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 99148 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 55657 times ]

We want to find x.

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

Attachment:

Capture.PNG [ 4.62 KiB | Viewed 55614 times ]

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

Attachment:

2.PNG [ 4.12 KiB | Viewed 55657 times ]

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

Therefore, \(x = 27\)

Attachments

3.PNG [ 4.33 KiB | Viewed 55573 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

bumpbot · Answer

Automated notice from GMAT Club BumpBot:

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

This post was generated automatically.

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

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Data Sufficiency (DS) Questions

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

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards