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

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Math Expert
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In a certain rural town, 250 households contain a dog or a cat or both  [#permalink]

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06 Nov 2019, 23:28
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Question Stats:

64% (01:50) correct 36% (01:46) wrong based on 53 sessions

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Competition Mode Question

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.

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Re: In a certain rural town, 250 households contain a dog or a cat or both  [#permalink]

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06 Nov 2019, 23:46
1
Cat No Cat Total
Dog x a = x+a
No Dog 75 0 = 75
Total x+75 a = 250

Therefore, if we know the value of a, we know the value of x

(1) 150 of the 250 households do not contain a cat.
No Cat: a=150. Solve for x. Sufficient

(2) The total number of households that contain a cat is 100.
x+75=100
Solve for x. Sufficient. Ans D
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Re: In a certain rural town, 250 households contain a dog or a cat or both  [#permalink]

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07 Nov 2019, 00:19
1
a= only dog
b= both dog and cat.....have to find
c= only cat

Given a+b+c=250, also c=75 then a+b=175

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

Here given that a=150 then b=25

Sufficient

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

Given b+c=100....then b=25.... sufficient

OA:D
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Re: In a certain rural town, 250 households contain a dog or a cat or both  [#permalink]

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07 Nov 2019, 01:08
1
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!

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Re: In a certain rural town, 250 households contain a dog or a cat or both  [#permalink]

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07 Nov 2019, 01:36
1
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.

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Re: In a certain rural town, 250 households contain a dog or a cat or both  [#permalink]

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07 Nov 2019, 06:55
1
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)
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Re: In a certain rural town, 250 households contain a dog or a cat or both  [#permalink]

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07 Nov 2019, 07:35
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
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Re: In a certain rural town, 250 households contain a dog or a cat or both  [#permalink]

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07 Nov 2019, 07:58
1
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.

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Re: In a certain rural town, 250 households contain a dog or a cat or both  [#permalink]

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07 Nov 2019, 13:37
1
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)

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Re: In a certain rural town, 250 households contain a dog or a cat or both  [#permalink]

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07 Nov 2019, 14:16
1
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

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Re: In a certain rural town, 250 households contain a dog or a cat or both  [#permalink]

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07 Nov 2019, 20:15
1
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
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Re: In a certain rural town, 250 households contain a dog or a cat or both  [#permalink]

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07 Nov 2019, 20:21
Key info: Everything is being considered WITHOUT NONE.
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Re: In a certain rural town, 250 households contain a dog or a cat or both  [#permalink]

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07 Nov 2019, 21:31
1
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.
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Re: In a certain rural town, 250 households contain a dog or a cat or both  [#permalink]

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08 Nov 2019, 02:27
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)
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In a certain rural town, 250 households contain a dog or a cat or both  [#permalink]

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08 Nov 2019, 02:48
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
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Re: In a certain rural town, 250 households contain a dog or a cat or both  [#permalink]

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09 Nov 2019, 02:08
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.
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Re: In a certain rural town, 250 households contain a dog or a cat or both   [#permalink] 09 Nov 2019, 02:08
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