**Percents**

Problems involving percent are common on the GRE. The word *percent* means “divided by one hundred.” When you see the word “percent,” or the symbol %, remember it means $\frac{1}{100}$ .

For example,

25 Percent

To convert a decimal into a percent, move the decimal point two places to the right. For example,

0.25 = 25%

0.023 = 2.3%

1.3 = 130%

Conversely, to convert a percent into a decimal, move the decimal point two places to the left. For example,

47% = .47

3.4% = .034

175% = 1.75

To convert a fraction into a percent, first change it into a decimal (by dividing the denominator [bottom] into the numerator [top]) and then move the decimal point two places to the right. For example,

$\frac{7}{8}=0.875=87.5\%$

Conversely, to convert a percent into a fraction, first change it into a decimal and then change the decimal into a fraction. For example,

80% =. 80 = $\frac{80}{100}$ = $\frac{4}{5}$

Following are the most common fractional equivalents of percents:

33 $\frac{1}{3}$% = $\frac{1}{3}$ 20% = $\frac{1}{5}$

66$\frac{2}{3}$% = $\frac{2}{3}$ 40% = $\frac{2}{5}$

25% = $\frac{1}{4}$ 60% = $\frac{3}{5}$

50% = $\frac{1}{2}$ 80% = $\frac{4}{5}$

Percent problems often require you to translate a sentence into a mathematical equation.

**Example 1:**

What percent of 25 is 5?

(A) 10%

(B) 20%

(C) 30%

(D) 35%

(E) 40%

The answer is (B).

**Example 2:**

2 is 10% of what number

(A) 10

(B) 12

(C) 20

(D) 24

(E) 32

The answer is (C).

**Example 3:**

What percent of a is 3

*a*?

(A) 100%

(B) 150%

(C) 200%

(D) 300%

(E) 350%

The answer is (D).

**Example 4:**

If there are 15 boys and 25 girls in a class, what percent of the class is boys?

(A) 10%

(B) 15%

(C) 18%

(D) 25%

(E) 37.5%

The answer is (E).

Often you will need to find the percent of increase (or decrease). To find it, calculate the increase (or decrease) and divide it by the original amount:

**Percent of change:** $\frac{Amountofchange}{Originalamount}$ × 100%

**Example:**

The population of a town was 12,000 in 1980 and 16,000 in 1990. What was the percent increase in the population of the town during this period?

(A) 33$\frac{1}{3}$ %

(B) 50%

(C) 75%

(D) 80%

(E) 120%

Percent of change: $\frac{Amountofchange}{Originalamount}$ × 100%

$\frac{4000}{12000}$ × 100% =

$\frac{1}{3}\times 100\%$ (by canceling 4000)

33$\frac{1}{3}$ %

The answer is (A).