GRE Math: Ratios and Proportions

GRE Math Ratios is a part of GRE arithmetic in the Quant section. A ratio is a mathematical expression , which is usually a comparison between 2 or more quantities. In other words, it can also be the comparison between one part to another part or one part to the whole. A ratio always compares two quantities of the same kind. In the real world ratios are used in measuring food items in recipes and in maps.

The ratio can be expressed in different ways as

Colon Notation: a:b, Fraction Notation: a/b, Word Notation: a to b

Here a is called the antecedent (numerator) and b is called the consequent (denominator). 

On the other hand, proportion is an arithmetic equation that states the relationship between two quantities. They state that the ratio of one pair is the same as the ratio of another pair. In the real world, proportions are used in solving financial calculations for interest rates, or comparing investment returns. 

The proportion is represented as

"a/b = c/d" or “a:b :: c:d” or “a is to b as c is to d”

In this blog we will provide you with GRE Ratios and Proportions sample problems with answers and explanations. 

Note: It is important to note that ratios and fractions are different concepts in mathematics. Ratio is a kind of fraction, but it compares two quantities, while fractions represent a part to whole. Every fraction is a ratio, but every ratio is not a fraction.

GRE Quantitative: Ratios and Proportions with Example

Ratios and Proportions are key concepts in GRE Math problems. Ratios compare quantities, such as the ratio of two intersecting lines or the rates at which a person drove. Proportions state that two ratios are equal, maintaining the same relationship between quantities. These concepts might seem challenging without a strong grasp of the basics, but they only require simple algebra to learn and understand.
Let’s see an example to understand the concepts better.

Ratios

You can find ratios between the one part to another such as ratio of boys to girls in a class, or of the parts to the whole, such as ratio of boys or girls to the whole class. Let us see in detail.

Example 

If there are 12 boys and 18 girls in a class, then

Number of boys: 12
Number of girls: 18
Number of students: (12+18) = 30

Ratio of Boys to Girls in the class - 12:18, which can be simplified to 2:3
Ratio of girls to total number of students - 18:30, which can be simplified to 3:5
Ratio of boys to total number of students - 12:30, which can be simplified to 2:5

Proportions

Proportions are equations that state that two ratios are equal. A proportion is denoted by the symbol “: :”. For example, in a proportion a:b :: c:d, a and d are called extremes and b and c are called the means. Cross multiplication method can be used to solve the proportion, where you equate the product of extremes to the product of means.

Example

1) If three eggs costs 16 cents, how many eggs can you buy for 80 cents?

Let us keep ‘x’ as the number of eggs that you can buy for 80 cents. Then we can form the equation as 3 is to 16 as x is to 80.

3/16 = x/80
Cross Multiply - 16(X) = 3(80)
16x=240
x= 240/16
X = 15

Hence 15 eggs can be bought for 80 cents.

Other than cross multiplication , there are also other properties of Proportion. 
For a proportion a/b = c/d , the other properties that can be applied are:

1. b/a = d/c
2. a/c = b/d
3. a+b/b = c+d/d
4. a-b/b = c-d/d
5. a+b/a-b = c+d/c-d

You can solve a proportion equation by applying the above properties.

GRE Math Ratios and Proportion Practice Problems

Practice Problem 1:

Mike’s coin collection consists of quarters, dimes and nickels. If the ratio of the number of quarters to the number of dimes is 5:2, and the ratio of the number of dimes to the number of nickels is 3:4, what is the ratio of the number of nickels?

1. 5:4
2. 7:5
3. 10:6
4. 12:7
5. 15:8

Answer 1:

We are given two ratios.
Quarters:Dimes = 5:2  and Dimes:Nickels = 3:4

The number corresponding to the Dimes in the first ratio is 2.
The number corresponding to the Dimes in the second ratio is 3.

To restate the ratios, find the least common multiple of 2 and 3, which is 6.
On restating the ratios with the number of dimes as 6, then
Quarters:Dimes = 5:2  and Dimes:Nickels = 3:4

Quarters:Dimes = 15:6  and Dimes:Nickels =6:8

Thus the ratio of Quarters to Dimes to Nickels is 15:6:8, and hence the ratio of quarters to nickels is 15:8, which is (e).

Practice Problem 2:

In a collection of 1,000 nickels, dimes and quarters has the ratio of nickels to dimes to quarters being 5:3:2, how many of each coin are in the collection?

Answer 2:

First let’s state the ratio

nickels to dimes to quarters - 5:3:2 =1000

This can be restated as

5x+3x+2x=1000
10x=1000
x=100.

Thus there are 

Nickels - 500 (5*100)
Dimes - 300 (3*100)
Quarters - 200 (2*100)

Practice Problem 3:

In a class, there are ⅓ of the students who like carrots, and ⅛ of the students who like turnips. Find the ratio of students who like carrots to turnips.?

1. ⅜
2. 8/3
3. 8/5
4. 5/3

Answer 3:

Number of students who like carrots - ⅓
Number of students who like Turnips - ⅛

Ratio of students who like carrots to Turnips - ⅓ to ⅛ 

c/t = ⅓ / ⅛ = ⅓ ÷ ⅛ 
⅓ * 8/1 = 8/3 

Practice Problem 4
If a foot-long hotdog was cut into two parts that have a ratio of 1:2, how long is each part?

4 inches, 8 inches
8 inches, 4 inches
4 inches, 4 inches
3 inches, 4 inches

Answer 4:
Here the foot long should be calculated as 12 inches. Only then we can formulate the ratio and find the answer.

1:2 = 12
1x + 2x = 12
3x = 12
X = 4

Each part length is 4 and 8(1:2 in turn 4 inches and 8 inches long). Hence the answer is (a).

Practice Problem 5

In a necklace, there are 36 Diamonds, ruby and emerald gems. If the ratio of ruby to emerald is 2:5, then which of the following could not be the number of diamonds in the necklace?

1. 8
2. 15
3. 12
4. 29

Answer 5:
Let us mark D as Diamonds, R as Ruby and E as Emerald. Let’s form the equation.

D+R+E = 36

Substituting the ratios in the equation. 

D+2x+5x = 36
D+7X = 36
D = 36-7X

To find which cannot be the number of diamonds, we need to substitute each answer in the above equation.

1. 36-7k = 8
7k = 28
K = 4. Since 4 is an integer 8 could be the number of diamonds

In the same way if we solve the equation for each answer. The value of K is integer for 15 and 29. But for 12, the value of K will be 3.43. In that way, 12 cannot be the number of diamonds in the necklace. Hence the answer is (C).

Practice Question 6

If there are 120 apples and oranges in a basket, and the ratio of apples to oranges is 5:1, how many more apples are in the basket than oranges?

1. 72
2. 96
3. 100
4. 80

Answer
First let us formulate the equation.

5x+1x = 120
6x = 120
x = 20, where x is the value of a single part.

Substituting the value of x to the ratio, then 

The number of apples - 5*20 = 100
The number of oranges - 1*20 = 20

So the number of apples more than oranges is (100-20) 80. Hence the answer is (d)

Practice Question 7

Solve the proportion

A recipe calls for 1 cup of flour to 2 cups of sugar. If the next batch uses 3 cups of flour, how much sugar is needed?

Let’s frame the proportion equation.

1:2 :: 3:x

½ = 3/x 

1x = 6
x=6

Hence 6 cups of sugar is needed to make the recipe.

Tips to Solve the GRE Ratios Effectively

The GRE ratios and proportion section is a bit tricky. To ace this section, we have given a few tips and tricks to solve ratios and proportions problems.

1. Look for keywords like “for every”, “Out of” or “to” words to determine if the problem is based on ratios.
2. Once you have read a ratio problem, visualize it. It will be easy if you write in words or form an equation out of the problem given.
3. Give attention to minor details in the question. Even the small hint will help you solve the problem quicker. 
4. Keep the track of time to solve each problem. You need to keep the time limit for solving each problem and try to solve it within the time limit. 
5. To master the GRE Math Ratios you need to practice more such problems. 

Thus, in this blog we have given a detailed explanation on what is GRE Math Ratios and Proportion with examples and practice problems. For more such practice samples and to get top-notch GRE training, you can contact Kanan International at 73555 73555. Our expert faculties can help you in clearing GRE with a good score.