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Percents

Problems involving percent are common on the SAT. The word percent means “divided by one hundred.” When you see the word “percent,” or the symbol %, remember it means . 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,

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

  1. 10%
  2. 20%
  3. 30%
  4. 35%
  5. 40%
Solution

Translate the sentence into a mathematical equation as follows:

What percent of 25 is 5
x . 25 = 5

 

 

x = 20

 

The answer is (B).
 

 

Example-2

2 is 10% of what number

  1. A.  10
  2. B.  12
  3. C.  20
  4. D.  24
  5. E.  32
Solution
Translate the sentence into a mathematical equation as follows:
2 is 10 % of what number
2 = 10 . x
 

 

 

20 = x

 
The answer is (C).

 

Example-3

What percent of a is 3a ?

  1. 100%
  2. 150%
  3. 200%
  4. 300%
  5. 350%
Solution

Translate the sentence into a mathematical equation as follows:

What percent of a is 3a
x . a = 3a
 

 

 (by canceling the a’s)

 

x = 300

 

The answer is (D).
 

 

Example-4

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

  1. 10%
  2. 15%
  3. 18%
  4. 25%
  5. 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:

 
what percent of the class is boys
x . 40 = 15
 

 

 

2x = 75

 

x = 37.5

 

The answer is (E).
 

 
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?

  1. 50%
  2. 75%
  3. 80%
  4. 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: 
The answer is (A).
 




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