GRE Math: How to Solve Percentages ? { Simple Solution }

GRE Math: How to Solve Percentages ? { Simple Solution }

A percent is really a comparison of a number to 100; for example 17% means 17 per 100.

Since a percent is a comparison, it can also be expressed as a fraction: 17% = 17/100.

Since the comparison is to 100, a percent can also be expressed as a decimal: 17% = 0.17.

This ease of conversion between fractions, decimals, and percents leads to many uses for percents and many opportunities for problems involving them.

Most percent problems involve three quantities - whole, part, and percent.

You are usually given two of the quantities and asked to find the third. First, recall the basic nature of a percent (a comparison of one number to another) and how to convert that ratio to a decimal and a percent.

To find a percent, find the ratio of the part to the whole and then write that ratio in percent form.

Example 1: What percent of 60 is 45?

To find a part when you know the percent and the whole, multiply the whole by the decimal or fraction equivalent of the percent.

Example 2: What is 20% of 80

Part = Percent x Whole

Part = 20% x 80 = 0.20 x 80 = 16

A useful trick that sometimes saves a step is to add or subtract a given percent from 100%.

For example, suppose an 80 item is marked down 40%.

To find the new price, you can find 40% of 80 and then subtract:

40% x 80 = 0.40 x 80 = 32

and 80 - 32 = 48

Or you can recognize that 100% - 40% = 60% and find 60% of 80:

60% x 80 = 0.60 x 80 = 48

As another example, suppose an 80 item is marked up 20. To find the new price, you can find 20% of 80 and then add:

20% x 80 = 0.20 x 80 = 16

and

80 + 16 = 96