### All GRE Math Resources

## Example Questions

### Example Question #1 : How To Find Percentage

A pair of shoes originally cost $40. It is on sale and now only costs $32. The sale was for what percentage off the original cost?

**Possible Answers:**

35%

15%

20%

25%

**Correct answer:**

20%

The difference in cost is $8 (40 – 32). The sale percentage can be found by figuring out this question: 8 is what percentage of 40? 8/40 = 0.20, or a 20% discount. You can check this. 40 * 0.20 = 8.

40 – 8 = 32

### Example Question #1 : Other Percentage

A group of five students averaged 85 points on an exam taken out of 100 total points. If the addition of two additional students raises the group average to 88 points, what is the minimum score that one of those two students can receive? Assume that 100 is the highest score for the exam.

**Possible Answers:**

95.5

93

None of the other answers

91

100

**Correct answer:**

91

If the average score was 85, we know that the total points earned by the 5 students must be 85 * 5 or 425 points. Upon adding two new scores, we know that the formula for the average will be:

(425 + x) / 7 = 88, where x stands for the combined points earened by the two new students.

Solve for x: 425 + x = 616; x = 191

This means that both students must score 191 points total. If this is the case, we can assume that one student earns the maximum points, i.e. 100. This will provide the minimum amount that could be earned by the other: 191 – 100 = 91.

### Example Question #31 : Percentage

A baker is able to sell doughnut holes made from his doughnuts in groups of 6 for $0.50. If he wastes one hole per dozen doughnuts, how much money does he fail to make when selling the holes that can be packaged from 22 dozen doughnuts?

**Possible Answers:**

$1.83

None of the other answers

$11

$3.33

$2

**Correct answer:**

$2

Given his waste rate, the baker would waste 22 holes. That is the equivalent 3 ^{2}/_{3} bags; however, since that would leave him with a ^{1}/_{3} of a bag, the waste really is 4 bags of holes. He therefore fails to make 4 * 0.5 or $2 on this batch of 22 dozen doughnuts and holes.

### Example Question #1 : Other Percentage

A college student takes out a loan of $8,000 per Quarter. A college student's average living cost is represented by the chart below.

.

What percentage of the student's loan goes toward housing and tutiton?

**Possible Answers:**

**Correct answer:**

The sum cost of housing and tutition is $6199.24. To find the percentage of the loan that equals $6199.24, we can set up the equation:

Percentage = .

We then round the percentage to 77.5%.

### Example Question #2 : How To Find Percentage

On a 30 question test, Mike answered 60% of the first 20 questions correctly. What percent of the remaining 10 questions does he need to answer correctly for his grade on the entire test to be 70%?

**Possible Answers:**

**Correct answer:**

To earn a 70%, Mike needs to correctly answer 21 questions (70% of 30). So far, he has answered 12 questions correctly (60% of 20).

Therefore, on the last 10 questions he needs correct answers.

which equals 90%.

### Example Question #3 : How To Find Percentage

of a alcohol solution is mixed with of a alcohol solution. What percentage of the new mixture is alcohol?

**Possible Answers:**

**Correct answer:**

For this problem, we must figure out what % alcohol the 10 gallon combined mixture contains. We know that 4 gallons of 15% alcohol is mixed together with 6 gallons of 45% alcohol.

First we will break down how much alcohol content is within the 4 gallons of 15% alcohol. . This means that of the 4 gallons, 0.6 gallons can be considered pure alcohol.

Next, we will break down how much alcohol content is in the 6 gallons of 45% alcohol. . This means that of the 6 gallons, 2.7 gallons can be considered pure alcohol.

Therefore, the 10 gallon mixture of both mixtures now contains of pure alcohol. To find the % alcohol content, we simply divide the amount of pure alcohol by the total volume, or 33% alcohol.

### Example Question #4 : How To Find Percentage

A man has three sons, aged . In the combined age of his sons will be equal to of this age. How old is the man currently?

**Possible Answers:**

**Correct answer:**

To solve this problem, we must first add up the ages of all his sons.

. The combined age of his three sons is currently .

The problem states that in , the combined age of the man's three sons will be of his age.

Therefore we add to all his sons ages and sum them up once again.

. In , the combined age of his three sons will be .

Now to find what number is of, we simply divide by , . This means that in , the man will be old. To find how old the man is currently, we simply subtract from , this means that the man is currently old.

### Example Question #1 : How To Find Percentage

is 30 percent of 410

is 25 precent of 480

Quantity A:

Quantity B:

**Possible Answers:**

The two quantities are equal.

Quantity B is greater.

Quantity A is greater.

The relationship cannot be determined.

**Correct answer:**

Quantity A is greater.

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

is 30 percent of 410

is 25 precent of 480

Quantity A is greater.

### Example Question #6 : How To Find Percentage

30 is percent of 210

20 is percent of 160

Quantity A:

Quantity B:

**Possible Answers:**

Quantity B is greater.

Quantity A is greater.

The two quantities are equal.

The relationship cannot be determined.

**Correct answer:**

Quantity A is greater.

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

30 is percent of 210:

20 is percent of 160:

Since Quantity A has the smaller denominator with an equivalent numerator, it is the larger value. Quantity A is greater.

### Example Question #1 : Other Percentage

is 25 percent of 80

13 is percent of 65

Quantity A:

Quantity B:

**Possible Answers:**

Quantity A is greater.

Quantity B is greater.

The two quantities are equal.

The relationship cannot be determined.

**Correct answer:**

The two quantities are equal.

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

is 25 percent of 80:

13 is percent of 65:

The two quantities are equal.

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