enigma123 wrote:

The ratio of cats to dogs to birds to fish is 4:5:2:10. There are no other types of animals in the pet store. If there are 20 of one type of animal at the store then which of the following cannot be the total number of animals in the store?

A) 42

B) 63

C) 84

D) 105

E) 210

We are given that the ratio of cats to dogs to birds to fish is 4 : 5 : 2 : 10 = 4x : 5x : 2x : 10x.

Thus, the total number of animals is 21x.

Let’s analyze each answer choice:

A) 42

21x = 42

x = 2

Since 20 is a multiple of 2 and, in particular, the number of fish = 10x = 10(2) = 20, there can be 42 animals in the store.

B) 63

21x = 63

x = 3

Since 20 is not a multiple of 3, there cannot be 63 animals in the store.

Alternate solution:

We are given that the ratio of cats to dogs to birds to fish is 4 : 5 : 2 : 10 = 4x : 5x : 2x : 10x.

Thus, the total number of animals is 21x.

Since the number of one type of animal is 20, we can see that x could be 5, 4, 10, and 2, respectively, for the number of cats, dogs, birds, and fish to be 20.

Since the total number of animals is 21x, the total number of animals could be 105, 84, 210, and 42. We see that all of these 4 numbers are in the given answer choices. However, the answer choice of 63 is not one of these 4 numbers, so it can’t be the total number of animals.

Answer: B

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