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# The number of cats in Libby’s house is twice the number of dogs and

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The number of cats in Libby’s house is twice the number of dogs and  [#permalink]

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30 Sep 2015, 12:23
2
2
00:00

Difficulty:

15% (low)

Question Stats:

78% (01:14) correct 22% (01:35) wrong based on 132 sessions

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The number of cats in Libby’s house is twice the number of dogs and one third the number of fish. If cats, dogs and fish are the only pets in Libby’s house, what is the probability of randomly selecting two cats?

(1) The number of cats in Libby’s house is 12.
(2) The total number of pets in Libby’s house is 54.

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Re: The number of cats in Libby’s house is twice the number of dogs and  [#permalink]

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01 Oct 2015, 14:03
1
Cats: 2X
Dogs: X
Fish: 6X

The probability is 1/9X * (2X-1)/(9X-1) >> In order to solve that equation we must know the value of X.

In given both statement we can find the value of X.

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Re: The number of cats in Libby’s house is twice the number of dogs and  [#permalink]

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02 Oct 2015, 22:00
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From the information in the question stem - c=2d, c=(1/3)f - To find probability of randomly selecting 2 cats

s1: c=12, so d=6, f=36 so we can get the probability. (Sufficient)

s2: c+c/2+3c=54, so we can get the probability.(Sufficient)

So D.
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Re: The number of cats in Libby’s house is twice the number of dogs and  [#permalink]

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27 Feb 2019, 06:13
alphaseeker wrote:
Cats: 2X
Dogs: X
Fish: 6X

The probability is 1/9X * (2X-1)/(9X-1) >> In order to solve that equation we must know the value of X.

In given both statement we can find the value of X.

The sentence says that the number of cats is 12. Doesn't that give us all the values?
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Re: The number of cats in Libby’s house is twice the number of dogs and  [#permalink]

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27 Feb 2019, 07:47
Let the number of dogs be denoted as D...
therefore dogs= D
Number of cats = 2D
Now , number of cats are 1/3 the number of fish...
Which means number of fishes are thrice the number of cats i.e 6D...
Total number of animals in the house = D+2D+6D = 9D...

Statement 1 -
Cats are 12 ... 12= 2D
D= 6.. sufficient...

Statement 2 -
Total number of animals are 54.. D+2D+6D = 54... D = 6...

Both statements individually are sufficient.. option D is the right answer.

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Re: The number of cats in Libby’s house is twice the number of dogs and  [#permalink]

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10 Jun 2019, 19:15
Given:
2C = D
1/3 C = F

=> 6C = 3D = 18F

St. 1
12 Cats means that 6C= 12 => C=2
therefore, we have
12 Cats, 6 dogs and 36 fishes

Probability = 12C2 / 36C2 = 11/105

St. 2
6x+ 3x + 18x = 54
=> x =2
We have,
12 Cats, 6 dogs and 36 fishes
Probability = 12C2 / 36C2 = 11/105

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Re: The number of cats in Libby’s house is twice the number of dogs and   [#permalink] 10 Jun 2019, 19:15
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