# GRE Math : How to find percentage

## Example Questions

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### Example Question #42 : Percentage

is  percent of

is  percent of

Quantity A:

Quantity B:

The two quantities are equal.

The relationship cannot be determined.

Quantity A is greater.

Quantity B is greater.

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 #261 : Arithmetic

is what percent of  ?

Explanation:

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

### Example Question #262 : Arithmetic

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?

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 #263 : Arithmetic

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?

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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