Percent

A percent means “per 100.” So:

$Percent = \dfrac{Part}{Whole} \times 100$

There are a few main types of SAT percent questions:

1. Finding the Part

If you know the whole and the percent:

$Part = \dfrac{Percent}{100} \times Whole$

Example:

What is 30% of 200?

$\dfrac{30}{100} \times 200 = 60$

If you know the part and percent:

$Whole = \dfrac{Part}{Percent / 100}$

Example:

If 40 is 20% of a number, what is the number?

$Whole = \dfrac{40}{0.20} = 200$

If you know the part and the whole:

$Percent = \dfrac{Part}{Whole} \times 100$

Example:

What percent of 80 is 20?

$\dfrac{20}{80} \times 100 = 25%$

$Percent Change = \dfrac{New - Old}{Old} \times 100$

Example:

A price goes from $50 to $65.

$\dfrac{65 - 50}{50} x 100 = \dfrac{15}{50} \times 100 = 30%$

So it’s a 30% increase.

Be careful: two percent changes don’t just add together.

Example:

A shirt costs $100. It’s reduced by 20%, then reduced by another 10%.

Final price = $72.

The total percent decrease is:

$\dfrac{100 - 72}{100} \times 100 = 28%$

(not 30%)

Always ask: Is the percent based on the original value or the new value?
For word problems, underline which number is the “whole” (what the percent is based on).
Watch out for percent increase/decrease questions—they always use the original value in the denominator.