All of the students of Music High School

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gmatdriller: Master | Next Rank: 500 Posts; Posts: 418; Joined: Sun Jul 04, 2010 12:48 pmFollowed by: 3 members; Thanked: 6 times

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

Source: Beat The GMAT — Problem Solving | Sun Jan 15, 2012 5:16 am

mj78ind: Master | Next Rank: 500 Posts; Posts: 265; Joined: Mon Dec 28, 2009 9:45 pmFollowed by: 2 members; Thanked: 26 times; GMAT Score:760

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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GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members; Location: New York, NY; Thanked: 13060 times; GMAT Score:790

by GMATGuruNY » Sun Jan 15, 2012 7:44 am

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ronnie1985: Legendary Member; Posts: 626; Joined: Fri Dec 23, 2011 2:50 amFollowed by: 10 members; Location: Ahmedabad; Thanked: 31 times

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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gmatdriller: Master | Next Rank: 500 Posts; Posts: 418; Joined: Sun Jul 04, 2010 12:48 pmFollowed by: 3 members; Thanked: 6 times

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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