# GMAT Math : DSQ: Calculating discounts

## Example Questions

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### Example Question #11 : Dsq: Calculating Discounts

A lawn-mower is initially listed at a full price of . Its the ticket lists a discount of  off the full price.  The item is placed in a 'extra discount' location where all prices are listed as being discounted  off the already discounted ticket price.

In terms of and , with discounts and  expressed in percent, what is the formula for the amount, , charged at the register.

Explanation:

The relationship between the original list price  and the price charged after two discounts is obtained by applying the formula for a discount serially:

The factors of  represent the conversion from  to decimal values.

### Example Question #12 : Dsq: Calculating Discounts

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 .

In terms of in dollars and  in percent, what is the formula for the employee discount,  in percent?

Explanation:

The relationship between the price charged at the register after two discounts is computed by applying the rule for discounts serially.

The factor of  converts  to decimal values.

Rearranging algebraically and solving for , we obtain

### Example Question #11 : Discount

A sewing machine is initially listed at . Its price is discounted  off the full price.  It fails to sell and is placed in a location where all items are discounted  off the already discounted ticket price. A customer carries it to the register and is charged .

In terms of ,  and dollars and  in percent, what is the formula for the original discount,  in percent?

Explanation:

The relationship between list price , the two serial discounts,  and E and the price charged is found by applying the formula for an individual discount serially:

The  represents the conversion from percent to decimal.

Rearranging to solve for  results in

### Example Question #14 : Dsq: Calculating Discounts

A lawn-mower is initially listed at . Its the ticket lists a discount of  off the full price.  The item is placed in a 'extra discount' location where all prices are listed as being discounted  off the listed ticket price.

The customer wants to know how much she saved, , in dollars. In terms of and , with discounts  and  expressed in percent, what is the formula for dollar savings off the initial list price, ?

Explanation:

The price charged at the register,  after two discounts is computed using the rule for a single discount applied serially.

The 100 represents the conversion from % to decimal.

The savings, , is the difference between the price charged and the list price. So,

### Example Question #101 : Data Sufficiency Questions

A lawn-mower is initially listed as  in dollars  but then discounted .  A customer wants to know how much she will save.

In terms of  in dollars, and the discount  in percent, what is the formula for savings,  in dollars?

Explanation:

When a single discount applies, the savings in dollars is the product of the discount,  in  and the list price,  in dolalrs:

The factor of  represents the conversion from  to decimal.

### Example Question #102 : Data Sufficiency Questions

What is the new price on a car after a certain promotional offer is applied?

(1) The promotional offer is equivalent to a $4000 cash back card. (2) The original price of the car is 1.2 times the new price after the promotional offer. Possible Answers: Both statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient. Each Statement ALONE is sufficient. Statement (1) ALONE is sufficient, but Statement (2) ALONE is not sufficient. Statement (2) ALONE is sufficient, but Statement (1) ALONE is not sufficient. Statements (1) and (2) TOGETHER are not sufficient. Correct answer: Both statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient. Explanation: (1) The promotional offer is equivalent to a$4000 cash back card.

Statement (1) alone is not sufficient because we do not know the original price of the car.

(2) The original price of the car is 1.2 times the new price after the promotional offer.

Using the information statement (2), we can write:

Let x be the original price of the car and y the price after the promotional offer

Statement (2) alone is not sufficient.

Combining both statements:

We can calculate the original price as:

So we can find the new price:

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