# Percents

Problems involving percent are common on the GMAT. The word

*percent*means “divided by one hundred.” When you see the word “percent,” or the symbol %, remember it means 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,

For example,

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

For example,

For example,

Following are the most common fractional equivalents of percents:

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

Example-1

What percent of 25 is 5?

- 10%
- 20%
- 30%
- 35%
- 40%

Solution

Translate the sentence into a mathematical equation as follows:

What | percent | of | 25 | is | 5 |

x |

*x*= 20

The answer is (B).

Example-2

2 is 10% of what number

- 10
- 12
- 20
- 24
- 32

Solution

Translate the sentence into a mathematical equation as follows:

20 =
The answer is (C).

2 | is | 10 | % | of | what number |

2 | = | 10 | . |
x |

20 =

*x*

Example-3

What percent of

*a*is 3*a*?- 100%
- 150%
- 200%
- 300%
- 350%

Solution

Translate the sentence into a mathematical equation as follows:

(by canceling the
The answer is (D).

What | percent | of | a |
is | 3a |

x |
. |
a |
= | 3a |

*a*’s)*x*= 300Example-4

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

- 10%
- 15%
- 18%
- 25%
- 37.5%

Solution

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

2
The answer is (E).

what | percent | of | the class |
is | boys |

x |
. |
40 | = | 15 |

*x*= 75*x*= 37.5

**Note: **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: **** **

Example-5

The population of a town was 12,000, and ten years later it was 16,000. What was the percent increase in the population of the town during this period?

- 50%
- 75%
- 80%
- 120%

Solution

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% =

× 100% = (by canceling 4000)

The answer is (A).

×100% =

× 100% = (by canceling 4000)

The answer is (A).