GRE Math : How to find percentage

Study concepts, example questions & explanations for GRE Math

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Example Questions

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Example Question #11 : How To Find Percentage

 is  percent of 

 is  percent of 

Quantity A: 

Quantity B: 

Possible Answers:

Quantity B is greater.

Quantity A is greater.

The relationship cannot be determined.

The two quantities are equal.

Correct answer:

Quantity B is greater.

Explanation:

To attempt this problem, translate the statements into mathematical equations.  When you see the word 'is', it very often means 'equals:

 is  percent of :

Now before we continue, look at this statement. We see that s is fourth fifths of r. That alone should tell us that r is greater!  However, we can continue with the calculations to see what these values are, if only for the sake of robustness. However, on the GRE, once you find the answer like this, fill it in and move on.

 is  percent of 

Again, this validates our result. We may not know what r and s are, but we know how they relate to each other, and that is enough.

Quantity B is greater.

Example Question #42 : Percentage

 is what percent of  ?

Possible Answers:

Correct answer:

Explanation:

To solve this problem, translate  is what percent of  into mathematical terms:

Example Question #43 : Percentage

In Dopolopolis, the first $20,000 dollars of a person's income is taxed at 6%, and any additional income they make is taxed at 10%. If Donny of Dopolopolis paid $2,000 in income tax this year, how much did Donny make?

Possible Answers:

Correct answer:

Explanation:

All of the answer choices are above $20,000, so assume that Donny paid the 6% on that:

That means of the $2,000 he paid in taxes

$800 was taken from any income he made above the $20,000 line, and was thus taxed at 10%:

Donny's income must therefore have been

Example Question #44 : Percentage

Forty percent of the 20 professors in a university's physics department are male. If two male professors and two female professors retire, what percentage of the department will be male after the change?

Possible Answers:

Correct answer:

Explanation:

Begin by finding out how many of the 20 professors are male:

That means that there are eight males and twelve females currently to sum up to twenty.

Now, two males and two females leave, meaning the faculty is reduced by four:

The amount of males has been reduced by two:

Therefore, the percentage of the faculty that is male can be found as the number of males divided by the total faculty size times 100:

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