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

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Manager
Joined: 09 Feb 2006
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Of the 75 houses in a certain community, 48 have a patio. [#permalink]  16 Jul 2006, 07:14
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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.
Intern
Joined: 11 Jul 2006
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Location: Boston
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Re: DS: Patio and swimming pool (from GMATPrep) [#permalink]  16 Jul 2006, 07:29
The stem can be depicted as

SP No SP Total
PAT 48
No PAT 27
Total 75

(1) Gives us
SP No SP Total
PAT 10 38 48
No PAT 27
Total 75

This is not SUFF

(2) Gives us
SP No SP Total
PAT x 48
No PAT 27-x x 27
Total x+27-x 75

TOtal Houses with SP = x+27-x = 27

So (2) alone is sufficient
--------------------------------------

likar 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.
Manager
Joined: 27 Jan 2006
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Location: Europe
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C, I think..... with B alone, from 0 to 27 can be answers...
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Manager
Joined: 01 Jun 2006
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I will go with B as well. I made a matrix with Have patio No Patio etc but then after thinking about it came up with a quicker accpoach.

Total = People with Pools + People with Patios + Peole with Neither and People with Either.

In 2 we are told People with Neither equals People with Either.

Hence we can write

75 = People with pool + Peole with Patios

We knoe People with Pool = 48. So People with Pools equals 27. I think this is a valid approach/ What do the math experts think?

OA ?
SVP
Joined: 30 Mar 2006
Posts: 1739
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jeunesis wrote:
C, I think..... with B alone, from 0 to 27 can be answers...

Whatever be the case the number will be 27. remember it is asking how many have swimming pool not how many have only swimming pool.

Let number of houses having both pool and patio be x hence number of people having neither is x

Let number of people having only pool be y

75 = 48 + (y+x) +x(neither) -x (both)
Therefore
y+x (pool) = 75-48 = 27
Manager
Joined: 04 Jul 2006
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C.

rbcola wrote:
In 2 we are told People with Neither equals People with Either.

Hence we can write

75 = People with pool + Peole with Patios

OA ?

This must be 75 = People with pool + Peole with Patios + 2*People with Neither

Hence, B is not sufficient.

But both statements together are sufficient.
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