Ratios and proportions are favorites of most standardized tests, and the GRE is no exception. They may be a bit intimidating if you are unfamiliar with how to approach them, but once you learn the basics, you’ll learn that ratio and proportions problems require only simple algebra.
A ratio is a kind of fraction that measures two or more quantities in a group.

For example, a ratio of boys to girls (Boys: Girls) at a party is 3:4. You can also write this ratio as 3/4. That means that for every 3 boys at the party, there are 4 girls. This does not mean that 3/4 of the party goers are boys, nor does it mean that 4/3 of the party goers are girls.

If you do want to find out what proportion or percentage of the party goers are boys or girls, respectively, you add the numerator and the denominator, and then form a fraction in which this sum is the denominator.

So, if I want to find out what proportion of the party goers are boys, I add 3 and 4 (=7), and then I take the ratio quantity of boys, 3, and form the fraction 3/7.

3/7, or 42.9 %, of the party goers are boys.

4/7, or 57.1%, of the party goers are girls.

Stated algebraically, if we have a ratio x:y, then x / x+y and y /x+y express the proportions of x to the group and y to the group, respectively.

Let’s see what an example using this rule might look like:

Example 1: At a party, 40% of the party goers are male. What is the ratio of male to female party goers?

This question uses the aforementioned rule, but reverses the process. We now have to find the ratio.

If 40% of the party is male, then 4/10 or 2/5 of the party is male and 3/5 of the party is female.

Since we have two proportions expressed with the same denominator (2/5 and 3/5), we can simply express the ratio of males to females as 2/3 or 2:3.
Note: If the question had asked for the proportion of females to males, the answer would be 3:2.

Though we cannot find the total number of items in a group (e.g. number of people at the party) if we are given a ratio, we can deduce some important information about the number of items. A GRE question testing this rule may look like this:

Example 2: If the ratio of men to women at a party is 4:7, which of the following could be the number of people at the party?
A. 50 B. 64 C. 66 D. 70 E. 78

At first, you may think that you do not have enough information to answer this question, but you do.

To answer a problem like this, just add the coefficient x to each quantity and add: 4x+7x=11x.
We know that the sum of the quantities, 11, represents a fraction of the total number of party goers, so our answer MUST be a multiple of 11.

The only multiple of 11 in our choices is C. 66.

Extra Credit: If there were 66 people at the party, how many males and females would be there?

If 11x=66, then x = 6.
4x= 4*6= 24 men
7x=7*6=42 women

That last example was pretty simple, but how about a tougher one that uses the same concept:

Example 3: In a right triangle, the two acute angles have a ratio of 1:5. What’s the measure of the larger acute angle?

Before we apply the same method, let’s write down some important info. If this is a right triangle, then the largest angle is 90 degrees. Since the sum of the angles of a triangle equal 180 degrees, then the two acute angles must equal 90 degrees.

so: 1x+5x =90
6x=90
x=15

The larger angle is 5x, so 5*15 = 75

Hopefully, ratios and proportions aren’t so scary anymore. See if you can spot some ratio problems when you’re practicing on Grockit.