Find all School-related info fast with the new School-Specific MBA Forum

 It is currently 24 Aug 2016, 20:03

### 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

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

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

# Of the 75 houses in a certain community, 48 have a patio.

Author Message
TAGS:

### Hide Tags

CEO
Joined: 21 Jan 2007
Posts: 2756
Location: New York City
Followers: 9

Kudos [?]: 731 [7] , given: 4

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

### Show Tags

21 Feb 2008, 13:37
7
KUDOS
26
This post was
BOOKMARKED
00:00

Difficulty:

95% (hard)

Question Stats:

43% (02:02) correct 57% (00:56) wrong based on 692 sessions

### HideShow timer Statistics

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.
[Reveal] Spoiler: OA

_________________

You tried your best and you failed miserably. The lesson is 'never try'. -Homer Simpson

Director
Joined: 30 Jun 2007
Posts: 793
Followers: 1

Kudos [?]: 146 [0], given: 0

### Show Tags

21 Feb 2008, 22:31

Number of swimming pools: 27
CEO
Joined: 21 Jan 2007
Posts: 2756
Location: New York City
Followers: 9

Kudos [?]: 731 [1] , given: 4

### Show Tags

21 Feb 2008, 22:35
1
KUDOS
GMATprep says OA is B.

i also chose C. I cannot figure out why it is B

thoughts?
_________________

You tried your best and you failed miserably. The lesson is 'never try'. -Homer Simpson

Manager
Joined: 02 Jan 2008
Posts: 159
Followers: 2

Kudos [?]: 103 [1] , given: 0

### Show Tags

21 Feb 2008, 22:58
1
KUDOS
1
This post was
BOOKMARKED
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
Manager
Joined: 15 Nov 2007
Posts: 135
Followers: 1

Kudos [?]: 46 [0], given: 2

### Show Tags

26 Feb 2008, 02:19
someone give a more detailed explanation please
CEO
Joined: 29 Mar 2007
Posts: 2583
Followers: 19

Kudos [?]: 372 [2] , given: 0

### Show Tags

26 Feb 2008, 07:27
2
KUDOS
bmwhype2 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.

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]

CEO
Joined: 21 Jan 2007
Posts: 2756
Location: New York City
Followers: 9

Kudos [?]: 731 [0], given: 4

### Show Tags

26 Feb 2008, 14:14
1
This post was
BOOKMARKED
GMATBLACKBELT wrote:
bmwhype2 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.

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

Intern
Joined: 14 May 2008
Posts: 5
Followers: 0

Kudos [?]: 8 [0], given: 3

### Show Tags

30 Dec 2009, 04:35
Total = A+B - A intersection B (Common to A and B) + (~A and ~B ---> Not part of Subset A or Subset B)

from the given problem we have the following

Total = 75

A = 48

A intersection B = (~A and ~B ---> Not part of Subset A or Subset B)

(~A and ~B ---> Not part of Subset A or Subset B) - A intersection B = 0

So Equation becomes

75=48+B

Thus B is sufficient
Manager
Joined: 25 Aug 2009
Posts: 175
Location: Streamwood IL
Schools: Kellogg(Evening),Booth (Evening)
WE 1: 5 Years
Followers: 12

Kudos [?]: 167 [8] , given: 3

### Show Tags

31 Dec 2009, 10:19
8
KUDOS
2
This post was
BOOKMARKED
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.
_________________

Rock On

Director
Joined: 29 Nov 2012
Posts: 900
Followers: 14

Kudos [?]: 872 [4] , given: 543

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

### Show Tags

24 Jul 2013, 06:20
4
KUDOS
3
This post was
BOOKMARKED
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
Attachments

Venn diagram.jpg [ 7.99 KiB | Viewed 15347 times ]

_________________

Click +1 Kudos if my post helped...

Amazing Free video explanation for all Quant questions from OG 13 and much more http://www.gmatquantum.com/og13th/

GMAT Prep software What if scenarios http://gmatclub.com/forum/gmat-prep-software-analysis-and-what-if-scenarios-146146.html

Intern
Joined: 03 Dec 2013
Posts: 16
Location: Uzbekistan
Concentration: Finance, Entrepreneurship
GMAT 1: 620 Q42 V33
GRE 1: 600 Q790 V400
GPA: 3.4
WE: Analyst (Commercial Banking)
Followers: 0

Kudos [?]: 13 [1] , given: 57

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

### Show Tags

09 Jan 2014, 04:49
1
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.

Senior Manager
Joined: 27 Dec 2013
Posts: 315
Followers: 0

Kudos [?]: 18 [0], given: 113

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

### Show Tags

01 Sep 2014, 01:23

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.

Thanks and kudos to every one
_________________

Kudos to you, for helping me with some KUDOS.

Math Expert
Joined: 02 Sep 2009
Posts: 34420
Followers: 6251

Kudos [?]: 79415 [0], given: 10016

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

### Show Tags

01 Sep 2014, 01:37
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 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.

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?
_________________
Senior Manager
Joined: 27 Dec 2013
Posts: 315
Followers: 0

Kudos [?]: 18 [0], given: 113

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

### Show Tags

01 Sep 2014, 01:48
Hi Bunuel,

There isnt mentioned anywhere about- houses (do not have either) or (have either).

But not thoroughly satisfied with the wording of the question.

Am I wrong in thinking this way.
_________________

Kudos to you, for helping me with some KUDOS.

Math Expert
Joined: 02 Sep 2009
Posts: 34420
Followers: 6251

Kudos [?]: 79415 [0], given: 10016

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

### Show Tags

01 Sep 2014, 03:07
shriramvelamuri wrote:
Hi Bunuel,

There isnt mentioned anywhere about- houses (do not have either) or (have either).

But not thoroughly satisfied with the wording of the question.

Am I wrong in thinking this way.

Yes, saying that there are no houses without a patio and a swimming pool would be an unsound assumption.
_________________
GMAT Club Legend
Joined: 09 Sep 2013
Posts: 11040
Followers: 509

Kudos [?]: 133 [0], given: 0

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

### Show Tags

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.
_________________
Joined: 28 Nov 2014
Posts: 441
Concentration: Strategy
Followers: 7

Kudos [?]: 65 [0], given: 25

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

### Show Tags

24 Nov 2015, 12:47
Did anyone tried solving this problem with double matrix? One of the guys did, but looks like his excel is incomplete
Intern
Joined: 03 Jun 2015
Posts: 8
Concentration: General Management, Finance
Schools: HBS '18 (D)
GMAT 1: 610 Q46 V28
GMAT 2: 690 Q47 V38
GMAT 3: 710 Q49 V36
Followers: 0

Kudos [?]: 1 [0], given: 41

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

### Show Tags

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.

--------------------Patio ------No Patio Total
------------ Swim b---------(27-b)----------(b+27-b)=27
--------No Swim-------------- (b)--------------
-------------------- 48---------(75-48=27)----(75)
Senior Manager
Status: Always try to face your worst fear because nothing GOOD comes easy. You must be UNCOMFORTABLE to get to your COMFORT ZONE
Joined: 15 Aug 2014
Posts: 373
Concentration: Marketing, Technology
GMAT 1: 570 Q44 V25
GMAT 2: 600 Q48 V25
WE: Information Technology (Consulting)
Followers: 5

Kudos [?]: 5 [0], given: 461

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

### Show Tags

01 May 2016, 08:22
Keats wrote:
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 [ 3.74 KiB | Viewed 2563 times ]

_________________

The path is long, but self-surrender makes it short; the way is difficult, but perfect trust makes it easy.

"When you want to succeed as bad as you want to breathe, then you’ll be successful.” - Eric Thomas

Intern
Joined: 16 Mar 2016
Posts: 30
Schools: Tuck '19
Followers: 0

Kudos [?]: 0 [0], given: 67

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

### Show Tags

01 Aug 2016, 02:23
bmwhype2 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.

I marked answer D thinking A is also sufficient because I didn't consider the case where a house has neither a swimming pool nor a patio. I did see the "neither" case in option B but thought it doesn't have relevance to option A and also in main question there wasn't anything mentioned about "neither" case. How do we come to know whether "neither" case is applicable to a question or not? If they haven't particularly mentioned in the question that 'each house has a patio or a swimming pool' then it is necessary to consider the "neither" case?
Re: Of the 75 houses in a certain community, 48 have a patio.   [#permalink] 01 Aug 2016, 02:23

Go to page    1   2    Next  [ 23 posts ]

Similar topics Replies Last post
Similar
Topics:
IF 75% of guest at a certain banquet ordered dessert,what 3 20 Aug 2010, 10:30
124 Six countries in a certain region sent a total of 75 16 27 Apr 2010, 09:57
4 Of the 75 houses in a certain community,48 have a patio.How 15 15 Aug 2009, 15:42
3 Six countries in a certain region sent a total of 75 4 27 Jul 2009, 00:54
1 Six countries in a certain region sent a total of 75 3 03 Jun 2007, 02:58
Display posts from previous: Sort by