A certain zoo has exactly five types of animals: alligators, buffalo,

Given,
1) a:b:c::4:3:1 Or, a:b:c::16:12:4
2) d:e:b::6:1:4 or, d:e:b::18:3:12

Now a+b+c+d+e=16k+12k+4k+6k+3k=53k or, the total animal population is a multiple of 53.

Among the options, 159=53*3 is the perfect match.

Ans. (D)

We have two ratios.
A : B : C
4 : 3 : 1

D :E : B
6 : 1 : 4

B is the term common to both ratios. B's value in both ratios must be equal. Right now the values for B are not equal. Take the LCM of 3 and 4 = 12.

In order to get B to = 12 in both ratios, multiply all numbers in the first ratio by 4 and all numbers in the second ratio by 3. (What we do to one part of a ratio we must do to all parts.)

First ratio: every number * 4
A : B : C
(4 : 3 : 1) ==> \(* 4\)
16 : 12 : 4

Second ratio: every number * 3
D : E : B
(6 : 1 : 4) ==> \(* 3\)
18 : 3 : 12

Combine the results
A : B : C : D : E
16:12 : 4 : 18 : 3

Sum the parts of the new ratio
(With \(x\) I am just making the multiplier explicit)
\((16x+12x+4x+18x+3x) = 53x\)

These animals must be in groups of (multiples of) 53.

Only one answer is a multiple of 53
(53 + 3) = 159

Answer D

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

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