Summer is Coming! Join the Game of Timers Competition to Win Epic Prizes. Registration is Open. Game starts Mon July 1st.

 It is currently 21 Jul 2019, 05:59

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

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

Author Message
TAGS:

### Hide Tags

Intern
Joined: 06 Oct 2010
Posts: 47
How many members of a certain country club play both squash  [#permalink]

### Show Tags

Updated on: 12 Apr 2011, 16:17
1
4
00:00

Difficulty:

25% (medium)

Question Stats:

76% (01:07) correct 24% (01:07) wrong based on 144 sessions

### HideShow timer Statistics

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.

Originally posted by skbjunior on 12 Apr 2011, 15:28.
Last edited by skbjunior on 12 Apr 2011, 16:17, edited 1 time in total.
Retired Moderator
Joined: 20 Dec 2010
Posts: 1733
Re: Data sufficiency overlapping sets  [#permalink]

### Show Tags

12 Apr 2011, 16:02
2
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"
_________________
Intern
Joined: 06 Oct 2010
Posts: 47
Re: Data sufficiency overlapping sets  [#permalink]

### Show Tags

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?
Retired Moderator
Joined: 16 Nov 2010
Posts: 1358
Location: United States (IN)
Concentration: Strategy, Technology
Re: Data sufficiency overlapping sets  [#permalink]

### Show Tags

12 Apr 2011, 19:14
1
(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.
_________________
Formula of Life -> Achievement/Potential = k * Happiness (where k is a constant)

GMAT Club Premium Membership - big benefits and savings
Retired Moderator
Joined: 20 Dec 2010
Posts: 1733
Re: Data sufficiency overlapping sets  [#permalink]

### Show Tags

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.
_________________
Manager
Joined: 23 Oct 2011
Posts: 83
Re: Data sufficiency overlapping sets  [#permalink]

### Show Tags

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.
Manager
Joined: 13 May 2011
Posts: 217
WE 1: IT 1 Yr
WE 2: Supply Chain 5 Yrs
Re: How many members of a certain country club play both squash  [#permalink]

### Show Tags

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 3323 times ]

Manager
Joined: 23 Oct 2011
Posts: 83
Re: How many members of a certain country club play both squash  [#permalink]

### Show Tags

26 Nov 2011, 10:58
2
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.
Intern
Joined: 11 Nov 2011
Posts: 14
Re: How many members of a certain country club play both squash  [#permalink]

### Show Tags

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!
Manager
Joined: 23 Oct 2011
Posts: 83
Re: How many members of a certain country club play both squash  [#permalink]

### Show Tags

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.
Manager
Joined: 17 Sep 2011
Posts: 164
Concentration: Strategy, Operations
Schools: ISB '15
GMAT 1: 720 Q48 V40
GPA: 3.18
WE: Supply Chain Management (Manufacturing)
Re: How many members of a certain country club play both squash  [#permalink]

### Show Tags

Updated on: 29 Nov 2011, 05:37
1
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 3241 times ]

Originally posted by Dreaming on 29 Nov 2011, 03:18.
Last edited by Dreaming on 29 Nov 2011, 05:37, edited 2 times in total.
SVP
Joined: 06 Sep 2013
Posts: 1647
Concentration: Finance
Re: How many members of a certain country club play both squash  [#permalink]

### Show Tags

13 Oct 2013, 07:11
1
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
J
Intern
Joined: 01 Feb 2018
Posts: 17
Re: How many members of a certain country club play both squash  [#permalink]

### Show Tags

26 Mar 2018, 04:30
IMO Statement (1) is not correctly articulated.

It should be "110 members of the country club play either squash or racquetball or both."

Because if it does not include the people who play both then we could not substract them in the first place. Is there any flaw in the reasoning?
Re: How many members of a certain country club play both squash   [#permalink] 26 Mar 2018, 04:30
Display posts from previous: Sort by