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by sparkle6 » Tue Sep 27, 2011 6:19 am
All of the students at Music High School are in the band, orchestra, or both. 80% of the students are in only one group. There are 119 students in the band. If 50% 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


[spoiler]Answer: B, but I'm not sure how to solve this...[/spoiler]
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by user123321 » Tue Sep 27, 2011 7:47 am
band only = x
orchestra only = y
both = z

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

solving above three equations for y, you will get y=51

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by Anurag@Gurome » Tue Sep 27, 2011 8:33 pm
sparkle6 wrote:All of the students at Music High School are in the band, orchestra, or both. 80% of the students are in only one group. There are 119 students in the band. If 50% 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


[spoiler]Answer: B, but I'm not sure how to solve this...[/spoiler]
Let T be the total number of students. Let X and Y represent the students in band and orchestra respectively.
X only = 0.5T
Y only + X only = 0.8T
Y only = 0.3T
X and Y = T - (0.8T) = 0.2T

Y = Y only + (X and Y) = 0.5T + 0.2T = 0.7T
It is given that Y = 119
0.7T = 119 implies T = 170
Y only = 0.3T = (0.3) * 170 = 51

The correct answer is B.
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by gmatboost » Tue Sep 27, 2011 9:25 pm
Y = Y only + (X and Y) = 0.5T + 0.2T = 0.7T
It is given that Y = 119
0.7T = 119 implies T = 170
Y only = 0.3T = (0.3) * 170 = 51
I believe this part should read:
X = X only + (X and Y) = 0.5T + 0.2T = 0.7T
It is given that X = 119
0.7T = 119 implies T = 170
Y only = 0.3T = (0.3) * 170 = 51
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by bijoyajj » Tue Sep 27, 2011 10:28 pm
sparkle6 wrote:All of the students at Music High School are in the band, orchestra, or both. 80% of the students are in only one group. There are 119 students in the band. If 50% of the students are in the band only, how many students are in the orchestra only?
119 students is the sum of band only + both students --- Eq 1

"80% of the students are in only one group".. which means 20% are in both band & orchestra..

so 119= 70% of total students (50+20).. from equation 1

hence total number of students is 170..
So 170-119 gives orchestra only students..
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