## If the drama club and music club

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Raj

### If the drama club and music club

Hello,

got this wrong on the test. I still can't figure out how the answer could be E.

If the drama club and music club are combined, what percent of the combined membership will be male?

(1) of the 16 members of the drama club, 15 are male
(2) of the 20 members of the music club, 10 are male

I thought this was real easy since C would give the total number of male and female members. What am I missing.. I am sure it is something really silly

Thanks for your help. My test is the coming weekend and this thing is bugging me..

-Raj.
divya

If the drama club and music club are combined, what percent of the combined membership will be male?

(1) of the 16 members of the drama club, 15 are male
(2) of the 20 members of the music club, 10 are male

Raj, one thing to note here is that you don't know the overlap, i.e the number of folks in the drama club, who are also members of the music club and vica versa.
Take this example,
20 members of the music club - 10 are male
all those 10 are also part of the drama club,
total ## of unique members: (16+ 20) - 10 = 26
## of males = 10
so % of males : 10/26 * 100

what if all members were exclusive, ie. no overlap
then % of males : 25/26 * 100

Therefore: E
divya

Just one slight correction.. the concept is still the same..

If the drama club and music club are combined, what percent of the combined membership will be male?

(1) of the 16 members of the drama club, 15 are male
(2) of the 20 members of the music club, 10 are male

Raj, one thing to note here is that you don't know the overlap, i.e the number of folks in the drama club, who are also members of the music club and vica versa.
Take this example,
20 members of the music club - 10 are male
all those 10 are also part of the drama club,
total ## of unique members: (16+ 20) - 10 = 26
## of males = 15
so % of males : 15/26 * 100

what if all members were exclusive, ie. no overlap
then % of males : 25/26 * 100

Therefore: E
Raj

### If the drama club and music club are

Yikes, I cant believe I missed that. Thank you Divya.

divya wrote:Just one slight correction.. the concept is still the same..

If the drama club and music club are combined, what percent of the combined membership will be male?

(1) of the 16 members of the drama club, 15 are male
(2) of the 20 members of the music club, 10 are male

Raj, one thing to note here is that you don't know the overlap, i.e the number of folks in the drama club, who are also members of the music club and vica versa.
Take this example,
20 members of the music club - 10 are male
all those 10 are also part of the drama club,
total ## of unique members: (16+ 20) - 10 = 26
## of males = 15
so % of males : 15/26 * 100

what if all members were exclusive, ie. no overlap
then % of males : 25/26 * 100

Therefore: E
RonPurewal
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wow, that's evil. usually, problems like this will actually give some sort of explicit indication that there's an overlap.

evil.

watch those assumptions!
MBA aspirant

RPurewal wrote:wow, that's evil. usually, problems like this will actually give some sort of explicit indication that there's an overlap.

evil.

watch those assumptions!

I am still wondering, if the problem states that there is no overlap in this case, then can both statements together be sufficient to solve such kind of problem? I think it is yes but don't know how to explain clearly. Please, show me your reasoning?
RonPurewal
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MBA aspirant wrote:I am still wondering, if the problem states that there is no overlap in this case, then can both statements together be sufficient to solve such kind of problem?

well, sure. if there's no overlap, then you can just add the given figures to produce totals, which you can then divide to find the percentage.

if there's no overlap:
total in the two clubs = 16 + 20 = 36
total males = 15 + 10 = 25
% male = 25/36 = (no need to find the actual number; SUFFICIENT)

of course, we should know that they aren't going to make life this easy.

--

side note:
15 males and 1 female would make one heck of an interesting drama club.
commit.gmat
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Location: San Francisco

### Re:

RonPurewal wrote:
of course, we should know that they aren't going to make life this easy.

Sometimes, if I solve a problem too quickly, I am worried that I might be missing something in the problem. They don't even make life easy on easier problems.

RonPurewal wrote:side note:
15 males and 1 female would make one heck of an interesting drama club.

:-) hehe...
Exam Date: July 18 2009
Target Score: 750+
Ben Ku
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### Re: If the drama club and music club

right. this is why the GMAT is not necessarily a hard test (although it is hard!), but it's more a tricky test!
Ben Ku
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ManhattanGMAT
jp.jprasanna
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### Re: If the drama club and music club

Thank you all for your explanations... very useful. However I did the double set matrix got the below..

-----------------Male--------No Male-------------Total
Drama --------15------------?-------------------- 16
*
*
Music----------10------------?---------------------20
*
*
Total-----------25------------?--------------------36

I was going to select E because C is too obvious to be correct in GMAT.
jnelson0612
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Joined: Fri Feb 05, 2010 10:57 am

### Re: If the drama club and music club

jp.jprasanna wrote:Thank you all for your explanations... very useful. However I did the double set matrix got the below..

-----------------Male--------No Male-------------Total
Drama --------15------------?-------------------- 16
*
*
Music----------10------------?---------------------20
*
*
Total-----------25------------?--------------------36

I was going to select E because C is too obvious to be correct in GMAT.

Here's the problem . . . when you use a double-set matrix you are assuming that every member fits into ONLY one of the four descriptive boxes you lay out. For example, maybe a problem says that a country club offers golf and tennis as activities. You would lay out your two sides as "golf"/"no golf" and "tennis"/"no tennis". Thus, your four descriptive boxes would be 1)golf/tennis, 2)tennis/no golf, 3)golf/no tennis, 4)no tennis/no golf. Notice that every member of the club would fit in ONLY one of those boxes. There is zero overlap among the four boxes. That is the beauty of the double-set matrix; it helps you strictly define who does what.

In this case your four boxes are Drama-Male, Drama-Female, Music-Male, Music-Female.

Notice that some of the males COULD be in both drama and music, but by setting up the table this way you are assuming that there is NO overlap. We can't make that assumption based on this problem, since it doesn't tell us that there is no overlap.

I hope that this clears things up!
Jamie Nelson
ManhattanGMAT Instructor
jp.jprasanna
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### Re: If the drama club and music club

jnelson0612 wrote:
jp.jprasanna wrote:Thank you all for your explanations... very useful. However I did the double set matrix got the below..

-----------------Male--------No Male-------------Total
Drama --------15------------?-------------------- 16
*
*
Music----------10------------?---------------------20
*
*
Total-----------25------------?--------------------36

I was going to select E because C is too obvious to be correct in GMAT.

Here's the problem . . . when you use a double-set matrix you are assuming that every member fits into ONLY one of the four descriptive boxes you lay out. For example, maybe a problem says that a country club offers golf and tennis as activities. You would lay out your two sides as "golf"/"no golf" and "tennis"/"no tennis". Thus, your four descriptive boxes would be 1)golf/tennis, 2)tennis/no golf, 3)golf/no tennis, 4)no tennis/no golf. Notice that every member of the club would fit in ONLY one of those boxes. There is zero overlap among the four boxes. That is the beauty of the double-set matrix; it helps you strictly define who does what.

In this case your four boxes are Drama-Male, Drama-Female, Music-Male, Music-Female.

Notice that some of the males COULD be in both drama and music, but by setting up the table this way you are assuming that there is NO overlap. We can't make that assumption based on this problem, since it doesn't tell us that there is no overlap.

I hope that this clears things up!

Jamie - perfect. Many thanks for your response... I think the key part of the question is " what percent of the combined membership will be male? " -This signifies a potential overlap CORRECT?

I found some other question where the over lap is also covered i.e the question is written in such a way that both and neither are covered.... (below link)

http://www.manhattangmat.com/forums/at-a-two-day-seminar-90-percent-of-those-registered-t285.html

The double set matrix for the above question is as below -

rows 1st day and not 1st day

Columns 2nd day and not 2nd day

AM i missing something fundamental here or is it just the way it is?

Cheers
jp
jnelson0612
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### Re: If the drama club and music club

Hey JP,
"What percent of the combined membership will be male" may or may not indicate that there is overlap between the males in the two groups. Let's go over again what we know:

The question:
If the drama club and music club are combined, what percent of the combined membership will be male?

1) of the 16 members of the drama club, 15 are male.
2) of the 20 members of the music club, 10 are male.

We COULD have absolutely no overlap between the clubs; people are only members of one club or the other. It could be that if we combine the clubs we have 36 total members, and 25 of those are male, or 25/36 (whatever that is as a percentage).

Or we COULD have overlap between the males in the clubs (assume no overlap between females to make things easier). What if all 10 males in the music club are also in the drama club? Let's do a count:
Music Club has 10 females and 10 males
Drama Club has 1 female and 15 males, but we have already counted 10 of them as members of the music club. There are 5 new males in the drama club that we need to count.

How many total people do we have in this scenario?
10 (music female) + 10 (music male/drama male) + 1 (drama female) + 5 (drama male) = 26 total people, and 15 of those are males or 15/26. This is a different percentage than the first one.

Let me know if you need further explanation. I especially want to make sure that you understand from my previous post why the double set matrix is not appropriate to use here. We just have too many categories: male/female, music/not music, drama/not drama.
Jamie Nelson
ManhattanGMAT Instructor
krishnan.anju1987
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### Re: If the drama club and music club

This problem is wicked.. I immediately decided and thought this problem was translated incorrectly or something. I never thought GMAT folks trick us like this.. WICKED!!!

Now this, I fear, will make me doubt every time I see a question whether the overlap criterion can be applied to that question or not.
RonPurewal
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### Re: If the drama club and music club

krishnan.anju1987 wrote:This problem is wicked.. I immediately decided and thought this problem was translated incorrectly or something. I never thought GMAT folks trick us like this.. WICKED!!!

Now this, I fear, will make me doubt every time I see a question whether the overlap criterion can be applied to that question or not.

the point of the problem is for you to have to think about these things.