Percents as Fractions: The Percent Table

A simple but useful way of structuring basic percent problems on the GRE is by relating percents to fractions through a percent table as shown here:


                         Numbers		 Percentage
Fraction		 A part is some percent of a whole.
PART                                              
WHOLE 100

Example 1: What is 30% of 80?

You are given the whole amount and the percent, and you are looking for the part. First, fill in the percent table. Then, set up a proportion, cancel, cross-multiply, and solve:

PART X 30
WHOLE 80 100

You can also solve this problem using decimal equivalents:

Example 2: 75% of what number is 21?

You are given the part and the percent, and you are looking for the whole amount. First, fill in the percent table. Then, set up a proportion, cancel, cross-multiply, and solve:

PART 21 75
WHOLE x 100

Likewise, you can also solve this problem using decimal equivalents:

then move the decimal →

Example 3: 90 is what percent of 40?

This time you are given the part and the whole amount, and you are looking for the percent. Note that the “part” (90) is greater than the “whole” (40). While potentially confusing, this can happen, so watch the wording of the question carefully. Just make sure that you are taking the percent of the “whole.” Here, you are taking a percent of 40, so 40 is the “whole.”

First, you fill in the percent table. Then, you set up a proportion again and solve:

PART 90 x
WHOLE 40 100

Note that 90 is 225% of 40. Notice that you wind up with a percent greater than 100%. That is what you should expect when the “part” is bigger than the “whole.”

Check Your Skills

  1. 84 is 70% of what number?

  2. 30 is what percent of 50?