GRE Math : Proportion / Ratio / Rate

Study concepts, example questions & explanations for GRE Math

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Example Questions

Example Question #1 :How To Find Proportion

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?

Possible Answers:

5 hours

6 hours

3 hours

2 hours

4 hours

Correct answer:

6 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

Example Question #91 :Fractions

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

Quantity A:

Quantity B:

Possible Answers:

Quantity B is greater

Quantity A is greater

The relationship cannot be determined from the information given

The two quantities are equal

Correct answer:

The relationship cannot be determined from the information given

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. Ifandare negative numbers, such asand, thenwould be the larger number. Similarly,is larger if bothandare positive numbers. Thus, it cannot be determined which variable is larger simply based on the information given.

Example Question #1 :How To Find Proportion

Jane has a collection of coins consisting of pennies, nickels, and dimes in the ratio 6:3:5.

If there are 42 coins in total, how many pennies are in the collection?

Possible Answers:

7

15

18

12

9

Correct answer:

18

Explanation:

First count the total number of parts in the ratio.

Then we can set up a proportion representing.

As the initial ratio shows, there are 6 pennies for every 14 total coins. In the total set, we have X pennies and 42 total coins. Plugging these numbers into the proportion gives.

Finally, we multiply both sides times 42 to isolate x.

Example Question #101 :Fractions

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

Possible Answers:

Quantity B is greater

The two quantities are equal

The relationship cannot be determined from the information given

Quantity A is greater

Correct answer:

The two quantities are equal

Explanation:

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

Example Question #12 :Proportion / Ratio / Rate

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

Possible Answers:

Correct answer:

Explanation:

这个问题的国家students in the class taking Calculus. Because the class has a total ofstudents, that means there are onlystudents in the class not taking Calculus. The problem also states that there arestudents in the class taking Chinese. Because onlystudents in the class aren't taking Calculus, this means that there is a minimum ofstudents in the class that are taking both Calculus and Chinese.

Example Question #13 :Proportion / Ratio / Rate

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

Possible Answers:

Correct answer:

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

.

Example Question #11 :Proportion / Ratio / Rate

1 : 1

2 : 3

3 : 4

1 : 3

There are 28 students in a room. The ratio of boys to girlscannotbe which of the above.

Possible Answers:

1 : 1

1 : 3

3 : 4

2 : 3

Correct answer:

2 : 3

Explanation:

When selecting ratios for two variables (boys and girls) the two sides of the ratio must add up to be a factor of the total student count. The factors of 28 include 14, 7, 4, and 2. (1 + 1 =2), (2 + 3 =5), (3 + 4 =7), and (1 + 3 =4).5is the only nonfactor and cannot be the ratio of boys to girls, thus making 2 : 3 the correct answer.

Example Question #1 :How To Find A Ratio

ForAll Sweets Bakery, the daily sales ratio of bread to cakes is 5:2. If the bakery sells 12 more loaves of bread on Tuesday than its daily sale of 40 loaves, how many cakes were sold on Tuesday? (round to the nearest integer)

Possible Answers:

Correct answer:

Explanation:

Since 40 loaves of bread are sold daily, and the ratio of bread to cakes is 5:2, thencakes are sold daily.

Using the ratio in the same way, we can find the additional amount of cakes sold:

cakes with approximation.

Thus, the total amount of cakes sold on Tuesday iscakes.

Example Question #1 :How To Find A Ratio

You are making a cake that requires, by volume, three times as much flour as sugar, twice as much sugar as milk, eight times more milk than baking powder and twice as much baking powder as salt. If you start with a teaspoon of salt, how many cups of flour do you need (there are 48 teaspoons in one cup)?

Possible Answers:

\dpi{100} \small 48

\dpi{100} \small 2

\dpi{100} \small 8

\dpi{100} \small 32

\dpi{100} \small 96

Correct answer:

\dpi{100} \small 2

Explanation:

One teaspoon of salt requires 2 teaspoons of baking powder, which requires 16 teaspoons of milk and 32 teaspoons of sugar. 32 teaspoons of sugar requires 96 teaspoons of flour, which equals two cups of flour.

Example Question #1 :How To Find A Ratio

A bakery stocks 3 cookies for every 2 cupcakes and 6 pastries for every 5 cookies. What is the ratio of cupcakes to pastries?

Possible Answers:

Correct answer:

Explanation:

First, you have to set up the given ratios, which is 3 cookies : 2 cupcakes and 5 cookies : 6 pastries. Then, you find a common multiple of cookies (i.e. 15) and convert the ratios to 15 cookies : 10 cupcakes and 15 cookies : 18 pastries. Since both ratios now have 15 cookies, you can infer that the ration of cupcakes to pastries is 10:18 or 5:9.

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