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Manager  Joined: 01 Jan 2008
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Schools: Booth, Stern, Haas
At a certain pet shop, 1/3 of the pets are dogs and 1/5 of the pets  [#permalink]

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Question Stats: 75% (01:10) correct 25% (01:18) wrong based on 269 sessions

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At a certain pet shop, 1/3 of the pets are dogs and 1/5 of the 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.

Originally posted by kbulse on 06 Jan 2008, 06:58.
Last edited by Bunuel on 04 Apr 2019, 21:18, edited 2 times in total.
Renamed the topic, edited the question, added the OA and moved to DS forum.
Math Expert V
Joined: 02 Sep 2009
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At a certain pet shop, 1/3 of the pets are dogs and 1/5 of the pets  [#permalink]

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At a certain pet shop, 1/3 of the pets are dogs and 1/5 of the pets are birds. How many of the pets are dogs?

(1) There are 30 birds at the shop --> $$\frac{1}{5}$$ of the pets are birds --> $$\frac{1}{5}t=30$$, where $$t$$ is the # of pets at the pet shop --> $$t=150$$ --> $$\frac{1}{3}$$ of the pets are dogs --> there are $$\frac{1}{3}*150=50$$ dogs at the pet shop. Sufficient.

(2) There are 20 more dogs than birds at the pet shop --> $$d=b+20$$ --> $$\frac{1}{3}t=\frac{1}{5}t+20$$, where $$t$$ is the # of pets at the pet shop --> $$t=150$$ --> $$\frac{1}{3}$$ of the pets are dogs --> there are $$\frac{1}{3}*150=50$$ dogs at the pet shop. Sufficient.

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Re: At a certain pet shop, 1/3 of the pets are dogs and 1/5 of the pets  [#permalink]

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Quote:
certain pet shop, 1/3 of pets are dogs, 1/5 of pets are birds. how many of pets are dogs

(1) there are 30 birds at the shop
(2) there are 20 more dogs than birds

You need to find out the total number of pets to solve this question. If you let x=total pets, D= 1/3 * x, B= 1/5 * x, then you get:

1) 1/5*x=30, so you know that x=150, SUFFICIENT

2) d=b+20
(1/3 *x)=(1/5 *x) +20
x/3= x/5 +20
5x/15 - 3x/15=20
2x/15 = 20
2x = 300
x= 150 SUFFICIENT
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At a certain pet shop, 1/3 of the pets are dogs and 1/5 of the pets  [#permalink]

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Can't understand how to get the answer from (2). Do we consider that dogs and pets are only animals in the shop?
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Re: At a certain pet shop, 1/3 of the pets are dogs and 1/5 of the pets  [#permalink]

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ulm wrote:
Can't understand how to get the answer from (2). Do we consider that dogs and pets are only animals in the shop?

Not so. We are told that $$\frac{1}{3}$$ of the pets are dogs and $$\frac{1}{5}$$ of the pets are birds --> $$\frac{1}{3}+\frac{1}{5}=\frac{8}{15}<1=total$$.

At a certain pet shop, 1/3 of the pets are dogs and 1/5 of the pets are birds. How many of the pets are dogs?

(1) There are 30 birds at the shop --> $$\frac{1}{5}$$ of the pets are birds --> $$\frac{1}{5}t=30$$, where $$t$$ is the # of pets at the pet shop --> $$t=150$$ --> $$\frac{1}{3}$$ of the pets are dogs --> there are $$\frac{1}{3}*150=50$$ dogs at the pet shop. Sufficient.

(2) There are 20 more dogs than birds at the pet shop --> $$d=b+20$$ --> $$\frac{1}{3}t=\frac{1}{5}t+20$$, where $$t$$ is the # of pets at the pet shop --> $$t=150$$ --> $$\frac{1}{3}$$ of the pets are dogs --> there are $$\frac{1}{3}*150=50$$ dogs at the pet shop. Sufficient.

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Re: At a certain pet shop, 1/3 of the pets are dogs and 1/5 of the pets  [#permalink]

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ulm wrote:
Can't understand how to get the answer from (2)
Do we consider that dogs and pets are only animals in the shop?

To answer your question, no we do not consider that dogs and birds are the only animals at the shop. In fact, we know they are not because $$\frac{1}{3} + \frac{1}{5} = \frac{8}{15}$$. So dogs and birds account for only 8/15th of the total animals.

Now, let's solve this question using ratios.

Dogs : Birds = $$\frac{1}{3} : \frac{1}{5}$$. Multiply this ratio by 15 to convert it into integers. Remember, when you multiply the entire ratio by the same number, the ratio remains the same.

Dogs : Birds = 5:3. For every 3 birds, there are 5 dogs.
Stmnt 1: If birds are 30, dogs will be 50. Sufficient.
Stmnt 2: The difference in number of dogs are birds in ratio terms is 2 (because 5 - 3 = 2), but is actually 20. So 5 will correspond to 50. Sufficient.

Ratios are a great way to quickly and easily solve questions. If this method is not clear, give me a couple of days. I will put up a blog explaining it in detail.
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Re: At a certain pet shop, 1/3 of the pets are dogs and 1/5 of the pets  [#permalink]

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Does this assume that there are only dogs and birds in the pet shop? If so, shouldn't the problem state it?
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Re: At a certain pet shop, 1/3 of the pets are dogs and 1/5 of the pets  [#permalink]

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Georgetowner wrote:
Does this assume that there are only dogs and birds in the pet shop? If so, shouldn't the problem state it?

If 1/3 of the pets are dogs, and 1/5 of the pets are birds, then only 1/3 + 1/5 = 8/15 of all pets are dogs or birds. So 7/15 of the pets need to be something other than dogs or birds. So no, the question is not assuming there are only dogs and birds in the shop.
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Re: At a certain pet shop, 1/3 of the pets are dogs and 1/5 of the pets  [#permalink]

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Hi Bunnel

Please clarify the quation

d=b+20..........or
b=d+20................... I have gone with the 2nd one and made mistake.

Rgds
Prasannajeet
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Re: At a certain pet shop, 1/3 of the pets are dogs and 1/5 of the pets  [#permalink]

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prasannajeet wrote:
Hi Bunnel

Please clarify the quation

d=b+20..........or
b=d+20................... I have gone with the 2nd one and made mistake.

Rgds
Prasannajeet

(2) says: there are 20 more dogs than birds at the pet shop, thus d=b+20.

Hope it's clear.
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Re: At a certain pet shop, 1/3 of the pets are dogs and 1/5 of the pets  [#permalink]

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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

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Re: At a certain pet shop, 1/3 of the pets are dogs and 1/5 of the pets  [#permalink]

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ulm wrote:
At a certain pet shop, 1/3 of the pets are dogs and 1/5 of the 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

Cheers,
Brent
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Re: GMATPrep#1: At a certain pet shop, 1/3 of pets... (DS)  [#permalink]

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