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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

1

This post received KUDOS

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.

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

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01 Sep 2014, 01:37

Expert's post

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 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? _________________

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

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05 Oct 2015, 13:50

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email. _________________

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.

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