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Ratio And Average

Expert replies
by phoenix9801 » Wed May 30, 2012 11:50 pm
1-
A dog caught 38 frisbees in his first 2.5 hours in the park. How many frisbees must the dog catch in the next hour in order to average at least 20 frisbees per hour?

Indicate all such values.

A) 30
B) 31
C) 32
D) 33
E) 34
F) 35


2-
A dog has caught 38 frisbees in his first 2.5 hours in the park. If the dog catches x frisbees in the next half-hour, what values of x would allow the dog to average at least 6x frisbees per hour?

Indicate all such values.
a) 0
b) 1
c) 2
d) 3
e) 4
f) 5


3-
In a certain zoo, 25% of the animals are reptiles. If there are 80% as many birds as reptiles, and the zoo only contains reptiles, birds, and mammals, then what is the ratio of reptiles to birds to mammals?

A) 4:5:11
B) 5:16:1
C) 16:1:5
D) 16:4:5
E) 5:4:11


4-
The ratio of gorillas to lions in a zoo was 5:4. After transferring 13 of the lions to another zoo, the new ratio of gorillas to lions is 7:3. How many gorillas currently reside in the zoo?
a) 35
b) 50
c) 70
d) 90
e) 105
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Source: — Problem Solving |

by aneesh.kg » Thu May 31, 2012 2:00 am
phoenix9801 wrote: 2-
A dog has caught 38 frisbees in his first 2.5 hours in the park. If the dog catches x frisbees in the next half-hour, what values of x would allow the dog to average at least 6x frisbees per hour?

Indicate all such values.
a) 0
b) 1
c) 2
d) 3
e) 4
f) 5
First of all, this is clearly your friend's GRE problem. :)

Average >= 6x in 3 hours
Total >= 18x
38 + x >= 18x
x =< 38/17
x =< 2.2
Since x is the number of frisbees, it has to be an integer. x = 2, 1 and 0 are acceptable.

[spoiler](A),(B),(C)[/spoiler]
Last edited by aneesh.kg on Thu May 31, 2012 2:12 am, edited 2 times in total.
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by aneesh.kg » Thu May 31, 2012 2:02 am
phoenix9801 wrote:1-
A dog caught 38 frisbees in his first 2.5 hours in the park. How many frisbees must the dog catch in the next hour in order to average at least 20 frisbees per hour?

Indicate all such values.

A) 30
B) 31
C) 32
D) 33
E) 34
F) 35
In a total of 3.5 hours, if the average >= 20 frisbees/hours.
Then
Number of Frisbees caught in 3.5 hours >= 20*3.5
38 + Number of frisbees caught in the next hour >= 70
Number of frisbees caught in the next hour >= 32

[spoiler](C), (D), (E), (F)[/spoiler]
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by GMATGuruNY » Thu May 31, 2012 2:13 am
phoenix9801 wrote: In a certain zoo, 25% of the animals are reptiles. If there are 80% as many birds as reptiles, and the zoo only contains reptiles, birds, and mammals, then what is the ratio of reptiles to birds to mammals?

A) 4:5:11
B) 5:16:1
C) 16:1:5
D) 16:4:5
E) 5:4:11
We can plug in the answers, which represent r:b:m.
Since reptiles are 25% of the total, the first value in the ratio must be 1/4 of the sum of the values in the ratio.
Only answer choice E works:
5/(5+4+11) = 5/20 = 1/4.

The correct answer is E.

An alternate approach would be to plug in numbers.
Let the number of reptiles = 10.
Since there are 80% as many birds, birds = 8.
Since the 10 reptiles are 25% of the total, the total number of animals = 40.
Thus, the number of mammals = total - reptiles - birds = 40-10-8 = 22.
Thus, r:b:m = 10:8:22 = 5:4:11.
Last edited by GMATGuruNY on Thu May 31, 2012 2:19 am, edited 1 time in total.
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by aneesh.kg » Thu May 31, 2012 2:15 am
phoenix9801 wrote: 3-
In a certain zoo, 25% of the animals are reptiles. If there are 80% as many birds as reptiles, and the zoo only contains reptiles, birds, and mammals, then what is the ratio of reptiles to birds to mammals?

A) 4:5:11
B) 5:16:1
C) 16:1:5
D) 16:4:5
E) 5:4:11
If there are 100 animals, then 25 are reptiles.
Numbers of birds = 80% of 25 = 20
Number of mammals = 100 - (25 + 20) = 55

Reptiles:Birds:Mammals = 25:20:55 = 5:4:11

[spoiler](E)[/spoiler] is correct.
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by aneesh.kg » Thu May 31, 2012 2:17 am
phoenix9801 wrote:4-
The ratio of gorillas to lions in a zoo was 5:4. After transferring 13 of the lions to another zoo, the new ratio of gorillas to lions is 7:3. How many gorillas currently reside in the zoo?
a) 35
b) 50
c) 70
d) 90
e) 105
Gorillas = 5x
Lions = 4x

If 13 Lions were transferred, New number of Lions = (4x - 13)
New Ratio = 7/3
(5x)/(4x - 13) = 7/3
15x = 28x - 91
x = 7

Gorillas = 5x = 5*7 = 35

[spoiler](A)[/spoiler] is correct.
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by GMATGuruNY » Thu May 31, 2012 2:37 am
phoenix9801 wrote: The ratio of gorillas to lions in a zoo was 5:4. After transferring 13 of the lions to another zoo, the new ratio of gorillas to lions is 7:3. How many gorillas currently reside in the zoo?
a) 35
b) 50
c) 70
d) 90
e) 105
We can plug in the answers, which represent the number of gorillas currently in the zoo.

Since g:l = 7:3, the number of gorilla must be a multiple of 7.
Eliminate B and D.

3 options remain:
A: g=35, l=15 (since 7:3 = 35:15)
C: g=70, l=30 (since 7:3 = 70:30)
E: g=105, l=45 (since 7:3 = 105:45)

Before the transfer, g:l = 5:4.
Thus, the number of lions before the transfer must be a multiple of 4.
Before the transfer, there were 13 more lions:
A: l = 15+13 = 28.
C: l = 30+13 = 43.
E: l = 45+13 = 58.
Only answer choice A works.

The correct answer is A.
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