Problem Solving

1) All of the students of Music High School are in the band, the 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

I found the answer here: https://www.beatthegmat.com/confusing-sets-t54521.html

But I'm trying to plug in the answer using MGMAT's method of a 2 dimensional box. I don't see the reason to remember venn diagrams if I've been using the 2 dimensional box.

Here is my box -

---- O ---- Not O ---- Total
- B - 0.5x 119
- Not B -
- Total - x

The problem that I'm experiencing is that just because we know that 80% of the students are in 1 band, does that mean that in the section [O/Not B] you're going to place 0.8x there or are you going to place 0.3x? How do we know that if 80% of the students are in 1 band are ONLY in the orchestra band and not the difference?

That's where i'm lost.

And I answered my own question. For those who care:

The [0] is placed in the center since all the students are in either 1 band or another or in both. Therefore you can't have a student who is not in both the orchestra and the band. They need to be in 1 place or another.

Since 80% of the students are in 1 band or another and 50% of them are in the band only, obviously the the rest are in the other band. I thought that 80% of the students are in the other band. If that was true, then you'd have 1230% of the students in either band - a statement that goes against the given premise.

So what happens to the 20% of the rest of the students? Either they are in no band or in both bands. Since we know that 0 is stuck in the middle and the students MUST be in one or both bands, the 20% of the rest of the students are in both bands. This puts the 0.2x there.

0.2x + 0.5x = 119; therefore x = 170, and to answer the question, 0.3x = 0.3(170) = 51.

Check out the image I've enclosed.

piyushdabomb wrote:1) All of the students of Music High School are in the band, the 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

I found the answer here: https://www.beatthegmat.com/confusing-sets-t54521.html

But I'm trying to plug in the answer using MGMAT's method of a 2 dimensional box. I don't see the reason to remember venn diagrams if I've been using the 2 dimensional box.

Here is my box -

---- O ---- Not O ---- Total
- B - 0.5x 119
- Not B -
- Total - x

The problem that I'm experiencing is that just because we know that 80% of the students are in 1 band, does that mean that in the section [O/Not B] you're going to place 0.8x there or are you going to place 0.3x? How do we know that if 80% of the students are in 1 band are ONLY in the orchestra band and not the difference?

That's where i'm lost.

Hi,

I'm not sure what you mean by "1 band" - that may be why you're confused.

We're told there are two different groups: band and orchestra. We know that every student belongs to at least one of these two groups. We also know that:

80% are in only one group; therefore, 20% are in both groups.
50% are in band only; therefore, 30% are in orchestra only (since 80% are in only one group)

So, setting up the matrix (formatting might get messed up, sorry!):

-------------------Band-------Not Band------Total

Orchestra..........(.2x)..........(.3x)..............(.5x)

Not Orch............(.5x)............(0)...............(.5x)

Total..................(.7x)...........(.3x)..............(x)

The key to solving is recognizing that the total for band is 119, so:

.7x = 119

and we want to solve for Orchestra only, or .3x.

There are many ways to solve, for example we could set up a ratio:

.3x/.7x = (orch only)/119

(3/7)119 = orch only

3*17 = orch only

51 = orch only... Choose (B).