Ratio And Average

[phoenix9801]

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

[aneesh.kg]

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]

[aneesh.kg]

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]

[GMATGuruNY]

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 rm.
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, rm = 10:8:22 = 5:4:11.

[aneesh.kg]

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.

[aneesh.kg]

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.

[GMATGuruNY]

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.