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All of the students of Music High School are in the band,

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All of the students of Music High School are in the band, [#permalink] New post 24 Aug 2008, 21:15
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Question Stats:

68% (02:15) correct 32% (01:28) wrong based on 143 sessions
All of the students of Music High School are in the band, the orchestra, or both. 80 percent of the students are in only one group. There are 119 students in the band. If 50 percent of the students are in the band only, how many students are in the orchestra only?

A. 30
B. 51
C. 60
D. 85
E. 11

OPEN DISCUSSION OF THIS QUESTION IS HERE: all-of-the-students-of-music-high-school-are-in-the-band-105432.html
[Reveal] Spoiler: OA

Last edited by Bunuel on 11 Nov 2012, 05:01, edited 2 times in total.
Renamed the topic, edited the question and moved to PS forum.
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Re: Music High School - set theory [#permalink] New post 24 Aug 2008, 21:54
gmatcraze wrote:
All of the students of Music High School are in the band, the orchestra, or both. 80 percent of the students are in only one group. There are 119 students in the band. If 50 percent of the students are in the band only, how many students are in the orchestra only?
30
51
60
85
119


not sure i got it...how the number in a group can be with 80% or 50% or 30% or 20%?

band = b
orchestra = o
band & orchestra = oc
total = b+o - oc

if 50% are only in the band then total in band = 80%
oc = 30%
c = 20%

so 80% of total = 119
total = 140
c = 31 or 30
A.
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Re: Music High School - set theory [#permalink] New post 24 Aug 2008, 22:27
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gmatcraze wrote:
All of the students of Music High School are in the band, the orchestra, or both. 80 percent of the students are in only one group. There are 119 students in the band. If 50 percent of the students are in the band only, how many students are in the orchestra only?
30
51
60
85
119


B = Band
O = Orchestra
T = Total

Only Band = 0.5T
Either Band or Orchestra but not both = 0.8T
Hence, Only Orchestra = 0.3T
Also, both is 1 - 0.8T = 0.2T

0.5T + 0.2T = 119
T = 170

Hence, Only Orchestra = 0.3T = 51
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Re: Music High School - set theory [#permalink] New post 25 Aug 2008, 09:41
D

let T= total
let X= orchestra only
80% in only one group means 20% or .2T in both groups

119 - .2T = .5T
119= .7T
T=170

119 + X - .2T =170

.2T=34 (.2*170)

119 + X -34 = 170

X=85
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Re: Music High School - set theory [#permalink] New post 07 Mar 2009, 16:29
I use a table for set theory with 2 sets.


Orch no-Orch Total
---------------------------------------
Band .2(x) .5(x) 119
No-Band ? 0
Total .5(x) .5(x) x

From this we can conclude

.2(x) + .5(x) = 119
.7(x) = 119
x = 170

fill in the rest and we get .5(x) - ? = .2(x)
which is 85-34 = 51

51

what is the OA?
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Re: Music High School - set theory [#permalink] New post 07 Mar 2009, 22:44
For me the answer is 51.

Given: % of students in one group only = 80% ---- 1.
Therefore % of students in both groups = 100 - 80 = 20% -----2.
Also given: % of students in the band only = 50% -----3.
Also given: Number of students who are in band = 119 -----4.

From 2, 3, and 4.

50% + 20% = 70% = 119 Students

Finding total students:

If 70 out of 100 then 119 out of x
Solving for x

x = (119 x 100)/70
x = 170

Students in orchestra only = 170 - 119 = 51
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Re: Music High School - set theory [#permalink] New post 09 Mar 2009, 17:47
I also got 51 (B)

Band = 50% of Students and Orchestra = 30% of students [both group consists of 80% of students]
Now students who are both in two groups are 20% of students.

So total Band:
50% of Students + 20% of students = 119
Students = 170.

Hence only orchestra = 30% of students = 30% of 170 = 51
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Re: All of the students of Music High School are in the band, [#permalink] New post 09 Nov 2012, 09:38
What level of question is this?
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Re: All of the students of Music High School are in the band, [#permalink] New post 11 Nov 2012, 05:00
Expert's post
Re: All of the students of Music High School are in the band,   [#permalink] 11 Nov 2012, 05:00
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