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

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A certain zoo has exactly five types of animals: alligators, [#permalink] New post 05 Aug 2018, 07:03
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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

*I'll post a solution in 2 days
[Reveal] Spoiler: OA

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Re: A certain zoo has exactly five types of animals: alligators, [#permalink] New post 05 Aug 2018, 08:53
There are five type of animals. Question stem mentions:-
Aligator(A):Buffalo(B):Camels(C) = 4:3:1
Deer(D): Elephant(E): Buffalo(B) = 6:1:4

Buffalo is common in both the ratios hence let us make the ratio with Buffalo as the reference. The LCM of 3 and 4 is 12. Therefore when the Raio of Buffalo is 12 in both the ratios of aniimals the new ratio would be:

A:B:C = 16:12:4
D:E:B = 18:3:12

A+B+c+D+E = 16+12+4+18+3 = 53x. X is the scale factor, the total number of animals in the zoo should be a multiple of 53.
Among ans choices only D is the multiple of 53.
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Re: A certain zoo has exactly five types of animals: alligators, [#permalink] New post 08 Aug 2018, 09:31
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GreenlightTestPrep 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
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Re: A certain zoo has exactly five types of animals: alligators,   [#permalink] 08 Aug 2018, 09:31
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A certain zoo has exactly five types of animals: alligators,

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