GMAT Quantitative Review

3.0 Math Review

3.1 Arithmetic

6. Percents

Percent means per hundred or number out of 100. A percent can be represented as a fraction with a denominator of 100, or as a decimal. For example:

image.

To find a certain percent of a number, multiply the number by the percent expressed as a decimal or fraction. For example:

image.

Percents greater than 100%.

Percents greater than 100% are represented by numbers greater than 1. For example:

image

image.

Percents less than 1%.

The percent 0.5% means image of 1 percent. For example, 0.5% of 12 is equal to image.

Percent change.

Often a problem will ask for the percent increase or decrease from one quantity to another quantity. For example, “If the price of an item increases from $24 to $30, what is the percent increase in price?” To find the percent increase, first find the amount of the increase; then divide this increase by the original amount, and express this quotient as a percent. In the example above, the percent increase would be found in the following way: the amount of the increase is image. Therefore, the percent increase is image.

Likewise, to find the percent decrease (for example, the price of an item is reduced from $30 to $24), first find the amount of the decrease; then divide this decrease by the original amount, and express this quotient as a percent. In the example above, the amount of decrease is image.

Therefore, the percent decrease is image.

Note that the percent increase from 24 to 30 is not the same as the percent decrease from 30 to 24.

In the following example, the increase is greater than 100 percent: If the cost of a certain house in 1983 was 300 percent of its cost in 1970, by what percent did the cost increase?

If n is the cost in 1970, then the percent increase is equal to image, or 200%.