GMAT Exam: A Simple Guide To Solving Word Problems - Percentage

Formula and Terminology
In simple percentage problems use the formula P = RB, where P is the percentage (the “part of the whole”), R is the rate (the quantity with a % sign or the word percent attached), and B is the base (the “whole amount”).
In word problems, a percent without a base is usually meaningless. Be sure to identify the base associated with each percent mentioned in a problem.

Finding the Percentage
If the percentage is missing, multiply the base by the rate.

Here is an example.
Devra works at an electronics store that pays a commission rate of 2% to employees for all sales. Last week, Devra’s sales totaled $2,428. What commission did Devra earn last week?
In this problem, Devra’s commission is P, which is unknown; R is 2%; and B is $2,428. So, P = RB = (2%)($2,428) = (0.02)($2,428) = $48.56.
Devra earned $48.56 in commission last week.

Change percents to decimals or fractions to perform calculations.

Finding the Base
If the base is missing, divide the percentage by the rate.

Here is an example.
An online store offered a 25% discount on all clothing items during a two-day sale. Laura got $74.75 off the price of a coat she purchased during the sale. What was the original price of the coat?
In this problem, the original price of the coat is B, which is unknown; R is 25%; and P is $74.75. So,

Notice that using an equivalent fraction for the percent in this problem can simplify the calculations.

For the GMAT, you will find it helpful to memorize the following fractional and decimal equivalents of common percentages.


Finding the Rate
If the rate is missing, divide the percentage by the base. Express your answer as a percent.


Example: Aaron paid a sales tax of $9.90 on a camera that cost $120. What was the sales tax rate for the purchase?
In this problem, the sales tax rate is R, which is unknown; P is $9.90, and B is $120. So,

The sales tax rate was 8.25%.

Do not expect the rate to be less than 100% or the percentage to be less than the base in every problem. When the rate is greater than 100%, the percentage will be greater than the base.

For example,

because (125%)(400) = (1.25)(400) = 500.

See the “Numbers and Operations” guide for additional discussion about percents.

Percentage Increase or Decrease
The percent change (increase or decrease) in the value of an item is

Always divide by the value that occurred first in time.

For example, suppose a necklace increased in value from $345.00 to $396.75.

Then (omitting the units), the percent increase is

Similarly, suppose a book decreased in value from $25.90 to $23.31.

Then (omitting the units), the percent decrease is

Percent change, whether it is an increase or a decrease, is always positive.
See the “Numbers and Operations” guide for additional discussion about percents.