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# UMAT test tactics and preparation part 3: UMAT questions involving percentages

## What you need to know about percentage % questions before starting your UMAT preparation:

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

# Sample UMAT percentage % problems with worked answers.

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

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

Example 3:       What percent of 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

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%

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%