# GRE Math : Fractions and Percentage

## Example Questions

### Example Question #1 : Percentage

What percentage of a solution is blood if it contains ml blood and ml water?  Round to the nearest thousandth?

Explanation:

First, you must find the total amount of solution.  This is , or .

Now, the percentage of the solution that is blood can be represented:

, or

This is the same as %  Rounded, it is %

### Example Question #2 : Percentage

What is the percentage increase of an account that began with a balance of  and increased to ?

Explanation:

Recall that the formula for percentage increase is:

For our numbers, this would be:

Recall that to find a percentage from a decimal, you multiply by :

### Example Question #3 : Percentage

If one of the employees across both industries were to be selected at random, what is the probability that the employee will be a construction industry worker who stayed in the same role for 5 years or more?

65%

10%

20%

26%

17%

26%

Explanation:

The first step is to figure out the percentage of construction employees that have stayed in the same role for 5 years or more—this would include both the "5 to 9 year" and "10+ years" ranges. This would be 0.25 + 0.4 = 65% of all construction employees.  To convert to the number of employees, we take the percentage of their total, 0.65 * 8,000,000 = 5,200,000 workers. However, since the probability we are attempting to find is of workers between both industries, we must add the 8 million to the 12 million = 20 million workers total. 5,200,000/20,000,000 = 0.26, or a 26% chance.

### Example Question #4 : Percentage

For every 1000 cookies baked, 34 are oatmeal raisin.

Quantity A: Percent of cookies baked that are oatmeal raisin

Quantity B: 3.4%

Quantity A is greater

Quantity B is greater

The two quantities are equal.

The relationship cannot be determined from the information given.

The two quantities are equal.

Explanation:

Simplify Quantity A by dividing the number of oatmeal raisin cookies by the total number of cookies to find the percentage of oatmeal raisin cookies. Since a percentage is defined as being out of 100, either multiply the resulting decimal by 100 or reduce the fraction until the denominator is 100. You will find that the two quantities are equal.

### Example Question #5 : Percentage

50 students took an exam. There were 4 A's, 9 B's, 15 C's, 8 D's, and the rest of the students failed. What percent of the students failed?

Explanation:

students failed.

which equals 28%.

### Example Question #6 : Percentage

Column A:

Column B:

Column A is greater.

Column B is greater.

The two quantities are equal.

The relationship cannot be determined from the given information.

Column B is greater.

Explanation:

2/5% = 0.40% = 0.004.  Therefore, Column B is greater.

### Example Question #1 : Percentage

is  percent of

is  percent of

Quantity A:

Quantity B:

The relationship cannot be determined.

The two quantities are equal.

Quantity B is greater.

Quantity A is greater.

Quantity B is greater.

Explanation:

To do this problem, translate each expression into mathematical terms:

is  percent of :

is  percent of :

Quantity B is greater.

### Example Question #8 : Percentage

Quantity A: 20% of

Quantity B: 30% of

The two quantities are equal.

Quantity A is greater.

The relationship cannot be determined.

Quantity B is greater.

Quantity B is greater.

Explanation:

To solve this problem, consider writing the quantities in terms of only fractions:

Quantity A: 20% of

Quantity B: 30% of

Quantity B has the smaller denominator for an equal numerator. There is no need for calculation beyond this, and time on the GRE would be best spent elsewhere.

Quantity B is greater.

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