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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]  11 Mar 2008, 11:18
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 patio nor a swimming pool.
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Re: gprep ratio [#permalink]  11 Mar 2008, 16:31
Given total houses = 75
House with Patio = 48

(1) 38 of the houses in the community have a patio but do not have a swimming pool.
Means there are 10 Houses that do have a swimming pool as well as patio. But does not tells us how many houses are with swimming pool, so it alone cannot answer the question.

(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 patio nor a swimming pool.
Suppose house with swimming pool is S.
House with Pool and Patio = P
House with No Pool or Patio = P (as statement 2 tell us)
Now employ set theory
That total number of house with Pool and Patio altogether = House with Pool + House with Patio - House with both Pool and Patio => S + 48 - P
75 = (S + 48 - P) + P (Total number of house will be sun of house with Pool and Patio altogether and house without any pool and patio)
So S = 75 - 48
Re: gprep ratio   [#permalink] 11 Mar 2008, 16:31
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