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All of the students of Music High School

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by gmatdriller » Sun Jan 15, 2012 5:16 am
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

Got confused with "80 percent of the students are in only one group"
How do we know whether 80% stands for Band only, orchestra only, or the sum
of both?

Source: Manhattangmat cat6.
OA B
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by mj78ind » Sun Jan 15, 2012 5:27 am
gmatdriller 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?

A:30 B:51 C:60 D:85 E:119

Got confused with "80 percent of the students are in only one group"
How do we know whether 80% stands for Band only, orchestra only, or the sum
of both?

Source: Manhattangmat cat6.
OA B
80% are in one group only => what are the "only" groups possible? "Band only" and "orchestra only".

Let x = People in band only, y = people in band and orchestra, z = people in orchestra only

Then as per the question:

(x+z) = 0.8(x+y+z) ------- (1)
x+y = 119 --------------- (2)
x = 0.5(x+y+z) ----------- (3)

3 equations 3 unknowns solve for z = 51.

Hence B
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by GMATGuruNY » Sun Jan 15, 2012 7:44 am
I posted two approaches here:

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by ronnie1985 » Sun Jan 15, 2012 8:14 pm
70% are in Band.
Therefore 0.7x = 119 => x = 170
Therefore, Orchestra only = 0.3*x = 51.
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by gmatdriller » Wed Jan 18, 2012 1:28 pm
got tricked by the wordings, but am ok now.

Thanks all for your contributions.
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