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

Question

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.

atish · Accepted Answer

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.

fozzzy · Answer

We have to find the value of X + Y = ?

we know from statement 1 that 10 is the area covered by both and 38 is only patio we have no info about neither not sufficient

Statement 2

We have 48 - x + x + y + x = 75

we can find the value for x + y = 27 sufficient

Good problem 8-)

Attachments

Venn diagram.jpg [ 7.99 KiB | Viewed 99279 times ]

srp · Answer

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

GMATBLACKBELT · Answer

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

crejoc · Answer

I dont know how to draw table here... attached a document file with the solution, let me know is that clear for you..

Economist · Answer

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.

Total = only s + only p + Neither -Both
Now, lets forget about stmt 1 for now.

We have, total =75, neither=both=x, and from the stem we have 48 houses with patio ( these 48 can include houses with Only patio or Both. So we are not sure if we can take s=48 in the above formula.

I may be wrong...not sure.

crejoc · Answer

since only is not given in the question , 48 includes both houses that contains patio with swimming pool and patio without swimming pool.. did you go through the document attached, i think that is very clear...

aja1991 · Answer

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.

The best answer is  B!

shriramvelamuri · Answer

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

Bunuel · Answer

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?

keats · Answer

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

sairam595 · Answer

using double set matrix and from option B, we can solve as below

S.P = swimming pool

DAllison2016 · Answer

Given the question, we have the following table:

\begin{array}{c|cc|c}

& 	extbf{P} & 	extbf{NP} & \ \hline
	extbf{S} & A & B & \color{green}{Z} \
	extbf{NS} & C & D & \ \hline
 & 48 & 27 & 75 \ 
\end{array}

(1) 38 of the houses in the community have a patio but do not have a swimming pool.

\begin{array}{c|cc|c}
& 	extbf{P} & 	extbf{NP} & \ \hline
	extbf{S} & A & B & \color{green}{Z} \
	extbf{NS} & 38 & D & \ \hline
 & 48 & 27 & 75 \ 
\end{array}

A = 10

We have no way of determining  B

Insufficient

(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.

\begin{array}{c|cc|c}
& 	extbf{P} & 	extbf{NP} & \ \hline
	extbf{S} & X & B & \color{green}{Z} \
	extbf{NS} & C & X & \ \hline
 & 48 & 27 & 75 \ 
\end{array}

We can see that although we cannot solve the matrix, we can see that a vertical and horizontal equation are equal due to the added symmetry.

B + X = 27 \implies Z = 27

Sufficient

(B) statement 2 alone is sufficient, but statement 1 alone is not sufficient to answer the question

anairamitch1804 · Answer

The matrix is a great way to solve these questions, but we can solve even quicker if we know the overlapping sets formula:

Total # of items = # in group 1 + # in group 2 + neither - both

From the original, we have:

75 = 48 + swimming pool + neither - both

(2) tells us that neither = both, or that neither - both = 0. Subbing into the equation we now get:

75 = 48 + swimming pool + 0

which we can certainly solve.
Hence B.

ramalcha · Answer

The easiest way to solve this question is to draw a table.

With the information given in the question stem, the table looks like this:

Attachment:

2.PNG [ 4.12 KiB | Viewed 55761 times ]

We want to find x.

Statement (1) is clearly insufficient from filling in the boxes.

Attachment:

Capture.PNG [ 4.62 KiB | Viewed 55716 times ]

Statement (2) seems wordy, but is as simple as the table below:

Attachment:

2.PNG [ 4.12 KiB | Viewed 55761 times ]

\((x-y) + y = 27\)

Therefore, \(x = 27\)

Attachments

3.PNG [ 4.33 KiB | Viewed 55675 times ]

KarishmaB · Answer

We know Total - Neither = n(Patio) + n(Pool) - Both 75 - Neither = 48 + n(Pool) - Both (1) 38 of the houses in the community have a patio but do not have a swimming pool. This means Only Patio = 38 so Both = 10 But we still do not know 'Neither' hence we cannot get n(Pool). Not sufficient alone. (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. Say Both = Neither = x 75 - x = 48 + n(Pool) - x n(Pool) = 27 Sufficient Answer (B) Both and Neither move together as long as other values remain the same. Think about it - as the overlap between the circles increases, the circles come together and the 'neither' region increases. Its application in Max-min Sets questions is discussed here: https://youtu.be/M3wJ15ZC1pY

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