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

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.

Answer: D.

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, check this video: https://youtu.be/5ODENGG5dvc

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.

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.

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

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

Cheers,
Brent

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