Extra practice with ratios: A certain zoo has exactly five

Brent@GMATPrepNow wrote:A certain zoo has exactly five types of animals: alligators, buffalo, camels, deer and elephants. The ratio of the number of alligators to buffalo to camels is 4 : 3 : 1. The ratio of the number deer to elephants to buffalo is 6 : 1 : 4. Which of the following could represent the total animal population at the zoo?

A) 88
B) 90
C) 121
D) 159
E) 168

The ratio of the number of alligators to buffalo to camels is 4 : 3 : 1
So we can write: , A : B : C = 4 : 3 : 1

The ratio of the number deer to elephants to buffalo is 6 : 1 : 4
So we can write: D : E : B = 6 : 1 : 4

Notice that both ratios have a B in common.
In order to COMBINE the two ratios, we need to have the same -B-value
So, let's write some EQUIVALENT ratios that share the same B-value.

Take the first ratio, 4 : 3 : 1, and multiply all values by 4 to get the equivalent ratio 16 : 12 : 4
In other words, A : B : C = 16 : 12 : 4

Now take the second ratio, 6 : 1 : 4 , and multiply all values by 3 to get the equivalent ratio 18 : 3 : 12
In other words, D : E : B = 18 : 3 : 12

Now that our two ratios have the same B-value (12 ), we can combine the ratios to get...
A : B : C : D : E = 16 : 12 : 4 : 18 : 3
So, it's possible that there are 16 alligators, 12 buffalo, 4 camels, 18 deer and 3 elephants for a TOTAL of 53 animals (NOT among the answer choices)

Take our ratio, 16 : 12 : 4 : 18 : 3, and multiply by 2 to get the EQUIVALENT ratio: A : B : C : D : E = 32: 24 : 8 : 36 : 6
So, it's also possible that there are 32 alligators, 24 buffalo, 8 camels, 36 deer and 6 elephants for a TOTAL of 106 animals (NOT among the answer choices)

At this point, we might recognize that the TOTAL number of animals must be a MULTIPLE of 53
Check the answer choices....
Only answer choice D is a MULTIPLE of 53

Answer: D

Cheers,
Brent