### All GRE Math Resources

## Example Questions

### Example Question #1 : Sale Prices

A winter shirt is regularly priced at $50. At the end of the Christmas season, it is marked down by 40%. A month after this initial markdown, it is marked back up by 50%.

Quantity A

The initial cost of the shirt.

Quantity B

The final cost of the shirt, after it is marked up.

**Possible Answers:**

Quantity B is greater.

The relationship cannot be determined from the information given.

The quantities are equal.

Quantity A is greater.

**Correct answer:**

Quantity A is greater.

There are two ways to consider the value of B. First, you can subtract 40% from the initial $50 dollars: $50 – 0.4 * $50 = $30. This gives you the value after the markdown. Then to mark up the price, add 50% of $30 to the $30: $30 + 0.5 * $30 = $45.

A shorter way to do this problem is to consider the first markdown as reducing the price to *60% of the original*, then considering the markup as making it *150% of the new price*. This can be done in one set of multiplications: $50 * 0.6 * 1.5 = $45. Either way, the answer is the same. A is the larger quantity.

### Example Question #2 : Sale Prices

A store puts a $200 dress on a 70% discount and then takes an additional 15% off the reduced price. How much of the original price was removed?

**Possible Answers:**

$51

$170

$161

$149

$30

**Correct answer:**

$149

If we multiply $200 by 0.7, we find the dress has been reduced by $140 on the first discount. Since the dress now costs $60, we multiply that by 0.15 and find the dress has been discounted by an additional $9. The final sale of the dress is $51, with $149 of the original price removed.

### Example Question #3 : Sale Prices

In a local store, pens that normally sell for 49 cents each are on sale at 3 for 99 cents. How much can be saved by purchasing 12 of these pens at the sale price?

**Possible Answers:**

$1.44

$2.00

$2.04

$3.00

$1.92

**Correct answer:**

$1.92

Normally, 3 pens cost 3 * .49 = $1.47. Thus, on each set of 3 pens, the sale price saves the customer $1.47 - 99 = 48 cents. Multiply this by 4 to get the savings for 12 pens, and you get .48 * 4 = **$1.92**.

### Example Question #4 : Sale Prices

A department store sells a set of hand weights for $X. If the store offers a 20% discount on the original price of the weights, and then an additional 10% employee discount, what will be the price of the weights if an employee purchases them?

**Possible Answers:**

0.72X

0.7X

0.8X

0.88X

0.64X

**Correct answer:**

0.72X

This is a straightforward percentage problem. After the first discount, the price of the weights is $0.8X. This price is then further reduced by 10% for the employee discount. 90% of 0.8X = 0.9(0.8X) = 0.72X.

### Example Question #5 : Sale Prices

A shirt is originally $20 and marked down 30%. After this it is marked up by 40% then marked down again by 10%. What is its final price?

**Possible Answers:**

$20

$7.56

$18.50

$17.64

None of the other answers

**Correct answer:**

$17.64

The easiest way to solve this is to note that a 30% markdown reduces the cost to 70% of the original cost. Likewise, a 40% markup is the same as making the price 140% of its current value. Using this, we can solve our problem in one string of multiplications:

New cost = Original * 0.7 * 1.4 * 0.9

New cost = 20 * 0.7 * 1.4 * 0.9 = 17.64

### Example Question #1 : How To Find The Sale Price

A dress originally costs $50 but is on sale for 25% off. In addition, you have a 10% off coupon. How much will the dress cost after these discounts?

**Possible Answers:**

$42.15

$35.25

$32.50

$33.75

**Correct answer:**

$33.75

To find 25% of $50 you multiply 50 and 0.25. This gives you 12.50. This means the dress is $12.50 cheaper, so it now costs 50 – 12.50 = $37.50. You have an additional 10% off, so you multiply 37.50 by 0.10 to get 3.75. 37.50 – 3.75 = $33.75. This is the cost of the dress. NOTE: You CANNOT add 25% and 10% and take 35% off of the $50 dress. You will get the wrong answer.

### Example Question #1 : How To Find The Sale Price

Product X costs $27 to manufacture at the rate of 50 per hour. Production can only be increased in groups of 10 units per hour. For each such increase, the production cost increases 30% of its previous amount. If the output is to be doubled, for how much must each unit be sold to make at least a 25% profit?

**Possible Answers:**

$213.75

$219.38

$125.32

$157.32

$198.28

**Correct answer:**

$125.32

To calculate a 30% increase in cost, you can multiply the base cost by 1.3; therefore, if we are going to increase the rate five times, we will multiply by 1.3 five times, which is the same as 1.3^{5}. The cost of creating 100 units per hour is 27 * 1.3^{5} = 100.25.

If we want to make a 25% profit, we can set up the equation:

Price = 1.25 * 100.25 or 125.3125. To make at least a 25%, this will be $125.32.

### Example Question #1 : How To Find The Sale Price

To promote a new ice cream flavor, an ice cream parlor is selling their $1.29 cones at 70% of the original price. Approximately how much will be saved by buying 4 of their cones?

**Possible Answers:**

$1.56

$1.29

$.90

$3.16

$3.20

**Correct answer:**

$1.56

First let's calculate what 70% of $1.29 is: .7(1.29) = .9

Next, calculate how much 4 cones would have cost at the original price vs. the sale price:

4(1.29) = 5.16

4(.9) = 3.60

5.16 – 3.60 =** $1.56 saved**

### Example Question #1 : Sale Prices

Betty buys a sweater for $36. The next week, Alice buys the same sweater on sale for 25% off. The week after that, Chelsea buys the same sweater that is now 15% off the sale price. How much did Chelsea spend on the sweater?

**Possible Answers:**

$21.60

$22.95

$30

$27

$30.60

**Correct answer:**

$22.95

The sweater price starts at $36. Alice pays $36 – (.25 * $36) = $27. Chelsea then pays $27 – (.15 * $27) = $22.95, which is the correct answer.

When solving percentage questions such as this one, do NOT try to add up the discounts and find the final sale price all in one step. If you tried to do that here, the answer would have been $36 – (.25 + .15) * $36 = $21.60. This is an answer choice, but the wrong answer! Most GRE percentage questions will always give you this as one of your answer choices to try and trick you!

### Example Question #10 : How To Find The Sale Price

How much does a sweater cost that is 18% more than a $50 dress?

**Possible Answers:**

68

55

54

64

59

**Correct answer:**

59

18% of the dress is .18 * 50 = $9. Then the sweater costs $50 + $9 = $59.