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# How many members of a certain country club play both squash

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How many members of a certain country club play both squash [#permalink]

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12 Apr 2011, 15:28
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How many members of a certain country club play both squash and racquetball?

(1) 110 members of the country club play either squash or racquetball.

(2) 70 members of the country club play squash and 65 members of the country club play racquetball.

[Reveal] Spoiler: OA

Last edited by skbjunior on 12 Apr 2011, 16:17, edited 1 time in total.
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Re: Data sufficiency overlapping sets [#permalink]

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12 Apr 2011, 16:02
2
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skbjunior wrote:
How many members of a certain country club play both squash and racquetball?

(1) 110 members of the country club play either squash or racquetball.

(2) 70 members of the country club play squash and 65 members of the country club play racquetball.

(1)
$$n(R \hspace{2} \cup \hspace{2} S)=110$$
Possible that all 110 play both.
OR
40 play only racquetball, 40 play only squash and 30 play both.
Not Sufficient.

(2)
$$n(R)=65$$
$$n(S)=70$$
Possible that 65 play both games.
OR
35 play both games.
Not Sufficient.

$$n(R \hspace{2} \cup \hspace{2} S)=n(R)+n(S)-n(R \hspace{2} \cap \hspace{2} S)$$
$$n(R \hspace{2} \cap \hspace{2} S)=n(R)+n(S)-n(R \hspace{2} \cup \hspace{2} S)=65+70-110=135-110=25$$
Sufficient.

Ans: "C"
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Re: Data sufficiency overlapping sets [#permalink]

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12 Apr 2011, 16:20
fluke wrote:
skbjunior wrote:
How many members of a certain country club play both squash and racquetball?

(1) 110 members of the country club play either squash or racquetball.

(2) 70 members of the country club play squash and 65 members of the country club play racquetball.

(1)
$$n(R \hspace{2} \cup \hspace{2} S)=110$$
Possible that all 110 play both.
OR
40 play only racquetball, 40 play only squash and 30 play both.
Not Sufficient.

(2)
$$n(R)=65$$
$$n(S)=70$$
Possible that 65 play both games.
OR
35 play both games.
Not Sufficient.

$$n(R \hspace{2} \cup \hspace{2} S)=n(R)+n(S)-n(R \hspace{2} \cap \hspace{2} S)$$
$$n(R \hspace{2} \cap \hspace{2} S)=n(R)+n(S)-n(R \hspace{2} \cup \hspace{2} S)=65+70-110=135-110=25$$
Sufficient.

Ans: "C"

Thanks for your response fluke. C is indeed an OA.
I chose E though because nowhere it is mentioned that 'all the members play either squash or racquetball' or '0 members play neither squash nor racquetball.' Is my thought-process wrong in this case?
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Re: Data sufficiency overlapping sets [#permalink]

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12 Apr 2011, 19:14
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(1) is insufficient as we don't know about the break-up of memebrs who play squash or racquetball

(2) is insufficient as we don't know how many total members are there

Combining (1) and (2)

110 = 70 + 65 - both

=> both = 135 - 110 = 25

@skbjunior
'all the members play either squash or racquetball' means that all the members play at least one of the two sports and a few of them *may* play both the sports.

As a rough example for visualization, If you draw a Venn diagram of two overlapping cirlces inside a rectangle, in this case the area outside of two circles and within the rectangle will be zero.
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Re: Data sufficiency overlapping sets [#permalink]

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12 Apr 2011, 22:49
skbjunior wrote:

Thanks for your response fluke. C is indeed an OA.
I chose E though because nowhere it is mentioned that 'all the members play either squash or racquetball' or '0 members play neither squash nor racquetball.' Is my thought-process wrong in this case?

True. Your thought process is not completely off-track.
There could be 1000 members, out of which only 110 play either racquetball or squash.

Note, there are few formulas to find different things:

If you are given total number of members, then you would use the following and here, you would need that extra piece of information that everyone plays either racquetball or squash.
$$n(Total \hspace{2} members)=n(R)+n(S)-n(R \hspace{2} \cap \hspace{2} S)+n(Neither)$$

But, if we are not given how many "Total Members" are there, then we would simply use:
$$n(R \hspace{2} \cup \hspace{2} S)=n(R)+n(S)-n(R \hspace{2} \cap \hspace{2} S)$$
Here, we don't need the total member count or the extra piece of information.
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Re: Data sufficiency overlapping sets [#permalink]

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26 Nov 2011, 06:31
fluke wrote:
skbjunior wrote:

Thanks for your response fluke. C is indeed an OA.
I chose E though because nowhere it is mentioned that 'all the members play either squash or racquetball' or '0 members play neither squash nor racquetball.' Is my thought-process wrong in this case?

True. Your thought process is not completely off-track.
There could be 1000 members, out of which only 110 play either racquetball or squash.

That is correct. Nowhere it is stated because you don't need this information to answer the question.

Note: It is wrong to assume from the first statement that the total number of members is 110 or that members who play neither sport are 0.
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Re: How many members of a certain country club play both squash [#permalink]

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26 Nov 2011, 09:24
I tried doing it MGMAT way. and keep getting E. Please see the attachment. W/o knowing formula, i ended up using matrix, and having hard time to understand the OA. Can someone please advice/explain a bit more?
Attachments

OS.gif [ 2.02 KiB | Viewed 2053 times ]

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Re: How many members of a certain country club play both squash [#permalink]

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26 Nov 2011, 10:58
2
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BDSunDevil wrote:
I tried doing it MGMAT way. and keep getting E. Please see the attachment. W/o knowing formula, i ended up using matrix, and having hard time to understand the OA. Can someone please advice/explain a bit more?

First of all cross out the 110 as total from the matrix. We don't know that.
Name the Question Mark (?) in your matrix as $$x$$.
The box below $$x$$ as $$y$$
The box on the right of $$x$$ as $$z$$.

Solution:

From Statement 1 we know that: $$x+y+z=110$$ (1)

From the Matrix we can see that $$x+y=70$$ (2) and $$x+z=65$$ (3)

(1)-(2) ---> $$z=40$$ : (3)--->$$x=65-40=25$$

So it is C.
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Re: How many members of a certain country club play both squash [#permalink]

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26 Nov 2011, 22:19
I feel that the wording in this question is not very clear. Saying that "110 members of the country club play either squash or racquetball" sounds to my ears like 110 member play one or the other, but not both (this is the normal English meaning of either ... or ...). Is this the wrong way to understand this construction on the GMAT? If so, how would you expect exclusive or to be expressed?

Obviously in this case it means inclusive or because otherwise you seem to end up with 12.5 people playing both sports!
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Re: How many members of a certain country club play both squash [#permalink]

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27 Nov 2011, 05:08
bobfirth wrote:
I feel that the wording in this question is not very clear. Saying that "110 members of the country club play either squash or racquetball" sounds to my ears like 110 member play one or the other, but not both (this is the normal English meaning of either ... or ...). Is this the wrong way to understand this construction on the GMAT? If so, how would you expect exclusive or to be expressed?

Obviously in this case it means inclusive or because otherwise you seem to end up with 12.5 people playing both sports!

Either A or B ---> A or B or Both.

http://mathforum.org/library/drmath/view/55692.html

If it said All 110 members play either squash or racquetball that would mean that the total is 110 and that neither is 0.
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Re: How many members of a certain country club play both squash [#permalink]

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29 Nov 2011, 03:18
1
KUDOS
BDSunDevil wrote:
I tried doing it MGMAT way. and keep getting E. Please see the attachment. W/o knowing formula, i ended up using matrix, and having hard time to understand the OA. Can someone please advice/explain a bit more?

your matrix will work as soon as you put 0 in the 'niether squash nor r ball region. This is because the data given is about r ball or squash players....nothing is said about other members of the club. The '110' you have fited in the total bosx is the same 110 members of the country club who play either squash or racquetball. (as given in statement1)

EDIT: i MADE A MISTAKE IN WRITING 35....IT SHOULD BE 45....
Attachments

untitled.jpg [ 12.41 KiB | Viewed 1969 times ]

Last edited by Dreaming on 29 Nov 2011, 05:37, edited 2 times in total.
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Re: How many members of a certain country club play both squash [#permalink]

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13 Oct 2013, 07:11
1
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skbjunior wrote:
How many members of a certain country club play both squash and racquetball?

(1) 110 members of the country club play either squash or racquetball.

(2) 70 members of the country club play squash and 65 members of the country club play racquetball.

I also tried using the Double-set matrix for this one, but in the middle of the problem changed to use the classic formula--> Total = A + B - Both + Neither
and realized I had everything. Sometimes, try to visualize the problem in its entirety and don't force a given method. There might be a better way to draw some logic conclusions, or use a backup approach.

Cheers
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Re: How many members of a certain country club play both squash [#permalink]

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