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%

Translate the sentence into a mathematical equation as follows:

Example 2:
2 is 10% of what number

(A) 10
(B) 12
(C) 20
(D) 24
(E) 32
Translate the sentence into a mathematical equation as follows:

Example 3:
What percent of a is 3a ?

(A) 100%
(B) 150%
(C) 200%
(D) 300%
(E) 350%

Translate the sentence into a mathematical equation as follows:

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 total number of students in the class is 15 + 25 = 40. Now, translate the main part of the sentence into a mathematical equation:

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: × 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%

The population increased from 12,000 to 16,000. Hence, the change in population was 4,000. Now, translate the main part of the sentence into a mathematical equation:

Percent of change: × 100%

$\frac{4000}{12000}$ × 100% =

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

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