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

BTGmoderatorDC wrote: ↑

Thu Aug 19, 2021 10:34 pm

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


OA B

Source: Veritas Prep

Given: The ratio of cats to dogs to birds to fish is 4 : 5 : 2 : 10
In this original ratio, the sum of all parts = 4 + 5 + 2 + 10 = 21

If we multiply all parts by 2, we get the EQUIVALENT ratio: 8 : 10 : 4 : 20. So, there COULD be 8 cats, 10 dogs, 4 birds, and 20 fish.
In this case, the TOTAL number of animals = (2)(21)= 42
Eliminate A.

If we multiply all parts of the original ratio by 5, we get the EQUIVALENT ratio: 20 : 25 : 10 : 50.
In this case, the TOTAL number of animals = (5)(21)= 105
Eliminate D.

If we multiply all parts of the original ratio by 4, we get the EQUIVALENT ratio: 16 : 20 : 8 : 40.
In this case, the TOTAL number of animals = (4)(21)= 84
Eliminate C.

If we multiply all parts of the original ratio by 10, we get the EQUIVALENT ratio: 40 : 50 : 20 : 100.
In this case, the TOTAL number of animals = (10)(21)= 210
Eliminate E.

By the process of elimination, the correct answer is B