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?


Can someone / Instructor make a Overlapping Set Table ( a strategy mentioned in MGMAT Guide) and than explain /solve the problem?

Not sure it is legible on the screen, but here is the Table and explanation.

Let us assume X be the total number of students.

The given facts in the question.

1) Total # of students in the Band = 119 (This is equal to # of students in Band only + # of students in Band & Orchestra).
2) 80% of the students are in only one group = 0.8X.
3) 50% of the students are in Band Only = 0.5X. So the number of students in Orchestra only is 0.3X (From statement (2) above 0.8X - 0.5X).
4) Also please note that all of the students are in either Band, Orchestra OR both. So there are 0 Students who neither in Band nor Orchestra.

Refer the table below and the rest of the explanation.



| Band Not Band |
---------------------------------------------
Orchestra | | 0.3x |
---------------------------------------------
Not orchestra | 0.5x | 0 |
---------------------------------------------
119 | 0.3x | x


119 + 0.3x = x
0.7x = 119

x = 119/0.7 = 170

So number of students in Orchestra only = 0.3x
= 170 x 0.3
= 51

Thanks, Harish - it's tough to get the formatting to work on the forums.

mridul12 - please remember to post the entire text of the question, including answer choices.

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Stacey Koprince
Instructor
Director of Online Community
ManhattanGMAT

Can someone / Instructor make a Overlapping Set Table ( a strategy mentioned in MGMAT Guide) and than explain /solve the problem?[/quote]

100% = Only B + Only O + Both B&O
100% = 50% + Only O + Both B&O
100% = 50% + 30% +20% [Since 80% are only in one group, Only B + Only O = 80%.]

So, 70% in Band. Now 70% is equivalent to 119 students. So, 30% is equivalent to 51 students. [ANS]

First of all, thank you to MGMAT for explaining this so clearly in your book. As someone who has trouble organizing numbers in complicated problems, such as this one, I find your method especially helpful. That said, I used a VD. It's kind of hard to draw it on the post but once you get the numbers straight it will only take a few seconds. I was able to solve this in about 45 seconds.

Draw two cricles that overlap in the middle

Band Orchestra

Over the circles, I labeled 0.8x and drew two arrows. One going to band and one going to orchestra. That means the middle piece, the area representing students who are in both) is 0.2x (0.2x + 0.8x=1 or 100%).

Now in the left circle, write 0.5x because the problem tells us 50% of the students are in band ONLY. This means .3x are in orchestra only. So in your cricles, going from left to right, you should have 0.5X, 0.2x, and 0.3x, which adds to 1X.

Now it's just simple multiplication. The problem tells us 119 students are in band. That's 0.7x=119, which means x equals 170. So .3x or 30% of 170 would be 17+17+17= 51.

Thank you MGMAT. You guys rock. I am a visual person so your method helped significantly.

Good method, too. We're glad you're finding our curriculum helpful.