Calculating discounts

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GMAT Quantitative › Calculating discounts

Questions 1 - 10
1

A clothing store offers a dress initally at $100. Then one week later, the store offers the dress at 15% off. The dress still doesn't sell, so after another week, the store reduces its new price by 20%. How much does the dress cost now?

$68

$65

$60

$69

$66

Explanation

For the first discount, we have . So the dress is worth $85

After the second discount, we have

So the final dress price is $68

2

A lawn-mower is initially listed at . Its price is discounted off the full price. An employee uses their discount at the register and is charged . What is the employee discount?

Explanation

The relationship between the list price, , price rung up at the register, , the listed discount and the unknown employee discount, is

Substituting values

Solving for ,

3

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:

_change

4

Carolyn won a $450 gift card, and she wants to spend it at the store where she works. Normally, she gets a 10% employee discount, but in one week, her store will be having an "Employee Appreciation Day" during which a 25% employee discount will apply. If, as an employee, she does not have to pay sales tax, how much more worth of merchandise (in terms of price before discount) will she be able to purchase by holding out to that day (nearest cent, if applicable)?

Explanation

Let be the price before discount of the merchandise Carolyn can purchase now using her 10% discount. Then Carolyn will pay 90% of that price, or . Set up and solve the equation:

So Carolyn can use that gift card to purchase $500 worth of merchandise now.

Now let be the price before discount of the merchandise Carolyn can purchase during Employee Appreciation Day using a 25% discount. Then Carolyn will pay 75% of that price, or . Set up and solve the equation:

So Carolyn can use that gift card to purchase $600 worth of merchandise on Employee Appreciation Day.

Carolyn can save $100 by holding out.

5

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?

$31.50

$32.00

$37.50

$38.00

$35.00

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

6

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?

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.

7

A certain shirt in a department store costs . If a discount of off the original price is applied, what is the new selling price for this shirt?

Explanation

The new price is less than the original price of . Therefore, the new price is:

8

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 .

9

A restaurant owner allows employees to purchase meals for 28% off list price. An employee purchases a meal with a list price of $16.50. What does she pay for the meal?

Explanation

If she gets a 28% discount, she pays 72% of the list price:

10

A refrigorator is on sale for 20% off the original price. A store-wide sale results in an additional reduction of 25%. What is the total discount based on the original price?

40%

45%

60%

55%

Explanation

Let equal the original price.

First discount: (sale price).

Second discount: (final sale price)

Therefore, the final price is 60% of the original price. To calculate the discount:

or 40%

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