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

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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.

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.

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...
_________________

You tried your best and you failed miserably. The lesson is 'never try'. -Homer Simpson

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.
_________________

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

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09 Jan 2014, 04:49

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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.

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

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01 Sep 2014, 01:23

My answer is D.

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.

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 answer is D.

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.

Please help me correct my reasoning.

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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05 Oct 2015, 13:50

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

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06 Mar 2016, 09:23

Steinbeck wrote:

Did anyone tried solving this problem with double matrix? One of the guys did, but looks like his excel is incomplete

From stem , we get 75-48 = 27 houses with no patio From Stem 2: Let b be the number of houses with a pool , which also happens to be number of houses without a pool.

b + (27-b) = houses with swimming pool only 27 = houses with swimming pool only.

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

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01 Aug 2016, 02:23

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.

I marked answer D thinking A is also sufficient because I didn't consider the case where a house has neither a swimming pool nor a patio. I did see the "neither" case in option B but thought it doesn't have relevance to option A and also in main question there wasn't anything mentioned about "neither" case. How do we come to know whether "neither" case is applicable to a question or not? If they haven't particularly mentioned in the question that 'each house has a patio or a swimming pool' then it is necessary to consider the "neither" case?

gmatclubot

Re: Of the 75 houses in a certain community, 48 have a patio.
[#permalink]
01 Aug 2016, 02:23

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