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

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Of the 75 houses in a certain community, 48 have a patio. [#permalink] New post 21 Feb 2008, 13:37
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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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Re: GMATprep - Matrix [#permalink] New post 21 Feb 2008, 22:31
Answer: C

Number of swimming pools: 27
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Re: GMATprep - Matrix [#permalink] New post 21 Feb 2008, 22:35
GMATprep says OA is B.

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

thoughts?
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Re: GMATprep - Matrix [#permalink] New post 21 Feb 2008, 22:58
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
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Re: GMATprep - Matrix [#permalink] New post 26 Feb 2008, 02:19
someone give a more detailed explanation please
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Re: GMATprep - Matrix [#permalink] New post 26 Feb 2008, 07:27
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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
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Re: GMATprep - Matrix [#permalink] New post 26 Feb 2008, 14:14
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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Re: GMATprep - Matrix [#permalink] New post 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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Re: GMATprep - Matrix [#permalink] New post 31 Dec 2009, 10:19
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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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Re: GMATprep - Matrix   [#permalink] 31 Dec 2009, 10:19
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