Problems involving percent are common on the UMAT. 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 

25 x 
1/100 = 
1/4 
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,
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 = 80/100 = 4/5
Following are the most common fractional equivalents of percents:
33.33% = 1/3 
20% = 1/5 
66.67% = 2/3 
40% = 2/5 
25% = 1/4 
60% = 3/5 
50% = 1/2 
80% = 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%
Translate the sentence into a mathematical equation as follows:
What 
percent 
of 
25 
is 
5 
x 
1/100 
* 
25 
= 
5 
(25/100)x = 5
(1/4)x = 5
x=20
The answer is (B).
Example 2: 2 is 10% of what number?
(A) 10 (B) 12 (C) 20 (D) 24
Translate the sentence into a mathematical equation as follows:
2 
is 
10 
% 
of 
what number 
2 
= 
10 
1/100 
* 
x 
2 = (10/100)x
2 = (1/10)x
20 = x
The answer is (C).
Example 3: What percent of a is 3a ?
(A) 100% (B) 150% (C) 200% (D) 300%
Translate the sentence into a mathematical equation as follows:
What 
percent 
of 
a 
is 
3a 
x 
1/100 
* 
a 
 
3a 
(x/100)a = 3a
x/100 = 3
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?
(A) 15%
(B) 18%
(C) 25%
(D) 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:
What 
percent 
of 
the class 
is 
boys 
x 
1/100 
* 
40 
= 
15 
(40/100)x = 15
(2/5)x = 15
2x = 75
x = 37.5%
The answer is (D).
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: (Amount of change/Original amount) xl00%
Example 5: 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 1/3%
(B) 50%
(C) 75%
(D) 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: (Amount of change/Original amount) * l00% =
(4000/12000) * l00% =
1/3 * 100% = (by canceling 4000)
= 33+1/3%
The answer is (A).
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