GMAT Math : Calculating percents

Study concepts, example questions & explanations for GMAT Math

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Example Questions

Example Question #31 : Percents

Ten students in a class of  students have a learning disability. What is the percentage of students who do not have a learning disability in the class?

Possible Answers:

Correct answer:

Explanation:

The number of students who don't have a learning disability is:

Using part over whole we get the percentage of students who don't have a learning disability as:

Example Question #32 : Percents

You bought  worth of a stock two years ago. After the first year, the value of the stock decreased by an average . During the second year, the value of the stock increased by an average . What is the value of your investment today?

Possible Answers:

Correct answer:

Explanation:

The value of the stock after the first year is 90% (0.9) of the value of the stock at time 0.

The value of the stock after the second year is 125% (1.25) of the value of the stock at the end of the first year.

The value of the investment today is:

Example Question #33 : Percents

Rob, Tim, and Peggy are the three managers at a local restaurant. Peggy's salary is  less than Tim's salary. Tim's salary is  less than Rob's salary. What percent of Rob's salary is Peggy's salary?

Possible Answers:

Correct answer:

Explanation:

Let  be Rob's salary.

Then, since Tim's salary is 10% less than Rob's salary, we can write Tim's salary as .

Since Peggy's salary is 20% less than Tim's salary, we can write Peggy's salary as .

Peggy's salary is 72% of Rob's salary as we can write:

Peggy salary/ Rob salary = 

Making the answer into a percent we get,

.

Example Question #34 : Percents

The percentage of accountants at a company that has 10,000 employees dropped from  at the end of last year to  at the end of this year. If the number of employees at the end of this year is 9,500, what is the approximate change in the number of accountants over this period?

Possible Answers:

Correct answer:

Explanation:

The number of accountants at the end of last year is:

The number of accountants at the end of this year is:

The approximate change in the number of accountants from the end of last year to the end of this year is:

There was a 43% decrease in the number of accountants over this period.

Example Question #16 : How To Find Percentage

There are  registered students in the math club. Students are deciding what activity they could do for their end of semester event. They have three choices: rock climbing, bowling, or outdoor laser tag.  students vote for rock climbing,  students vote for bowling, and  students vote for outdoor laser tag.

What percent of students did not vote?

Possible Answers:

Correct answer:

Explanation:

The number of students who did not vote is:

The percent of students who did not vote is therefore:

 of the students did not vote.

Example Question #35 : Percents

 is  of , which is  of . All three are positive integers. In which range does the smallest possible value of  fall?

Possible Answers:

From  to  inclusive

From  to  inclusive

From  to  inclusive

From  to  inclusive

From  to  inclusive

Correct answer:

From  to  inclusive

Explanation:

 is  of , so .

 is  of , so .

For  to be an integer,  must be a multiple of . Therefore, the smallest positive integer value of  is  itself;  is  of  is , and  is  of , or .

Add these to get

The correct response is thus "From 31 to 40 inclusive."

Example Question #36 : Percents

 is  of  and  of ; all are positive integers. Give the smallest possible value of .

Possible Answers:

Correct answer:

Explanation:

 is  of  and  of , so

 and .

Equivalently,  and 

 must be the least possible number divisible by both  and , so 

.

Example Question #37 : Percents

 is  of . Which of the following expressions is equal to ?

Possible Answers:

None of the other responses is correct.

Correct answer:

Explanation:

If  is  of , then .

Equivalently,

Example Question #38 : Percents

A randomly selected study sample includes  women. Of all the women in the sample,  have an income greater than . What is the percentage of women in the sample who have an income greater than ?

Possible Answers:

Not enough information

Correct answer:

Explanation:

The percentage of women who have an income greater than  in the sample is simply the product of the percentage of women in the sample and the percentage of these women who earn more than .

The percentage of women who earn more than  in the sample is .

Or, we could assume there are  people in the sample. The number of women in the sample would then be . And the number of women who earn more than  in the sample would be .

The percentage of women who earn more than  in the sample is .

Let's verify this answer by taking another sample size, let's say there are  people in the sample.

The number of women who earn more than  in the sample would then be .

The percentage of women who earn more than  in the sample is .

We still get the same result because the number of people in the sample is not necessary to find that percentage since we are given the percentage of women in the sample and the percentage of these women in the sample who earn more than .

Example Question #39 : Percents

 of the adults in a certain city are unemployed, and  of the adults in the city are unemployed women. What percent of the unemployed adults in that city are men?

Possible Answers:

Correct answer:

Explanation:

Assume there are  adults in the city.  of these adults are unemployed, which means the number of unemployed adults is  given there are  adults. Also,  of the adults in the city are unemployed women, so the number of unemployed adult women in the city is . We can then find the number of unemployed adult men in that city, which is .

At this point, we can calculate the percentage of unemployed adults in the city who are men: 

 of the unemployed adults in that city are men.

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