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Music high School

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love_with_uuuu
 Post subject: Music high School
 Post Posted: Sat Aug 01, 2009 4:08 pm 
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Students


Posts: 2
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) 119

I was not able to understand the explanation :(
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love_with_uuuu
 Post subject: Re: Music high School
 Post Posted: Sat Aug 01, 2009 4:10 pm 
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Students


Posts: 2
I got it.. Moderators please delete the thread..
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cfaking
 Post subject: Re: Music high School
 Post Posted: Sun Aug 02, 2009 1:50 am 
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Students


Posts: 39
Location: India
very good Q.
hats off to MGMAT team

Band only + both + orchestra only = total students

soln:
band only =50%

also band only + orchestra only = 80%
hence, orchestra only =30%


Now, 70%(Total)=119===>total=170===>orchestra (only) =51

_________________
Many of the great achievements of the world were accomplished by tired and discouraged men who kept on working.
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RonPurewal
 Post subject: Re: Music high School
 Post Posted: Thu Aug 13, 2009 5:58 am 
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ManhattanGMAT Staff


Posts: 7146
looks like everything is good with this thread.

peace
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bonsfi
 Post subject: Re: Music high School
 Post Posted: Fri Dec 09, 2011 7:22 am 
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Forum Guests


Posts: 1
Another way to solve using plugIN!
Answers give the values for orchestra only:
30
51
60
85
119

Because we know that the band has 119 students, we have the total # of students (band + orchestra only = total):
30 + 119 = 149
51 + 119 = 170
60 + 119 = 179
85 + 119 = 204
119 + 119 = 238

Because 50% of total is band only, we can check the results:
149/2 = not halve person!
170/2 = 85
179/2 = not halve person!
204/2 = 102
238/2 = 119
A and C are OUT!

Because 80% total are only one group, 20% total are for both:
149 OUT!
170/2 = 85
179/2 OUT!
204*0,2 is not an integer
238*0,2 is not an integer
D and E are OUT!

ONLY B works with integers!
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Ahmed_elghaflol
 Post subject: Re: Music high School
 Post Posted: Sun Dec 11, 2011 10:34 am 
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Forum Guests


Posts: 1
thanks for the q

i have another solution which i think more simple:

imagine that this is a schedule

___________orchestra______not orchestra______total
.
Band__________20%___________50%_____________70%
.
Not band______30%_____________0%____________30%
.
Total_________50%____________50%___________100%
..
..
the numbers in bold is from the question
20% ==> 100% - 80%
30% ==> 80% - 50%
..
so the question if 70% =119 student , how many is 30%?
the answer is 51 students
..
..
..
This technique in answer of sets is from Manhattan GMAT Prep
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tim
 Post subject: Re: Music high School
 Post Posted: Tue Dec 13, 2011 2:50 am 
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ManhattanGMAT Staff


Posts: 2242
Location: Southwest Airlines, seat 21C
Thanks for all of your input..

_________________
Tim Sanders
Manhattan GMAT Instructor
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