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
Answer: D
Difficulty level: 550 - 600
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Extra practice with ratios: A certain zoo has exactly five
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The ratio of the number of alligators to buffalo to camels is 4 : 3 : 1Brent@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
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
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Brent
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Let, Alligator = a
Buffalo = b
Camel = c
Deer = d
Elephant = e
Given that,
a : b : c = 4 : 3 : 1
d : e : b = 6 : 1 : 4
b is common to both ratios, the value of b in the 2 ratios must be equal. Hence, we find the LCM of 3 and 4 (value of b in the two ratios respectively) which is = 12.
For us to get B = 12 in both ratios, We multiply all numbers in the first ratio by 4 and all numbers in the second ratio by 3.
Therefore, a : b : c = (4 * 4) : (3 * 4) : (1 * 4) = 16 : 12 : 4
d : e : b = (6 * 3) : (1 * 3) : (4 * 3) = 18 : 3 : 12
Combining the results we have
a : b : c : d : e
16 : 12 : 4 : 18 : 3
Adding all parts of the ratio together we have ;
16 + 12 + 4 + 18 + 3 = 53
That is, Total animal population at the Zoo is a multiple of 53.
$$\frac{159}{53}=\ 3$$
Option D is the correct answer.
Buffalo = b
Camel = c
Deer = d
Elephant = e
Given that,
a : b : c = 4 : 3 : 1
d : e : b = 6 : 1 : 4
b is common to both ratios, the value of b in the 2 ratios must be equal. Hence, we find the LCM of 3 and 4 (value of b in the two ratios respectively) which is = 12.
For us to get B = 12 in both ratios, We multiply all numbers in the first ratio by 4 and all numbers in the second ratio by 3.
Therefore, a : b : c = (4 * 4) : (3 * 4) : (1 * 4) = 16 : 12 : 4
d : e : b = (6 * 3) : (1 * 3) : (4 * 3) = 18 : 3 : 12
Combining the results we have
a : b : c : d : e
16 : 12 : 4 : 18 : 3
Adding all parts of the ratio together we have ;
16 + 12 + 4 + 18 + 3 = 53
That is, Total animal population at the Zoo is a multiple of 53.
$$\frac{159}{53}=\ 3$$
Option D is the correct answer.