GRE Quantitative: Percents

Because of their broad applicability to real life, percent problems are common in standardized tests. We calculate percents every day, from leaving fair tips at restaurants to figuring out which sale will save the most money. While the percent problems on the GRE quantitative may be a little more complicated than those everyday calculations, they all follow the same basic rules.

The word “percent” means “per hundred,” so 19% can be written as either 0.19 or 19/100. To convert a decimal to a percent, multiply by 100, moving the decimal point two places to the right. For example, 0.19 becomes 19%, and 0.00031 becomes 0.031%. To convert a percent to a decimal, divide by 100, moving the decimal point two places to the left.

To convert a percent to a fraction, drop the percent symbol, write the number over 100, and then reduce. Here are a few familiar examples and some not so familiar ones.

See a full chart of conversions here > 

Common percent problems involve finding the percent of number and its many variations. Check out these simple examples below:

These kinds of questions should look familiar. The arithmetic involved is rather simple, but if you’re unfamiliar with the technique for solving them, they could pose a challenge. Let’s go over how to solve each one.
In each case, we want to translate each sentence by replacing “what” with x (since ‘what’ means the unknown variable), ‘is’ with ‘=’, ‘of’ with * (multiplication symbol), and also convert any percents to decimals.

GRE percent change questions compare the amount of an increase or decrease with the original value. The key is to divide the change by the original amount, then multiply by 100:

Percent increase = [(new value − original value) ÷ original value] × 100%

Percent decrease = [(original value − new value) ÷ original value] × 100%

For questions asking how much greater or smaller one quantity is than another, the comparison value is the denominator. For example, “What percent more than 6 is 8?” uses 6 as the base. “What percent less than 8 is 6?” uses 8.

“Percent Of” vs. “Percent Change” on the GRE

Small changes in wording can produce different answers, even when the numbers stay the same. “Percent of” compares one amount with another. “Percent more” or “percent less” compares the difference between the amounts with the stated base.

Question	Calculation	Answer
6 is what percent of 8?	(6 ÷ 8) × 100%	75%
8 is what percent of 6?	(8 ÷ 6) × 100%	133⅓%
8 is what percent more than 6?	[(8 − 6) ÷ 6] × 100%	33⅓%
6 is what percent less than 8?	[(8 − 6) ÷ 8] × 100%	25%

The difference between 6 and 8 is always 2, but the base changes. That is why increasing from 6 to 8 is a 33⅓% increase, while decreasing from 8 to 6 is a 25% decrease. Equal numerical changes do not necessarily produce equal percentage changes.

For the most part, if you are not dealing with quantitative comparisons, you’ll have to solve percent problems in the word problem form. Here’s a common type that you might encounter.