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# A certain zoo has mammal and reptiles and birds, and no other animals.

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A certain zoo has mammal and reptiles and birds, and no other animals.  [#permalink]

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27 Sep 2015, 12:19
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Question Stats:

79% (01:32) correct 21% (01:47) wrong based on 154 sessions

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A certain zoo has mammal and reptiles and birds, and no other animals. The ratio of mammals to reptiles to birds is 11: 8:5. How many birds are in the zoo?

(1) there are twelve more mammals in the zoo than there are reptiles

(2) if the zoo acquired 16 more mammals, the ratio of mammals to birds would be 3:1

Kudos for a correct solution.

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Re: A certain zoo has mammal and reptiles and birds, and no other animals.  [#permalink]

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27 Sep 2015, 13:04
Bunuel wrote:
A certain zoo has mammal and reptiles and birds, and no other animals. The ratio of mammals to reptiles to birds is 11: 8:5. How many birds are in the zoo?

(1) there are twelve more mammals in the zoo than there are reptiles

(2) if the zoo acquired 16 more mammals, the ratio of mammals to birds would be 3:1

Kudos for a correct solution.

Target question: How many birds are in the zoo?

Given: The ratio of mammals to reptiles to birds is 11: 8:5.
Given this ratio, we could say that there are:
11x mammals
8x reptiles
5x birds
for some value of x
.

Statement 1: there are twelve more mammals in the zoo than there are reptiles
We can write: number of mammals = number of reptiles + 12
Or we can write: 11x = 8x + 12
Solve to get x = 4
Once we know the value of x, we can see that the number of birds = 5x = (5)(4) = 20
Since we can answer the target question with certainty, statement 1 is SUFFICIENT

Statement 2: if the zoo acquired 16 more mammals, the ratio of mammals to birds would be 3:1
So, (current number of mammals + 16)/(current number birds) = 3/1
Or we can write: (11x +16)/5x = 3/1
Cross multiply to get: 11x + 16 = 15x
Solve, to get x = 4
Once we know the value of x, we can see that the number of birds = 5x = (5)(4) = 20
Since we can answer the target question with certainty, statement 2 is SUFFICIENT

Cheers,
Brent
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Re: A certain zoo has mammal and reptiles and birds, and no other animals.  [#permalink]

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27 Sep 2015, 14:07
Bunuel wrote:
A certain zoo has mammal and reptiles and birds, and no other animals. The ratio of mammals to reptiles to birds is 11: 8:5. How many birds are in the zoo?

(1) there are twelve more mammals in the zoo than there are reptiles

(2) if the zoo acquired 16 more mammals, the ratio of mammals to birds would be 3:1

Kudos for a correct solution.

Statement 1:
Let x be the number of mammals and y be the number of reptiles.
Then,
x/y=11/8
or 8x=11y
There are 12 more mammals in the zoo than reptiles.
or x=12+y
putting this in above equation we have
8(12+y)=11y
or 96+8y=11y
or 96=3y
or y=32
So there are total 32 reptiles. There are 8 reptiles in the ratio.So the common multiplier is 32/8=4
and the number of birds is 5*4=20.
SUFFICIENT

Statement 2:
Let x be the common multiplier.
When zoo acquired 16 more mammals, the ratio of mammals to birds would be 3:1
or $$\frac{11x+16}{5x}=\frac{3}{1}$$
or 11x+16=15x
or 4x=16
or x=4
So the number of birds will be 4*5=20
SUFFICIENT

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GMAT 1: 590 Q42 V29
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Re: A certain zoo has mammal and reptiles and birds, and no other animals.  [#permalink]

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27 Sep 2015, 19:44
Bunuel wrote:
A certain zoo has mammal and reptiles and birds, and no other animals. The ratio of mammals to reptiles to birds is 11: 8:5. How many birds are in the zoo?

(1) there are twelve more mammals in the zoo than there are reptiles

(2) if the zoo acquired 16 more mammals, the ratio of mammals to birds would be 3:1

Kudos for a correct solution.

by 1st statement
diff between ratio is 3 units, and those 3 units are equal to 12, hence 1 unit equal to 4, so birds are 20,sufficient.
by 2nd statement,
16 more additions in mammals will make that ratio 15:8:5, hence 4 units of ratio are equal to 16, again by above method the ans is same
hence ans is D
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A certain zoo has mammal and reptiles and birds, and no other animals.  [#permalink]

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28 Sep 2015, 00:26
Bunuel wrote:
A certain zoo has mammal and reptiles and birds, and no other animals. The ratio of mammals to reptiles to birds is 11: 8:5. How many birds are in the zoo?

(1) there are twelve more mammals in the zoo than there are reptiles

(2) if the zoo acquired 16 more mammals, the ratio of mammals to birds would be 3:1

Kudos for a correct solution.

My Solution:

Initial ratio of mammal to reptiles to birds 11:8:5.

Lets say Mammals=11x,
Reptiles=8x,
Birds=5x

Number of birds in the zoo?

St 1) says 11x=8x+12
Solving for x we get x=4
So, number of birds=5x=5*4=20 sufficient.

St 2) says if zoo acquired 16 more mammals, the ratio of mammals to birds would be 3:1
therefore (11x+16):5x=3:1
Solving for x we get x= 4
So, statement 2 is Sufficient to count the number of birds i.e, 5x or 5*4=20

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Re: A certain zoo has mammal and reptiles and birds, and no other animals.  [#permalink]

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28 Sep 2015, 11:36
Given:
M : R : B = 11 : 8 : 5

Say x is a multiplier,

No of mammals = 11x
No of Reptiples = 8x
No of birds = 5x

Statement 1:

11x = 8x +12
x = 4

No of birds = 20.

Sufficient

Statement 2:

ratio of M: B after adding 16 mammals

(11x + 16) / 5x = 3: 1

solving we get x = 4, Birds = 20.

Sufficient

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Re: A certain zoo has mammal and reptiles and birds, and no other animals.  [#permalink]

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28 Sep 2015, 11:50
Bunuel wrote:
A certain zoo has mammal and reptiles and birds, and no other animals. The ratio of mammals to reptiles to birds is 11: 8:5. How many birds are in the zoo?

(1) there are twelve more mammals in the zoo than there are reptiles

(2) if the zoo acquired 16 more mammals, the ratio of mammals to birds would be 3:1

Kudos for a correct solution.

Let, the number of animals be -
mammals - 11x
reptiles - 8x
birds - 5x
We need to find the value of 5x.

Analysis
(1) mammals = reptiles + 12
or 11x = 8x +12;
Clearly, this can be solved for x and therefore we can find out number of birds from 5x. So SUFFICIENT

(2) if mammals population increase from 11x to 11x + 16, the ratio of mammals to birds will become 3:1
i.e. $$\frac{11x+16}{5x}$$ = $$\frac{3}{1}$$.
This can also be solved for x, so again we can find the number of birds from 5x. So SUFFIENT.

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A certain zoo has mammal and reptiles and birds, and no other animals.  [#permalink]

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28 Sep 2015, 12:22
A certain zoo has mammal and reptiles and birds, and no other animals. The ratio of mammals to reptiles to birds is 11: 8:5. How many birds are in the zoo?

(1) there are twelve more mammals in the zoo than there are reptiles

(2) if the zoo acquired 16 more mammals, the ratio of mammals to birds would be 3:1

M: 11X
R: 8X
B: 5X

Statement 1 - 11X-8X=3X=12, then X=4 -- # of birds=5*4=20 >> Sufficient
Statement 2 - (11X+16)/5X=3, then X=4 -- # of birds=5*4=20>> Sufficient
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Re: A certain zoo has mammal and reptiles and birds, and no other animals.  [#permalink]

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30 Sep 2015, 06:19

0) From the question we get that the ratio of Mammals to reptiles to birds is 11:8:5 and we are asked how many birds are there in the zoo?

(1) There are twelve more mammals in the zoo than there are reptiles

From this we get M = R +12. I number the number plugin approach as I didn't remember I could use the ratios to find x.

M:R:B
11:8:5 different between M and R = 3
22:16:10 different between M and R = 6
33:24:15 different between M and R = 9
44:32:20 different between M and R = 12

Thus the number of Birds is 20. Sufficient.

(2) if the zoo acquired 16 more mammals, the ratio of mammals to birds would be 3:1

For this we get (M + 16 / B ) = 3 : 1 and from the question stem we get that M / B = 11 / 5 thus 2 equations and 2 unknowns. Sufficient.

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Re: A certain zoo has mammal and reptiles and birds, and no other animals.  [#permalink]

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18 Dec 2017, 02:32
Jonas84 wrote:

0) From the question we get that the ratio of Mammals to reptiles to birds is 11:8:5 and we are asked how many birds are there in the zoo?

(1) There are twelve more mammals in the zoo than there are reptiles

From this we get M = R +12. I number the number plugin approach as I didn't remember I could use the ratios to find x.

M:R:B
11:8:5 different between M and R = 3
22:16:10 different between M and R = 6
33:24:15 different between M and R = 9
44:32:20 different between M and R = 12

Thus the number of Birds is 20. Sufficient.

(2) if the zoo acquired 16 more mammals, the ratio of mammals to birds would be 3:1

For this we get (M + 16 / B ) = 3 : 1 and from the question stem we get that M / B = 11 / 5 thus 2 equations and 2 unknowns. Sufficient.

Can someone elaborate on the highlighted approach?
Re: A certain zoo has mammal and reptiles and birds, and no other animals.   [#permalink] 18 Dec 2017, 02:32
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