How to find proportion

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GRE Quantitative Reasoning › How to find proportion

Questions 1 - 10
1

If an a train is traveling at 8 feet per second, how many feet does it travel in 2 hours?

Explanation

For this problem, you must do conversions of from hours to seconds.

Two hours is equal 120 minutes

.

120 minutes is equal to 7200 second

.

The train travels 8 feet per second so in 7200 seconds it travels 57600 feet

.

2

16 ounces of lemonade mix makes 2 gallons of lemonade (one gallon is equivalent to 4 quarts).

Quantity A: Amount of mix needed to make 3 quarts of lemonade

Quantity B: 6 ounces of mix

The two quantities are equal

Quantity A is greater

Quantity B is greater

The relationship cannot be determined from the information given

Explanation

2 gallons of lemonade equals 8 quarts of lemonade. To make 3 quarts of lemonade, you need of the amount needed to make 2 gallons of lemonade, or 6 ounces of mix.

3

Bob can paint a house in 3 hours. If Bob and his friend Ron work together to paint the house, it takes 2 hours. How long would it take Ron to paint the house if he worked alone?

3 hours

4 hours

5 hours

6 hours

2 hours

Explanation

The easiest way to solve this is with a rate formula: 1 / combined time = 1 / Bob's time + 1 / Ron's time. We know the combined time and Bob's time, so we can solve for Ron's time:

1/2 = 1/3 + 1/Ron's time

1/Ron's time = 1/2 – 1/3 = 1/6

Ron's time = 6 hours

4

Flour, eggs, sugar, and chocolate chips are mixed by weight in the ratio of 12 : 5 : 3 : 5, respectively. How many pounds of chocolate chips are there in 75 pounds of the mixture?

5

15

18

25

Explanation

First, add up the four parts of the ratio. This equals 25 parts. These 25 parts make up the 75 pound mixture, which means the 75 pound mixture is composed of 3 times the 25 parts (25x = 75 so x = 3).

This allows you to know that the number of pounds of chocolate chips is 3 times the ratio, i.e. 3 * 5 = 15. The mixture includes 15 pounds of chocolate chips. The answer is 15.

5

\frac{x}{y}=\frac{3}{5}

Quantity A:

Quantity B:

The relationship cannot be determined from the information given

Quantity A is greater

The two quantities are equal

Quantity B is greater

Explanation

Although it seems as though "Quantity B is greater" is the correct answer at first glance, a further analysis indicates that this answer is a trap. If and are negative numbers, such as and , then would be the larger number. Similarly, is larger if both and are positive numbers. Thus, it cannot be determined which variable is larger simply based on the information given.

6

In a class with students, if are taking Calculus and are taking Chinese, what is the lowest amount of students possible in the class that are taking both Calculus and Chinese?

Explanation

This problem states that there are students in the class taking Calculus. Because the class has a total of students, that means there are only students in the class not taking Calculus. The problem also states that there are students in the class taking Chinese. Because only students in the class aren't taking Calculus, this means that there is a minimum of students in the class that are taking both Calculus and Chinese.

7

If the sum of a, b and c is 400, and a is 1/3 b and b is 1/4 c, what is the value of a?

33

66

20

25

300

Explanation

Answer: 25
Explanation: For this type of problem, build an equation that represents the relationships between the quantities and solve for the quantitiy you need. The problem states that b=1/4c and a = 1/3b. Thus, a = 1/3(1/4)c, or 1/12 of c. Now put everything in terms of c, thus 1/12c + 1/4c +c = 400. Now comes the tricky step--combine like terms and create the improper fraction (1/12c + 3/12c + 12/12c = 16/12c). Reduce the fraction to 4/3. So 400 is 4/3 of c. Thus c is 3/4 of 400, or 300. a is 1/12 of 300, or 25.

8

Erin went to the movies with her friends. She spent 1/4 of her allowance on movie tickets and 3/5 of the remaining money on popcorn. If her allowance is $10, how much money remains?

$1.50

$3.00

$5.00

$7.00

$8.50

Explanation

Since she spent 1/4 on the ticket, 3/5 of the remaining 3/4 of the money was spent on popcorn: 3/5 x 3/4 = 9/20. This means 9/20 of the money was spent on popcorn so in total: 1/4 + 9/20 = 14/20 = 7/10 of her money was spent. This leaves 3/10 of her money behind: 3/10x 10 = 3.00.

9

3 men can paint 3 rooms in 3 hours. How long would it take 1 man to paint 1 room?

1 hour

2 hours

1.5 hours

2.5 hours

3 hours

Explanation

It's tempting to pick 1 hour, but that is a trick answer! Picture 3 men each painting 1 room. All 3 of the rooms are done after 3 hours, so each man actually spends 3 hours painting his room, not 1 hour.

10

You have a rope of some length, but 2/3rds of it is cut off and thrown away. 1/4th of the remaining rope is cut off and thrown away. What proportion of the original rope remains?

1/6

1/3

1/4

1/10

The answer cannot be determined from the given information.

Explanation

If 2/3 is cut off and thrown away, that means 1/3 of the original length remains. Of this, 1/4 gets cut off and thrown away, meaning 3/4 of 1/3 still remains. Multiplying 3/4 * 1/3, we get 1/4.

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