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.

this is a canonical overlapping sets problem, so set up the double-set matrix.

a solution is here:
http://xs228.xs.to/xs228/08263/pool_pat ... ion565.jpg

answer = b

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if you don't like using x for the number quoted in statement (2), you could always try plugging in a couple of different numbers, and noting that you get the same answer no matter what number you plug in.

from stmt 2

48 + x(swimming pool) -(y(common house)) + y(neither ) = 75
48 + x = 75
x = 27

thanks ron for the solution. i have question for you.

i get a bit confused - when to set up a matrix and when to go for venn diagram.

in short, what are the hints i should look for in the problem?

Shouldn't the answer be C??

The question stem is asking us to find the number of houses that have a swimming pool...and not only a swimming pool. bBut the answer "27" that we get from B is the number of houses with ONLY a swimming pool. So we need A as well to get "x" and hence the total number of houses that have a swimming pool - that is, "27+x".

Pls let me know if I am going wrong anywhere....

Take a look at Ron's diagram again. 27 is the number of houses with pools that have patios and no patios. Thus, these are all the houses with swimming pools. 48 is the number of houses with no swimming pools. 27 is the number of houses with no patios. 48 is the number of houses with patios. We don't know the details, but we do know the totals.

yep. actually, all of this work is wrong (although your interpretation of the problem is correct).

as the poster below you (and above this post) has noted, 27 is, indeed, the TOTAL number of houses with pools.
regardless of whether there's a patio.

the number of houses with only a swimming pool is actually still unknown in statement 2; note that there's still an "x" in the expression.

actually, this is pretty straightforward.

if there are 2 overlapping criteria, then use the matrix.
if there are 3 overlapping criteria, then use a venn diagram.
that's it.

do not EVER use a venn diagram to solve problems with 2 overlapping criteria, unless you like to make things harder than they should be.

Ron -

Can you repost the link to the double matrix for this question? I know how to get to the answer algebraically but I took one look at the matrix I drew, said "no way" and moved on. Perhaps your matrix makes the answer a little more evident :)

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.


It probably looked something like this:



Statement (1) tells us:

This is insufficient.

Statement (2) tells us:


So 27 - y = x - y
x = 27
Statement (2) is sufficient, so the answer is (B).

_________________
Ben Ku
Instructor
ManhattanGMAT

Hi there Ben,
I am unable to understand that part when u have gotten 38.
sorry pls tell me how did u get that.

According to me since x=27,
y= 0.

so how did we arrive at 30 for patio with no pool. Pls help as this is crucial to get the right answer.
i would have happily chosen c and moved on. what does statement b have that i could nt see.

Regards
Poonam

Statement 1 says there are 38 people who have a patio but no pool. However, this is insufficient.

_________________
Ben Ku
Instructor
ManhattanGMAT

Ron,

You say that always use the 2 set matrix and not the venn unless you want to make life harder.

I am attaching below 3 problems. All of them are from the GMAT Prep software. I have tried using the 2 set matrix but it does not work (at least for me). I also tried 'googling' these questions and the solutions are either the venn diagram or the T = A+B-Both+Neither formula, which i understand is nothing but the venn diagram algebraic representation.

If you could please throw some light, I will indeed be glad. Perhaps i am missing the concept or doing something wrong, but this if you reply, it will indeed help.


1) A seminar consisted of morning session and afternoon session. If each of the 128 people attending attended at least one of the two sessions, how many of the people attended the morning session only?
a. ¾ attended both sessions
b. 7/8 attended the afternoon session

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2]If 75 percent of the guests at a certain banquet ordered dessert, what percent of the guests ordered coffee?
(1) 60 percent of the guests who ordered dessert also ordered coffee.
(2) 90 percent of the guests who ordered coffee also ordered dessert.

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3) Last year in a group of 30 businesses, 21 reported a net profit and
15 had investments in foreign markets. How many of the businesses
did not report a net profit nor invest in foreign markets last year?

(1) last year 12 of the 30 businesses reported a net profit and had investments in foreign markets.
(2) last year 24 of the 30 businesses reported a net profit or invested in
foreign markets, or both.
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Any Chance that some expert might reply to my question.

When to use a Venn Diag & when to use a 2 set matrix for [2 overlapping sets] .

The examples are listed above.