### Introduction

“Percent” literally translates into “per hundred” or “out of 100;” it’s denoted by this symbol: %.

100% = 100 hundredths = 100 × (1/100) = 1

50% = 50 hundredths = 50 × (1/100) = ½

Percents can be expressed as fractions or as decimals.

30% = 30/100 = 0.30

To convert a percent to a fraction, drop the percent sign and divide the number by 100.

75% = 75/100 = ¾

To convert a percent to a decimal, drop the percent sign and divide the number by 100. You can easily divide by 100 by moving the decimal point two places to the left, inserting zeros if necessary.

5% = 0.05

Percents greater than 100% are often written as numbers greater than 1.

320% = 320/100 = 3.2

Whenever a calculation involves percents, it is almost always easier to solve the problem by converting the percent to decimal form.

Example

What is 22% 350?

First convert the percentage to decimal form, then multiply as normal

### How to Calculate Percent Change

The GMAT often tests if you can find the percent increase or decrease from an original value.

Use the above formula whenever you are dealing with percent change. Take the percentage change and divide by the original percentage. This applies to both percent increase and percent decrease.

Example

A retail store purchase a television wholesale for \$158. The store sells prices the item for sale at \$199. What is the percent markup?

### Percent Approximation

Similar to working with decimals, the math sometimes gets too tedious to calculate the answer within the allotted time. If the answer choices contain nice round numbers, use approximation to save time.

Example

7.4 is what percent of 16,000?

What is 10% of 16,000? 1600
What is 1% of 16,000? 160
What is 0.1% of 16,000? 16
What is 0.01% of 16,000? 1.6

We know the answer must be between 0.01% and 0.1%

### Successive Percents

Example

Jim’s Wearhouse sells custom suits for \$299. During the summer season, all suits have a 15% discount. The Los Angeles branch store is going out of business and all suit inventory is sold at an additional 50% off. What is the final sale price of a custom suit during the summer?

It may be tempting to solve by adding 15% to 50% and subtracting 65% from the original purchase price. But this is incorrect! The actual solution should be as follows:

The answer is approximately 127 dollars. The problem is logically solved by:

However, in the first solution above, I simply multiply the original purchase price by 0.85 because price * 0.85 directly yields the final summer price paid. Successive multiplication by 0.5 yields the final purchase price of the suit. This is a very effective shortcut that can be used to save time on any problem involving successive percents. See proof below.