Last visit was: 17 Jul 2024, 11:48 It is currently 17 Jul 2024, 11:48
Toolkit
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
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

# In a certain rural town, 250 households contain a dog or a cat or both

SORT BY:
Tags:
Show Tags
Hide Tags
Math Expert
Joined: 02 Sep 2009
Posts: 94383
Own Kudos [?]: 641737 [1]
Given Kudos: 85693
Manager
Joined: 30 Nov 2017
Posts: 61
Own Kudos [?]: 79 [1]
Given Kudos: 95
GMAT 1: 690 Q49 V35
Director
Joined: 01 Mar 2019
Posts: 591
Own Kudos [?]: 520 [1]
Given Kudos: 207
Location: India
Concentration: Strategy, Social Entrepreneurship
GMAT 1: 580 Q48 V21
GPA: 4
ISB School Moderator
Joined: 23 Nov 2018
Posts: 302
Own Kudos [?]: 256 [1]
Given Kudos: 358
Location: India
GMAT 1: 710 Q48 V39
GPA: 2.88
Re: In a certain rural town, 250 households contain a dog or a cat or both [#permalink]
1
Kudos
In a certain rural town, 250 households contain a dog or a cat or both. How many of these households contain both a dog and a cat if 75 of 250 households do not contain a dog?

given:

no of houses with dog= 175
no of houses without dog/ houses with only cat= 75

(1) 150 of the 250 households do not contain a cat.

no of houses with cat = both + only cat
100-72= both

25= both - sufficient!

(2) The total number of households that contain a cat is 100.

100-75= 25(both with house and cat)!!- sufficient!

D is the correct answer!
CEO
Joined: 07 Mar 2019
Posts: 2620
Own Kudos [?]: 1868 [1]
Given Kudos: 763
Location: India
WE:Sales (Energy and Utilities)
Re: In a certain rural town, 250 households contain a dog or a cat or both [#permalink]
1
Kudos
In a certain rural town, 250 households contain a dog or a cat or both. How many of these households contain both a dog and a cat if 75 of 250 households do not contain a dog?
Let households with dogs only = Hd
households with cats only = Hc
households with both dogs and cats = Hdc

Now, Hd + Hc + Hdc = 250
Also Hc = 75
Hdc = 250 - 75 - Hd = 175 - Hd

Hdc = ? OR Hd = ?

(1) 150 of the 250 households do not contain a cat.
Statement suggests that Hd = 150

SUFFICIENT.

(2) The total number of households that contain a cat is 100.
Hc + Hdc = 100
Hdc = 100 - 75 = 25

SUFFICIENT.

SVP
Joined: 24 Nov 2016
Posts: 1712
Own Kudos [?]: 1360 [1]
Given Kudos: 607
Location: United States
Re: In a certain rural town, 250 households contain a dog or a cat or both [#permalink]
1
Kudos
Quote:
In a certain rural town, 250 households contain a dog or a cat or both. How many of these households contain both a dog and a cat if 75 of 250 households do not contain a dog?

(1) 150 of the 250 households do not contain a cat.

(2) The total number of households that contain a cat is 100.

T=D+G-both+neither

.......dogs: xdog: total:
cats...............75........
xcats..............0.........
total....175....75...250

(1) 150 of the 250 households do not contain a cat. sufic.

.......dogs: xdog: total:
cats..(25)........75..(100)
xcats..............0...(150)
total....175....75...250

both=25

(2) The total number of households that contain a cat is 100. sufic.

.......dogs: xdog: total:
cats..(25)........75..(100)
xcats..............0...(150)
total....175....75...250

both=25

Ans. (D)
GMAT Club Legend
Joined: 18 Aug 2017
Status:You learn more from failure than from success.
Posts: 7990
Own Kudos [?]: 4228 [0]
Given Kudos: 243
Location: India
Concentration: Sustainability, Marketing
GMAT Focus 1:
545 Q79 V79 DI73
GPA: 4
WE:Marketing (Energy and Utilities)
Re: In a certain rural town, 250 households contain a dog or a cat or both [#permalink]
from 1 &2
2x2 matrix
---D--ND----total
C--x ---- ----100
NC-- --- ---- 150
total-- 175--75---250

value of x is to be determined , both statements are insufficient
IMO E

In a certain rural town, 250 households contain a dog or a cat or both. How many of these households contain both a dog and a cat if 75 of 250 households do not contain a dog?

(1) 150 of the 250 households do not contain a cat.

(2) The total number of households that contain a cat is 100
Retired Moderator
Joined: 18 May 2019
Posts: 782
Own Kudos [?]: 1055 [1]
Given Kudos: 101
Re: In a certain rural town, 250 households contain a dog or a cat or both [#permalink]
1
Kudos
From the question stem, we know that the 250 households contain either a dog, a cat, or both. We can deduce from this statement that there is no household that contains neither dog nor cat. We also know from the question stem that 75 out of the 250 household do not contain a dog. This implies that there are 75 households that contain only cats.

We are to determine the number of households that contain both a dog and a cat.

Statement 1: 150 of the 250 households do not contain a cat.
This is sufficient because we can determine that the number of households that contain both a dog and a cat, x, from the given statement as follows:
150+75+x=250
hence x=25.
There are 25 households that contain both a dog and a cat.

Statement 2: The total number of households that contain a cat is 100.
We can determine the number of households that contain both a cat and a dog from statement 2 as follows:
100=75+x
implying x=25.
Statement 2 is also sufficient on its own.

The answer is therefore D.
Manager
Joined: 31 Oct 2015
Posts: 92
Own Kudos [?]: 110 [1]
Given Kudos: 179
Re: In a certain rural town, 250 households contain a dog or a cat or both [#permalink]
1
Kudos
Given : Total no of Cats & Dos i.e D Union C = 250
~D=75 . This implies D=175

Equation : (D Union C) = D+C - (D Intersection C)

Statement 1 given us ~C=150.This implies C=100

Sufficient to calculate (D Intersection C)

Statement 2 gives us C=100

Sufficient to calculate (D Intersection C)

Thefore Both statement alone is sufficient to calculate (D Intersection C)

Director
Joined: 25 Jul 2018
Posts: 663
Own Kudos [?]: 1146 [1]
Given Kudos: 69
Re: In a certain rural town, 250 households contain a dog or a cat or both [#permalink]
1
Kudos
In a certain rural town, 250 households contain a dog or a cat or both.
—> cats +dogs—both +neither=250
neither = 0(zero)

75 of 250 households do not contain a dog —> 250–75= 175 dogs

—> both= ???

(Statement1): 150 of the 250 households do not contain a cat —100 cats
—> 100+ 175 —both = 250
both = 25
Sufficient

(Statement2): ) The total number of households that contain a cat is 100

—> 100+ 175– both = 250
both = 25
Sufficient

The answer is D

Posted from my mobile device
Manager
Joined: 11 Feb 2013
Posts: 201
Own Kudos [?]: 305 [1]
Given Kudos: 60
Location: United States (TX)
Concentration: Finance
GMAT 1: 490 Q44 V15
GMAT 2: 690 Q47 V38
GRE 1: Q165 V155
GPA: 3.05
WE:Analyst (Commercial Banking)
Re: In a certain rural town, 250 households contain a dog or a cat or both [#permalink]
1
Kudos
I would go for D.

2*2 diagram

Given
————————Dog——————No Dog —————-Total
Cat———————X———————-75————————(x+75)
No cat———— (175-x)—————-NO INFO————-NO INFO
TOTAL—————-175———————no info.————— No info
X=?

Statement 1: 175-x=150. So x=25 SUFFICIENT
Statement 2: x+75=100. So x=25 SUFFICIENT
Manager
Joined: 11 Feb 2013
Posts: 201
Own Kudos [?]: 305 [0]
Given Kudos: 60
Location: United States (TX)
Concentration: Finance
GMAT 1: 490 Q44 V15
GMAT 2: 690 Q47 V38
GRE 1: Q165 V155
GPA: 3.05
WE:Analyst (Commercial Banking)
Re: In a certain rural town, 250 households contain a dog or a cat or both [#permalink]
Key info: Everything is being considered WITHOUT NONE.
Director
Joined: 22 Feb 2018
Posts: 784
Own Kudos [?]: 1059 [1]
Given Kudos: 135
Re: In a certain rural town, 250 households contain a dog or a cat or both [#permalink]
1
Kudos
Imo. D

In a certain rural town, 250 households contain a dog or a cat or both. How many of these households contain both a dog and a cat if 75 of 250 households do not contain a dog?

No. of households having cat: x+y
No. of households having dog: y+z
No. of households having both: y
No. of households have none, n= 0
Total no. of households, x+y+z+n= 250
75 of 250 households do not contain a dog, x = 75
Need to find, y?

(1) 150 of the 250 households do not contain a cat. - z = 150, x= 75 , so y = 25. Sufficient

(2) The total number of households that contain a cat is 100. - x+y = 100, x =75, so y = 25. Sufficient.
GMAT Club Legend
Joined: 18 Aug 2017
Status:You learn more from failure than from success.
Posts: 7990
Own Kudos [?]: 4228 [0]
Given Kudos: 243
Location: India
Concentration: Sustainability, Marketing
GMAT Focus 1:
545 Q79 V79 DI73
GPA: 4
WE:Marketing (Energy and Utilities)
Re: In a certain rural town, 250 households contain a dog or a cat or both [#permalink]
exc4libur
could you please share the reason why have you considered 75 under no dogs but cats ? whereas the question says that 5 of 250 households do not contain a dog ; so wont this 75 come under total of NO dog part only ?

exc4libur wrote:
Quote:
In a certain rural town, 250 households contain a dog or a cat or both. How many of these households contain both a dog and a cat if 75 of 250 households do not contain a dog?

(1) 150 of the 250 households do not contain a cat.

(2) The total number of households that contain a cat is 100.

T=D+G-both+neither

.......dogs: xdog: total:
cats...............75........
xcats..............0.........
total....175....75...250

(1) 150 of the 250 households do not contain a cat. sufic.

.......dogs: xdog: total:
cats..(25)........75..(100)
xcats..............0...(150)
total....175....75...250

both=25

(2) The total number of households that contain a cat is 100. sufic.

.......dogs: xdog: total:
cats..(25)........75..(100)
xcats..............0...(150)
total....175....75...250

both=25

Ans. (D)
SVP
Joined: 24 Nov 2016
Posts: 1712
Own Kudos [?]: 1360 [0]
Given Kudos: 607
Location: United States
In a certain rural town, 250 households contain a dog or a cat or both [#permalink]
Archit3110 wrote:
could you please share the reason why have you considered 75 under no dogs but cats ? whereas the question says that 5 of 250 households do not contain a dog ; so wont this 75 come under total of NO dog part only ?

Hey Archit3110

We must consider two things:

Quote:
250 households contain a dog or a cat or both

Thus "neither" = 0, or "no dogs and no cats" = 0;

………dogs: xdog: total:
cats............................
xcats.............[0].........
total.......................250

Quote:
75 of 250 households do not contain a dog

So households with dogs = 250-75 = 175;

………dogs: xdog: total:
cats.............................
xcats...........................
total.....[175]...[75]....250

If we combine these informations we get:

………dogs: xdog: total:
cats.................75.........
xcats...............[0].........
total.....175.....75.....250
Current Student
Joined: 24 Jul 2019
Posts: 206
Own Kudos [?]: 389 [0]
Given Kudos: 162
GMAT 1: 730 Q46 V45
GPA: 3.9
Re: In a certain rural town, 250 households contain a dog or a cat or both [#permalink]
I generally would advise people to always solve such questions with the matrix, it can't get easier than that.
The hardest part is reading the stem properly. This example consists of a trap I've seen so many times:

"250 households contain a dog or a cat or both"

If you are too mechanic and fill in the blanks of the matrix right away without digesting the stem properly you tend to answer E) on this question as you only are given information to fill in the blanks outside the matrix but not the center.

This statement allone already tells you what do fill in on the "=! cats, =! dogs" box in your matrix. (zero)

Hope this post is helpful for some, I've got trapped on such DS questions very often when I relied solely on the matrix and not my understanding of the prompt in general.
Re: In a certain rural town, 250 households contain a dog or a cat or both [#permalink]
Moderator:
Math Expert
94383 posts