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

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A certain zoo has exactly five types of animals: alligators, buffalo,  [#permalink]

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05 Aug 2018, 08:04
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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

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Re: A certain zoo has exactly five types of animals: alligators, buffalo,  [#permalink]

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05 Aug 2018, 08:32
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

HI GMATPrepNow (Brent)

Combine the ration a:b:c:d:e = 16:12:4:18:3 = 53

Hence Only E multiple of 53
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Re: A certain zoo has exactly five types of animals: alligators, buffalo,  [#permalink]

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05 Aug 2018, 09:00
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
Attachment:

Capture.PNG [ 3.16 KiB | Viewed 699 times ]

Thus the number of animals in the zoo must be multiple of 53 ( ie , 16+12+4+18+3), Answer must be (D)
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Re: A certain zoo has exactly five types of animals: alligators, buffalo,  [#permalink]

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05 Aug 2018, 09:27
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

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)
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A certain zoo has exactly five types of animals: alligators, buffalo,  [#permalink]

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05 Aug 2018, 15:08
1
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

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

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Re: A certain zoo has exactly five types of animals: alligators, buffalo,  [#permalink]

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08 Aug 2018, 10:33
Top Contributor
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
Only answer choice D is a MULTIPLE of 53

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Re: A certain zoo has exactly five types of animals: alligators, buffalo,   [#permalink] 08 Aug 2018, 10:33
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