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# Of the 75 houses in a certain community, 48 have a patio.

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CEO
Joined: 21 Jan 2007
Posts: 2666
Location: New York City
Of the 75 houses in a certain community, 48 have a patio.  [#permalink]

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21 Feb 2008, 13:37
17
46
00:00

Difficulty:

95% (hard)

Question Stats:

43% (01:58) correct 57% (01:58) wrong based on 1127 sessions

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Of the 75 houses in a certain community, 48 have a patio. How many of the houses in the community have a swimming pool?

(1) 38 of the houses in the community have a patio but do not have a swimming pool.
(2) The number of houses in the community that have a patio and a swimming pool is equal to the number of houses in the community that have neither a swimming pool nor a patio.

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Manager
Joined: 25 Aug 2009
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31 Dec 2009, 10:19
17
5
Here is my standard approach to solve such problems
P= # of houses with patio only.
Q= # of houses with pool only.
R= # of houses with patio & pool.
S= # of houses with no patio & no pool.

Given P+Q+R+S=75
& P+R=48
What is Q+R? (1)

Solving the first two equations
Q+S+48=75
Q+S=27 (2)

Now let's look at the statements
Statement 1
P=38 unnecessary and insufficient.

Statement 2
R=S
Substituting in (1)
Q+S?
We know form (2) that Q+S=27
hence sufficient.
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##### General Discussion
CEO
Joined: 21 Jan 2007
Posts: 2666
Location: New York City

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21 Feb 2008, 22:35
2
GMATprep says OA is B.

i also chose C. I cannot figure out why it is B

thoughts?
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Manager
Joined: 02 Jan 2008
Posts: 153

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21 Feb 2008, 22:58
2
1
B
--
From B, we have
x = number of houses without P and S = number of houses having P and S

75-x = P + S - x; 75=48+S; S=27
Manager
Joined: 15 Nov 2007
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26 Feb 2008, 02:19
someone give a more detailed explanation please
SVP
Joined: 29 Mar 2007
Posts: 2465

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26 Feb 2008, 07:27
6
2
bmwhype2 wrote:
Of the 75 houses in a certain community, 48 have a patio. How many of the houses in the community have a swimming pool?

(1) 38 of the houses in the community have a patio but do not have a swimming pool.
(2) The number of houses in the community that have a patio and a swimming pool is equal to the number of houses in the community that have neither a swimming pool nor a patio.

finally can got my computer log in for work... so I can participate on GClub when I have nuffin to do.

Tricky problem. This is why its important to write everything out and not do it in your head.

youl notice we want x+z, which = m.

notice carefully that x+z also =27... its that simple, but so easy to miss... I missed it and said C at first.

B
Attachments

Matrix problem.xls [13.5 KiB]

CEO
Joined: 21 Jan 2007
Posts: 2666
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26 Feb 2008, 14:14
1
1
GMATBLACKBELT wrote:
bmwhype2 wrote:
Of the 75 houses in a certain community, 48 have a patio. How many of the houses in the community have a swimming pool?

(1) 38 of the houses in the community have a patio but do not have a swimming pool.
(2) The number of houses in the community that have a patio and a swimming pool is equal to the number of houses in the community that have neither a swimming pool nor a patio.

finally can got my computer log in for work... so I can participate on GClub when I have nuffin to do.

Tricky problem. This is why its important to write everything out and not do it in your head.

youl notice we want x+z, which = m.

notice carefully that x+z also =27... its that simple, but so easy to miss... I missed it and said C at first.

B

hmmm very tricky. we dont even need to know what z is. just M...
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Senior Manager
Joined: 17 Mar 2009
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16 Aug 2009, 18:32
5
nitindas wrote:
Can you please elaborate what table method did you use to solve??

sure,.. i dont know how to draw table here... attached a document file with the solution, let me know is that clear for you..
Attachments

File comment: Solution attached

Director
Joined: 01 Apr 2008
Posts: 811
Name: Ronak Amin
Schools: IIM Lucknow (IPMX) - Class of 2014

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Updated on: 17 Aug 2009, 04:28
Stmt 2 is sufficient if the question says "Of the 75 houses in a certain community,48 ONLY have a patio.

out of these 48, 40 can have only patio and 8 can have both..Then we have 8 houses which have neither S nor P.

I dont think the wording is right. Else, the solution should be C because we need to get houses that ONLY have a patio.

Originally posted by Economist on 17 Aug 2009, 02:31.
Last edited by Economist on 17 Aug 2009, 04:28, edited 1 time in total.
Director
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17 Aug 2009, 04:31
Of the 75 houses in a certain community,48 have a patio.How many of the houses in the community have a swimming pool?
1. 38 of the houses in the community have a patio but do not have a swimming pool.
2. The number of houses in the community that have a patio and a swimming pool is equal to the number of houses in the community that have neither a swimming pool nor a patio.

Total = only s + only p + Neither -Both
Now, lets forget about stmt 1 for now.

We have, total =75, neither=both=x, and from the stem we have 48 houses with patio ( these 48 can include houses with Only patio or Both. So we are not sure if we can take s=48 in the above formula.

I may be wrong...not sure.
Senior Manager
Joined: 17 Mar 2009
Posts: 251

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17 Aug 2009, 06:55
2
Economist wrote:
( these 48 can include houses with Only patio or Both. So we are not sure if we can take s=48 in the above formula.

I may be wrong...not sure.

since only is not given in the question , 48 includes both houses that contains patio with swimming pool and patio without swimming pool.. did you go through the document attached, i think that is very clear...
Director
Joined: 01 Apr 2008
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Name: Ronak Amin
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17 Aug 2009, 07:11
crejoc wrote:
Economist wrote:
( these 48 can include houses with Only patio or Both. So we are not sure if we can take s=48 in the above formula.

I may be wrong...not sure.

since only is not given in the question , 48 includes both houses that contains patio with swimming pool and patio without swimming pool.. did you go through the document attached, i think that is very clear...

Yup got it, its clear:) Thanks! I shall try to use tables for such questions as well, +1 to you.
Intern
Joined: 14 May 2008
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30 Dec 2009, 04:35
Total = A+B - A intersection B (Common to A and B) + (~A and ~B ---> Not part of Subset A or Subset B)

from the given problem we have the following

Total = 75

A = 48

A intersection B = (~A and ~B ---> Not part of Subset A or Subset B)

(~A and ~B ---> Not part of Subset A or Subset B) - A intersection B = 0

So Equation becomes

75=48+B

Thus B is sufficient
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Joined: 26 Feb 2010
Posts: 75
Location: Argentina

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13 May 2010, 07:34
1
B
Nice explanation!
with statement 2 we don't care about what is in the middle of the table, we just know that the houses with swimming pool are 75 - 48
Director
Joined: 29 Nov 2012
Posts: 801
Re: Of the 75 houses in a certain community, 48 have a patio.  [#permalink]

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24 Jul 2013, 06:20
5
6
We have to find the value of X + Y = ?

we know from statement 1 that 10 is the area covered by both and 38 is only patio we have no info about neither not sufficient

Statement 2

We have 48 - x + x + y + x = 75

we can find the value for x + y = 27 sufficient

Good problem
Attachments

Venn diagram.jpg [ 7.99 KiB | Viewed 29580 times ]

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Re: Of the 75 houses in a certain community, 48 have a patio.  [#permalink]

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09 Jan 2014, 04:49
2
We have a universal formula: Total= A + B - Both(A&B) + Neither

(1) is obviously insufficient.

(2) is sufficient because from the given conditions we get this: Both(A&B) = Neither = T(Let it be T, to make it simple)
=> 75 = 48 + B - T + T => B = 27.

Senior Manager
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Re: Of the 75 houses in a certain community, 48 have a patio.  [#permalink]

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01 Sep 2014, 01:23

My Reasoning ;From the main question and also from statement 1-> it is apparent that all the houses have a swimming pool or a Patio. Hence you can answer the question with just A.

Statement B introduces that some houses do no have either. Also you can answer the question with statement B.

Thanks and kudos to every one
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Joined: 02 Sep 2009
Posts: 49430
Re: Of the 75 houses in a certain community, 48 have a patio.  [#permalink]

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01 Sep 2014, 01:37
shriramvelamuri wrote:
Of the 75 houses in a certain community, 48 have a patio. How many of the houses in the community have a swimming pool?

(1) 38 of the houses in the community have a patio but do not have a swimming pool.
(2) The number of houses in the community that have a patio and a swimming pool is equal to the number of houses in the community that have neither a swimming pool nor a patio.

My Reasoning ;From the main question and also from statement 1-> it is apparent that all the houses have a swimming pool or a Patio. Hence you can answer the question with just A.

Statement B introduces that some houses do no have either. Also you can answer the question with statement B.

Thanks and kudos to every one

Why it is obvious that all houses there have either a patio or a swimming pool? Why there could not be a house without either of them?
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Re: Of the 75 houses in a certain community, 48 have a patio.  [#permalink]

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01 Sep 2014, 01:48
Hi Bunuel,

There isnt mentioned anywhere about- houses (do not have either) or (have either).

But not thoroughly satisfied with the wording of the question.

Am I wrong in thinking this way.
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Posts: 49430
Re: Of the 75 houses in a certain community, 48 have a patio.  [#permalink]

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01 Sep 2014, 03:07
shriramvelamuri wrote:
Hi Bunuel,

There isnt mentioned anywhere about- houses (do not have either) or (have either).

But not thoroughly satisfied with the wording of the question.

Am I wrong in thinking this way.

Yes, saying that there are no houses without a patio and a swimming pool would be an unsound assumption.
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Re: Of the 75 houses in a certain community, 48 have a patio. &nbs [#permalink] 01 Sep 2014, 03:07

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