Last visit was: 19 Nov 2025, 06:09 It is currently 19 Nov 2025, 06:09
Close
GMAT Club Daily Prep
Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track
Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
Close
Request Expert Reply
Confirm Cancel
User avatar
bmwhype2
Joined: 21 Jan 2007
Last visit: 08 Mar 2010
Posts: 1,338
Own Kudos:
5,433
 [284]
Given Kudos: 4
Location: New York City
Posts: 1,338
Kudos: 5,433
 [284]
26
Kudos
Add Kudos
257
Bookmarks
Bookmark this Post
Most Helpful Reply
User avatar
atish
Joined: 25 Aug 2009
Last visit: 24 May 2011
Posts: 70
Own Kudos:
374
 [54]
Given Kudos: 3
Location: Streamwood IL
Concentration: Finance
Schools:Kellogg(Evening),Booth (Evening)
GPA: 3.4
WE 1: 5 Years
Posts: 70
Kudos: 374
 [54]
35
Kudos
Add Kudos
19
Bookmarks
Bookmark this Post
avatar
fozzzy
Joined: 29 Nov 2012
Last visit: 17 May 2015
Posts: 574
Own Kudos:
6,801
 [21]
Given Kudos: 543
Posts: 574
Kudos: 6,801
 [21]
13
Kudos
Add Kudos
8
Bookmarks
Bookmark this Post
General Discussion
User avatar
srp
Joined: 02 Jan 2008
Last visit: 01 May 2009
Posts: 76
Own Kudos:
268
 [5]
Posts: 76
Kudos: 268
 [5]
4
Kudos
Add Kudos
1
Bookmarks
Bookmark this Post
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
User avatar
GMATBLACKBELT
Joined: 29 Mar 2007
Last visit: 03 Jun 2013
Posts: 1,139
Own Kudos:
1,878
 [12]
Posts: 1,139
Kudos: 1,878
 [12]
9
Kudos
Add Kudos
3
Bookmarks
Bookmark this Post
bmwhype2
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
Attachments

Matrix problem.xls [13.5 KiB]
Downloaded 2049 times

User avatar
crejoc
Joined: 17 Mar 2009
Last visit: 14 Jul 2022
Posts: 132
Own Kudos:
2,007
 [11]
Given Kudos: 21
Posts: 132
Kudos: 2,007
 [11]
11
Kudos
Add Kudos
Bookmarks
Bookmark this Post
I dont know how to draw table here... attached a document file with the solution, let me know is that clear for you..
Attachments

File comment: Solution attached
Question houses with swimming pool.doc [34 KiB]
Downloaded 2394 times

User avatar
Economist
Joined: 01 Apr 2008
Last visit: 24 Dec 2018
Posts: 383
Own Kudos:
Given Kudos: 18
Name: Ronak Amin
Schools: IIM Lucknow (IPMX) - Class of 2014
Schools: IIM Lucknow (IPMX) - Class of 2014
Posts: 383
Kudos: 4,450
Kudos
Add Kudos
Bookmarks
Bookmark this Post
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.
User avatar
crejoc
Joined: 17 Mar 2009
Last visit: 14 Jul 2022
Posts: 132
Own Kudos:
2,007
 [2]
Given Kudos: 21
Posts: 132
Kudos: 2,007
 [2]
2
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Economist
( 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.

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...
avatar
aja1991
Joined: 03 Dec 2013
Last visit: 23 Oct 2017
Posts: 6
Own Kudos:
31
 [8]
Given Kudos: 57
Location: Uzbekistan
Concentration: Finance, Entrepreneurship
GMAT 1: 620 Q42 V33
GRE 1: Q790 V400
GPA: 3.4
WE:Analyst (Commercial Banking)
Products:
GMAT 1: 620 Q42 V33
GRE 1: Q790 V400
Posts: 6
Kudos: 31
 [8]
7
Kudos
Add Kudos
1
Bookmarks
Bookmark this Post
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!
avatar
shriramvelamuri
Joined: 27 Dec 2013
Last visit: 29 Jun 2016
Posts: 162
Own Kudos:
Given Kudos: 113
Posts: 162
Kudos: 137
Kudos
Add Kudos
Bookmarks
Bookmark this Post
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
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 19 Nov 2025
Posts: 105,388
Own Kudos:
Given Kudos: 99,977
Products:
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 105,388
Kudos: 778,218
Kudos
Add Kudos
Bookmarks
Bookmark this Post
shriramvelamuri
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?
User avatar
keats
Joined: 28 Nov 2014
Last visit: 08 Jun 2019
Posts: 739
Own Kudos:
Given Kudos: 86
Concentration: Strategy
GPA: 3.71
Products:
Posts: 739
Kudos: 1,361
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Did anyone tried solving this problem with double matrix? One of the guys did, but looks like his excel is incomplete
User avatar
sairam595
Joined: 15 Aug 2014
Last visit: 23 Dec 2016
Posts: 219
Own Kudos:
658
 [8]
Given Kudos: 470
Status:Always try to face your worst fear because nothing GOOD comes easy. You must be UNCOMFORTABLE to get to your COMFORT ZONE
Concentration: Marketing, Technology
GMAT 1: 570 Q44 V25
GMAT 2: 600 Q48 V25
WE:Information Technology (Consulting)
Products:
GMAT 2: 600 Q48 V25
Posts: 219
Kudos: 658
 [8]
7
Kudos
Add Kudos
1
Bookmarks
Bookmark this Post
Keats
Did anyone tried solving this problem with double matrix? One of the guys did, but looks like his excel is incomplete

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

S.P = swimming pool
Attachments

double set.png
double set.png [ 3.74 KiB | Viewed 61916 times ]

User avatar
DAllison2016
Joined: 07 Jul 2016
Last visit: 30 Sep 2016
Posts: 57
Own Kudos:
67
 [4]
Given Kudos: 51
GPA: 4
Posts: 57
Kudos: 67
 [4]
Kudos
Add Kudos
4
Bookmarks
Bookmark this Post
bmwhype2
Of the 75 houses in a certain community, 48 have a patio. How many of the houses in the community have a swimming pool?

Given the question, we have the following table:

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

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

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

\(A = 10\)

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.

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

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
User avatar
anairamitch1804
Joined: 26 Oct 2016
Last visit: 20 Apr 2019
Posts: 506
Own Kudos:
3,564
 [6]
Given Kudos: 877
Location: United States
Concentration: Marketing, International Business
Schools: HBS '19
GMAT 1: 770 Q51 V44
GPA: 4
WE:Education (Education)
Schools: HBS '19
GMAT 1: 770 Q51 V44
Posts: 506
Kudos: 3,564
 [6]
6
Kudos
Add Kudos
Bookmarks
Bookmark this Post
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.
User avatar
ramalcha
Joined: 18 Mar 2018
Last visit: 19 May 2023
Posts: 17
Own Kudos:
6
 [1]
Given Kudos: 45
Location: Malaysia
GMAT 1: 650 Q48 V31
GMAT 1: 650 Q48 V31
Posts: 17
Kudos: 6
 [1]
Kudos
Add Kudos
1
Bookmarks
Bookmark this Post
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
2.PNG [ 4.12 KiB | Viewed 54410 times ]

We want to find x.

Statement (1) is clearly insufficient from filling in the boxes.
Attachment:
Capture.PNG
Capture.PNG [ 4.62 KiB | Viewed 54369 times ]

Statement (2) seems wordy, but is as simple as the table below:
Attachment:
2.PNG
2.PNG [ 4.12 KiB | Viewed 54410 times ]

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

Therefore, \(x = 27\)
Attachments

3.PNG
3.PNG [ 4.33 KiB | Viewed 54324 times ]

User avatar
KarishmaB
Joined: 16 Oct 2010
Last visit: 18 Nov 2025
Posts: 16,267
Own Kudos:
Given Kudos: 482
Location: Pune, India
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 16,267
Kudos: 76,993
Kudos
Add Kudos
Bookmarks
Bookmark this Post
bmwhype2
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.

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
Moderators:
Math Expert
105388 posts
496 posts