EMPOWERgmatRichC wrote:

QUANT 4-PACK SERIES Data Sufficiency Pack 3 Question 3 A pet store sells three...

A pet store sells three types of animals: cats, dogs and exotic fish. If the ratio of cats to dogs in the store is currently 5 to 13 and there are currently 168 total pets in the store, then how many more dogs than exotic fish are currently in the store?

(1) The ratio of cats to exotic fish in the store is currently 1 to 2

(2) There are currently 30 more exotic fish than cats in the store

This DS prompt is based on ratios and ratio rules. Understanding how the ratios interact with one another (and the other pieces of information) will help you to answer this question without necessarily having to do that many calculations.

To start, we're told a number of facts about a pet store:

1) There are three types of animals: cats, dogs and fish.

2) The ratio of cats to dogs at the store is 5:13

3) There are a total of 168 pets at the store.

We're asked how many MORE dogs there are at the store than fish.

1) The ratio of cats to exotic fish in the store is currently 1 to 2

With this Fact, we can now construct a 'grand ratio' of how the number of cats, dogs and fish all relate to one another:

C:D

5:13

C:F

1:2

Since we cannot have a 'fraction' of an animal, the ratio of cats to dogs to fish is...

C:D:F

5:13:10

This means that the number of cats MUST be a multiple of 5, the number of dogs MUST be a multiple of 13 and the number of fish MUST be a multiple of 10. By extension, the total number of animals MUST be a multiple of 5+13+10 = 28.

Given this information, and the fact that the total number of animals is 168, the multiple must be 168/28 = 6. This would allow you to calculate the total number of each animal (even though you don't technically have to - those numbers are 30 cats, 78 dogs and 60 fish).

Fact 1 is SUFFICIENT.

2) There are currently 30 more exotic fish than cats in the store

Depending on how you interpret ratio data, you might have to do a bit more work with this Fact to prove that it's sufficient. We know the current ratio of cats to dogs (5 to 13) and the total number of pets (168), so we can create a table of possible 'total animals' that incorporate this new Fact (that there are 30 MORE fish than cats):

C/D/F

5/13/35 = 55 animals

10/26/40 = 76 animals

15/39/45 = 99 animals

20/52/50 = 122 animals

25/65/55 = 145 animals

30/78/60 = 168 animals

Etc.

There's just ONE WAY for the total number of animals to be 168.

Fact 2 is SUFFICIENT

Final Answer:

GMAT assassins aren't born, they're made,

Rich

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