# GMAT Math : Calculating discounts

## Example Questions

### Example Question #11 : Discount

Phillip wants to buy a new pair of shoes, but he can find the style and size he wants in only two stores. At Shoe Festival, where he works - and receives a 25% associate discount - the shoes are available for $220. At the rival Costless Shoe Store, they sell for$150. If he shops at Shoe Festival, he does not have to pay the sales tax of 8.5%; if he shops at Costless, he does.

At which store will he get the shoes cheaper, and how much will he save by going there?

Phillip will save $16.28 if he buys the shoes at Shoe Festival. Phillip will save$2.25 if he buys the shoes at Costless.

Phillip will save $16.28 if he buys the shoes at Costless. Phillip will save$15.00 if he buys the shoes at Costless.

Phillip will save $2.25 if he buys the shoes at Shoe Festival. Correct answer: Phillip will save$2.25 if he buys the shoes at Costless.

Explanation:

If Phillip buys the shoes at Shoe festival, their cost including the discount will be 25% off $220, or 75% of$220. This will be

If he buys the shoes at Costless, he will pay $150 plus 8.5% tax - that is, he will pay 1.085 times$150, or

Phillip will save

### Example Question #72 : Problem Solving Questions

The price of a dress after a 15% store discount and a 15% employee discount is . In terms of , give the price of the dress before the discounts.

Explanation:

Call  the price before the two discounts. The amount of the store discount is 15% of this; the final purchase price is , or , of the original price, so the price after the store discount, but before the employee discount, is .

Similarly, the price after the employee discount will be  of this, or

So

and, consequently,

or

### Example Question #11 : Discount

The price of a hat after a 15% discount is . In terms of , what was the price before the discount?

Explanation:

Call  the price before the 15% discount. The amount of the discount is 15% of this; the final purchase price is , or , of the original price, so

or

### Example Question #11 : Discount

A stereo system costs  after applying a discount and adding the sales tax.

What was the original price of the stereo system?

Explanation:

discount implies that the discounted price is  of the original price; a tax means that  of the price will have to be paid. Let  be the original price.

We can now write an equation and solve for :

### Example Question #83 : Word Problems

After a  discount, a shirt costs . What is the original price of the shirt? (Round your answer to the nearest cent.)

Explanation:

The formula to find the percentage change in the price is the following:

We plug the new price and the percentage of discount into the equation to determine the shirt's original price.

Let  be the original price:

Another approach is to think as the new price as  times the original price, since after the discount, the shirt costs only  of the original price. So:

### Example Question #81 : Problem Solving Questions

After applying a discount to his insurance policy, John is supposed to save a total of  on his car insurance payments for the next year. What is the percentage of the discount if his last monthly premium was ?

Explanation:

John is supposed to save a total of  for the next year. Therefore, the difference between the sum of all his monthly premiums from the previous year and the sum of all his monthly premiums from the next year is .

Using the following formula:

We can see that  is the difference between his new annual payments and his original annual payments before the discount. The value of the annual payments is twelve times the monthly premium:

This means that John saves  due to the discount.

Another way to calculate the percentage of discount is to first find John's new monthly premium.

Let  be John's monthly premium after applying the discount:

The percentage of the safe driver discount is then:

The safe driver discount is 15.6% off his previous monthly premium.

### Example Question #81 : Word Problems

A store owner is considering selling his new brand of t-shirts at a discounted price. The t-shirts cost  each to make and the store owner was initially thinking of selling them for  each. What percentage of discount should he offer if he is willing to reduce his gross margin per t-shirt by ?

Explanation:

Let  be the percentage of discount. If the store owner sells the t-shirts at the full price, his gross margin per t-shirt sold is:

The discounted price will be , and the cost of making a t-shirt remains the same.

We can write the following equation to find the percentage of discount if we reduce the gross margin per t-shirt by :

The store owner can offer a  discount if he is willing to reduce his gross margin by .

### Example Question #11 : Calculating Discounts

Jane sells bracelets that she gets from a supplier for  apiece. She sells each bracelet for . A new supplier offers to provide similar-quality bracelets at a discounted price. If Jane buys the same quantity from the new supplier, her gross profit will increase by . What percentage of discount is the new supplier offering? (Round to the nearest percentage point.)

Explanation:

We need to algebraically model the cost per bracelet from the old supplier vs. the cost per bracelet from the new supplier, who is offering a "discount" on the cost of the bracelet from the old supplier. We know that if Jane orders from the new supplier, her gross profit will increase by , so we can model the situation as a percent increase and solve for a the missing variable of the discount the new supplier is offering on the cost of each bracelet from the old supplier.

Jane sells each bracelet for , and we are solving for the discount the new supplier is offering on the cost of each bracelet, which from the old supplier was . We can consider this as a percentage subtracted from the cost of each bracelet from the old supplier, .

Jane's profit when buying from her current supplier is:

If Jane buys from the new supplier, her profit will be:

Distributing the  and then combining like terms:

We can then write the percentage increase as:

The new supplier's price is  less than the current supplier.

### Example Question #81 : Gmat Quantitative Reasoning

A local supermarket applies a  discount on all dairy products supposed to expire within the next five days. If you buy a gallon of milk that will expire three days from the purchase date at , what was the original price of that gallon of milk? (Round your answer to a cent.)

Explanation:

We will use the formula for percentage of change.

Let  be the original price of the gallon of milk. The new price is , and the percentage of discount is .

### Example Question #82 : Word Problems

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?