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Pet Shop DS

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by SG1492 » Sun Jul 20, 2014 5:21 am
At a certain pet shop, 1/3 of pets are dogs & 1/5 of pets are birds. How many of the pets are dogs?
1) There are 30 birds at the pet shop
2) There are 20 more dogs than birds at the pet shop.

OA D

Explanation plz
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by GMATinsight » Sun Jul 20, 2014 5:27 am
Drishti wrote:At a certain pet shop, 1/3 of pets are dogs & 1/5 of pets are birds. How many of the pets are dogs?
1) There are 30 birds at the pet shop
2) There are 20 more dogs than birds at the pet shop.
Question : Number of Dogs = ?

Let the total number of pets be = P

Given, (1/3)P = Dogs

and (1/5)P = Birds

We can find the number of dogs if we can find the value of P

Statement 1) Number of birds = 30

=> (1/5)P = 30 => P = 150, therefore Dog = 150/3 = 50

SUFFICIENT

Statement 2) 20 more Dogs than Birds

=> Dogs = Birds + 20

=> (1/3)P = (1/5)P + 20

i.e. (2/15)P = 20
i.e. P = 150 therefore Dog = = 150/3 = 50

SUFFICIENT

Answer: Option D
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by mcdesty » Sun Jul 20, 2014 5:41 am
See my scratch paper below; If you can't, just create an account: It only takes a minute.
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by Brent@GMATPrepNow » Sun Jul 20, 2014 6:42 am
At a certain pet shop, 1/3 of pets are dogs & 1/5 of pets are birds. How many of the pets are dogs?

1) There are 30 birds at the pet shop
2) There are 20 more dogs than birds at the pet shop.
Target question: How many of the pets are dogs?

Given: 1/3 of pets are dogs & 1/5 of pets are birds
Let T = TOTAL number of pets.
So, T/3 = number of dogs
And T/5 = number of birds

Statement 1: There are 30 birds at the pet shop
So, T/5 = 30
This means that T = 150, which means T/3 = 50 (i.e., there are 50 dogs)
Since we can answer the target question with certainty, statement 1 is SUFFICIENT

Statement 2: There are 20 more dogs than birds at the pet shop.
In other words, (# of birds) + 20 = # of dogs
We can now write: T/5 + 20 = T/3
IMPORTANT: We could solve this equation for T, but we're not going to waste time doing so. We need only recognize that we could solve the equation for T, which means we can definitely find the value of T/3 (the number of dogs)
Since we can answer the target question with certainty, statement 2 is SUFFICIENT

Answer = D

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Brent
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by GMATGuruNY » Sun Jul 20, 2014 11:59 am
Drishti wrote:At a certain pet shop, 1/3 of pets are dogs & 1/5 of pets are birds. How many of the pets are dogs?
1) There are 30 birds at the pet shop
2) There are 20 more dogs than birds at the pet shop.
Alternate approach:

To determine the ratio of birds to dogs, plug in a TEST VALUE for the total number of pets.
Let b = the number of birds and d = the number of dogs.
Let the test value for the total number of pets = the LCM of 3 and 5 = 15.
Since 1/5 are birds, b = 1/5 * 15 = 3.
Since 1/3 are dogs, d = 1/3 * 15 = 5.
Thus:
b/d = 3/5.

Statement 1: There are 30 birds at the pet shop
Since b/d = 3/5 = 30/50, b=30 and d=50.
SUFFICIENT.

Statement 2: There are 20 more dogs than birds at the pet shop
The values yielded by statement 1 -- b=30 and d=50 -- are the only values for b and d such that b/d = 3/5 and d=b+20.
SUFFICIENT.

The correct answer is D.
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