# GMAT Math : Calculating discounts

## Example Questions

### Example Question #82 : Word Problems

Annie purchased some books at her university’s bookstore. She had a student coupon worth  off her whole purchase. The total amount paid showed on her receipt is , and that amount includes a  tax. What is the value of the books purchased before applying any discount or tax?

Explanation:

Let  be the value of all books purchased. First, a discount of  is applied to , then a tax of  is applied to get . We can then write the following equation:

The value of the books purchased is .

### Example Question #90 : Word Problems

An airline company sells a third of the seats in their less-popular flights to a third-party merchant at a  discount. Customers who buy tickets through the third-party merchant pay on average  less than the full price but do not have some privileges, such as changing or canceling their reservation. If a customer who booked their flight through the airline company paid the full price of  for their ticket, how much on average would a customer who booked their flight through the third-party merchant pay for the same flight?

Explanation:

Basically, the customers who buy through the third party merchant buy tickets at a  discount. As customers who book through the airline company pay the full price, customers who buy through the third party merchant would then pay  of the full price since, they benefit from a  discount.

A customer booking the same flight through the third-party merchant would then pay  for that flight.

This result is equivalent to using the percent of change formula:

### Example Question #91 : Word Problems

Mary finds a sweater on a clearance rack of items that are 25% off. If the ticket price is $42.00, how much will she pay for the sweater after the discount? Possible Answers:$37.50

$35.00$38.00

$32.00$31.50

$31.50 Explanation: First we find how much money Mary will save with the discount. If the sweater is 25% off, then the amount saved will be 25% of the original price: 0.25($42.00) = $10.50 Now we subtract the discount from the original price of the sweater to find the price Mary will pay at the register:$42.00 - $10.50 =$31.50

### Example Question #92 : Word Problems

A style of chair that Brian wants to purchase can be found in five different stores in town. Brian wants to buy the chair this weekend, and, as luck would have it, four of the stores are running specials this weekend:

Carter Brothers Furniture is discounting the price of the chair, which normally sells for $600, by 30%. Edison Furniture is discounting the price of the chair, which normally sells for$575, by 20%.

General Grant Furniture is discounting the price of the chair, which normally sells for $560, by 10%. Irving Furniture is discounting the price of the chair, which normally sells for$720, by 40%.

King of Furniture is not running any specials; the chair will sell for its normal price of $540. To get the chair for the lowest price, where should Brian go? NOTE: Assume all sales tax and other charges are equal. Possible Answers: Carter Brothers Furniture General Grant Furniture Irving Furniture King of Furniture Edison Furniture Correct answer: Carter Brothers Furniture Explanation: At Carter Brothers Furniture, the chair sells for 30% off the normal price of$600. This is 70% of $600, or At Elm Street Furniture, the chair sells for 20% off the normal price of$575. This is 80% of $575, or At General Grant Furniture, the chair sells for 10% off the normal price of$560. This is 90% of $560, or At Irving Furniture, the chair sells for 40% off the normal price of$720. This is 60% of $720, or At King of Furniture the chair sells for$540.

Carter Brothers Furniture is selling the chair for the lowest price, and it is where Brian should go.

### Example Question #93 : Word Problems

After a 20% employee discount and 5% sales tax, Catherine pays  dollars for a dress. What is the regular price of the dress before tax or discounts, in terms of ?

Explanation:

Call  the price before discount or tax. The amount of the discount is 20% of this, so the price after discount but before tax is  of this, or  of ; this is .

Similarly, the amount paid will be this price plus 5% of this as tax, or  of . 105% is , so the final amount paid is

Therefore,

and

### Example Question #93 : Word Problems

Jenkins received a 15% discount on a new bicycle. If he paid $635 for the bike, what was the dollar amount of his discount on the bike? Possible Answers: Correct answer: Explanation: To calculate discounts, it is often easiest to write out an equation. Before we do that, though, we need to make note of one detail. Jenkins receives a 15% discount on his bike. This means his bike is 85% of the original cost. So, we can set up the following equation: Here, is our original price and is our sale price. Plug in 635 for and divide over the 0.85 to get: We can round this to$747. We are not done yet, though, because we need to find the dollar amount saved. To find that , simply take the difference between the sale price and the original price.

Our answer is $112. ### Example Question #94 : Word Problems Tom finds a pair of jeans that are 40% off. If the original price of the jeans is$40, how much will Tom pay for them after the discount?

Explanation:

If the jeans are originally $40 and are 40% off, then Tom will pay 40% of$40 less than the original price for them. This gives us:

### Example Question #94 : Word Problems

Neil bought a new computer for  off its original price. If he paid  for the computer, what was its original price to the nearest dollar?

Explanation:

Set up a short equation to get our answer. We know that if we take  off of the original price, we get . That means  is  of the original price. So:

Solve for , the original price of the computer:

The computer's original price was .

### Example Question #97 : Word Problems

A very unique pair of shoes costs . After the designer did not find any buyer for his pair of shoes, he decides to decrease the price to . By how many percent was the pair of shoes discounted?

Explanation:

To solve this problem, we should use the decrease/increase formula: .

To find the change in the price we simply calculate the difference of the new price minus the original price, which gives us .

Then we just need to divide this change in value by the original value, wich gives us or , which is  discount.

### Example Question #21 : Calculating Discounts

The teacher says that at the end of the year she will increase all grades by  points. If my grade is , what will be the percent increase in my grade?