### All GMAT Math Resources

## Example Questions

### Example Question #81 : Gmat Quantitative Reasoning

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

**Possible Answers:**

**Correct answer:**

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 #12 : Discount

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

What was the original price of the stereo system?

**Possible Answers:**

**Correct answer:**

A 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 #81 : Gmat Quantitative Reasoning

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

**Possible Answers:**

**Correct answer:**

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 : Gmat Quantitative Reasoning

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 ?

(There is no interest on the monthly premiums. Round your answer to the nearest tenth.)

**Possible Answers:**

**Correct answer:**

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 #11 : Discount

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 ?

**Possible Answers:**

**Correct answer:**

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 #81 : Problem Solving Questions

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.)

**Possible Answers:**

**Correct answer:**

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 #11 : Discount

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.)

**Possible Answers:**

**Correct answer:**

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 #81 : Gmat Quantitative Reasoning

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?

**Possible Answers:**

**Correct answer:**

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

### Example Question #81 : 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?

**Possible Answers:**

**Correct answer:**

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 #21 : Discount

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?

**Possible Answers:**

**Correct answer:**

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:

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