. Not sufficient.

(2) The Performing Arts Academy has a total of 450 students --> {Total} = 450. Not sufficient.

(1)+(2) From above: 450 = {Both}/0.15 + {Both}/0.1 + {Both} --> we can solve for {Both}. Sufficient.

Hope it's clear.

Something may be wrong with the question and also there is a typo:

final equation should be Both/.15 +both/.1 - both = 450

even if we were to solve Both/.15 +both/.1 - both= 450 we would get Both = 1350/47 not an integer.

Number of students should be an integer.
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- Stne

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Joined: 20 Nov 2013
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Schools: LBS '17
Re: Every student at the Performing Arts Academy must take at [#permalink]

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06 Sep 2014, 10:08
Bunuel wrote:
Every student at the Performing Arts Academy 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?

Given:
{Total} = {Classical Theater} + {Improvisation} - {Both} (notice that we are told that every student must take at least one of the two courses, which implies that {neither}=0).
0.15{Classical Theater} = {Both} --> {Classical Theater} = {Both}/0.15.

The question asks to find the value of {Both}.

(1) Ten percent of the students who take Improvisation also take Classical Theater --> 0.1{Improvisation} = {Both} --> {Improvisation} = {Both}/0.1. Not sufficient.

(2) The Performing Arts Academy has a total of 450 students --> {Total} = 450. Not sufficient.

(1)+(2) From above: 450 = {Both}/0.15 + {Both}/0.1 - {Both} --> we can solve for {Both}. Sufficient.

Hope it's clear.

Maybe i misread the question but when the question states that 15% of the students who take classical theater also take Improvisation , i do not think that means that both = 0.15C. That means that Both = 0.15C + x where x would be 0.10I so both here would equal 0.15C + 010I . 15% of Classical Theater students do not equal all students who take both but rather a portion of those who take both which we do not know how much.

0.10I + 0.15C = Both

and C + I - (0.10I + 0.15C) = 450

I solved it to be E.
Manager
Joined: 30 Jul 2013
Posts: 124
Concentration: Strategy, Sustainability
GMAT 1: 710 Q49 V39
Re: Every student at the Performing Arts Academy must take at [#permalink]

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10 Sep 2014, 07:18
Whats wrong with the question? I'm not getting an integer figure myself

Someone help!!!
Math Expert
Joined: 02 Sep 2009
Posts: 39598
Re: Every student at the Performing Arts Academy must take at [#permalink]

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10 Sep 2014, 07:35
ramalo wrote:
Whats wrong with the question? I'm not getting an integer figure myself

Someone help!!!

I think it should be 470 instead of 450.
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Re: Every student at the Performing Arts Academy must take at [#permalink]

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11 Mar 2017, 01:29
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Re: Every student at the Performing Arts Academy must take at   [#permalink] 11 Mar 2017, 01:29
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# Every student at the Performing Arts Academy must take at

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