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by AIM TO CRACK GMAT » Mon Jan 14, 2013 8:04 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
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by GMATGuruNY » Mon Jan 14, 2013 9:13 am
AIM TO CRACK GMAT 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
(Band only) + (Band and Orchestra) + (Orchestra only) = Total.

The TOTAL number of students in the band = 119.
Thus:
119 + (Orchestra only) = Total.

We can plug in the answers, which represent the number of students in only the orchestra.
Since 80% = 4/5 of the students are in only one group, the total number of students must be a multiple of 5.
Only B will yield a total number of students that is a multiple of 5:
119 + 51 = 170.

The correct answer is B.

Algebraically:
The total percentage in only one group = 80%.
The percentage in only the band = 50%.
Thus, the percentage in only the orchestra = 60-50 = 30%.

This means that everyone else -- the 119 students in only the band or in both groups -- is equal to 70% of the total:
119 = .7x
x = 119/.7 = 1190/7 = 170.

Since 30% are in only the orchestra:
.3(170) = 51.
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