GMAT Math : DSQ: Calculating discounts

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Example Question #91 : Data Sufficiency Questions

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

In terms of $\displaystyle P$, $\displaystyle D$ and $\displaystyle E$, with discounts $\displaystyle D$ and $\displaystyle E$ expressed in percent, what is the formula for the amount, $\displaystyle Q$, charged at the register.

Possible Answers:

$Q= P\cdot D\cdot E$ $\displaystyle Q= P\cdot D\cdot E$

$Q=100\cdot P\cdot (1-D)\cdot (1-E)$ $\displaystyle Q=100\cdot P\cdot (1-D)\cdot (1-E)$

$Q= P\cdot (D+E)/100$ $\displaystyle Q= P\cdot (D+E)/100$

$Q=P\cdot (D/100)\cdot (E/100)$ $\displaystyle Q=P\cdot (D/100)\cdot (E/100)$

$Q=P\cdot (1-D/100)\cdot (1-E/100)$ $\displaystyle Q=P\cdot (1-D/100)\cdot (1-E/100)$

Correct answer:

$Q=P\cdot (1-D/100)\cdot (1-E/100)$ $\displaystyle Q=P\cdot (1-D/100)\cdot (1-E/100)$

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:

$Q=P\cdot (1-D/100) \cdot (1-E/100)$ $\displaystyle Q=P\cdot (1-D/100) \cdot (1-E/100)$

The factors of 100 $\displaystyle 100$ represent the conversion from $\%$ $\displaystyle \%$ to decimal values.

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Example Question #2211 : Gmat Quantitative Reasoning

A lawn-mower is initially listed at $\displaystyle P$. Its price is discounted $D\%$ $\displaystyle D\%$ off the full price. An employee uses their discount, $E\%$ $\displaystyle E\%$, at the register and is charged $\displaystyle Q$.

In terms of $\displaystyle P$, $\displaystyle Q$ in dollars and $\displaystyle D$ in percent, what is the formula for the employee discount, $\displaystyle E$ in percent?

Possible Answers:

$E=\frac{P}{Q} (1-D/100)$ $\displaystyle E=\frac{P}{Q} (1-D/100)$

$E=100\cdot \left(1-\frac{P}{Q\cdot (1-D/100)}\right)$ $\displaystyle E=100\cdot \left(1-\frac{P}{Q\cdot (1-D/100)}\right)$

$E=100\cdot \frac{P}{Q}\cdot (1-D/100)$ $\displaystyle E=100\cdot \frac{P}{Q}\cdot (1-D/100)$

$E= 100\cdot \left(1-\frac{Q}{P\cdot (1-D/100)} \right)$ $\displaystyle E= 100\cdot \left(1-\frac{Q}{P\cdot (1-D/100)} \right)$

$E=\frac{Q}{P}\cdot (1-D/100)$ $\displaystyle E=\frac{Q}{P}\cdot (1-D/100)$

Correct answer:

$E= 100\cdot \left(1-\frac{Q}{P\cdot (1-D/100)} \right)$ $\displaystyle E= 100\cdot \left(1-\frac{Q}{P\cdot (1-D/100)} \right)$

Explanation:

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

$Q=P\cdot (1-D/100)\cdot (1-E/100)$ $\displaystyle Q=P\cdot (1-D/100)\cdot (1-E/100)$

The factor of 100 $\displaystyle 100$ converts $\displaystyle %$ to decimal values.

Rearranging algebraically and solving for $\displaystyle E$, we obtain

$E= 100\cdot \left(1-\frac{Q}{P\cdot (1-D/100)} \right)$ $\displaystyle E= 100\cdot \left(1-\frac{Q}{P\cdot (1-D/100)} \right)$

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Example Question #2212 : Gmat Quantitative Reasoning

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

In terms of $\displaystyle P$,$\displaystyle Q$ and dollars and $\displaystyle E$ in percent, what is the formula for the original discount, $\displaystyle D$ in percent?

Possible Answers:

$D= 100\cdot \left(1-\frac{Q}{P\cdot E/100} \right)$ $\displaystyle D= 100\cdot \left(1-\frac{Q}{P\cdot E/100} \right)$

$D= \left(1+\frac{Q}{P\cdot (1-E/100)} \right)$ $\displaystyle D= \left(1+\frac{Q}{P\cdot (1-E/100)} \right)$

$D= 100\cdot \left(1-\frac{Q}{P\cdot (1-E/100)} \right)$ $\displaystyle D= 100\cdot \left(1-\frac{Q}{P\cdot (1-E/100)} \right)$

$D= \frac{100\cdot Q}{P\cdot (1-E/100)}$ $\displaystyle D= \frac{100\cdot Q}{P\cdot (1-E/100)}$

$D= 100\cdot \left(1+\frac{Q}{P\cdot (1+E/100)} \right)$ $\displaystyle D= 100\cdot \left(1+\frac{Q}{P\cdot (1+E/100)} \right)$

Correct answer:

$D= 100\cdot \left(1-\frac{Q}{P\cdot (1-E/100)} \right)$ $\displaystyle D= 100\cdot \left(1-\frac{Q}{P\cdot (1-E/100)} \right)$

Explanation:

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

$Q=P\cdot (1-D/100)\cdot (1-E/100)$ $\displaystyle Q=P\cdot (1-D/100)\cdot (1-E/100)$

The 100 $\displaystyle 100$ represents the conversion from percent to decimal.

Rearranging to solve for $\displaystyle D$ results in

$D= 100\cdot \left(1-\frac{Q}{P\cdot (1-E/100)} \right)$ $\displaystyle D= 100\cdot \left(1-\frac{Q}{P\cdot (1-E/100)} \right)$

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Example Question #2213 : Gmat Quantitative Reasoning

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

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

Possible Answers:

$S=P\cdot (D+E)$ $\displaystyle S=P\cdot (D+E)$

$S=P\cdot \left(\frac{D}{100}+\frac{E}{100}\right)$ $\displaystyle S=P\cdot \left(\frac{D}{100}+\frac{E}{100}\right)$

$S=P\cdot \left(1-\frac{D}{100}\right)\cdot \left(1-\frac{E}{100}\right)$ $\displaystyle S=P\cdot \left(1-\frac{D}{100}\right)\cdot \left(1-\frac{E}{100}\right)$

$S=P\cdot \left(1-\frac{D}{100}-\frac{E}{100}\right)$ $\displaystyle S=P\cdot \left(1-\frac{D}{100}-\frac{E}{100}\right)$

$S=P\left(1-\left(1-\frac{D}{100}\right)\cdot \left(1-\frac{E}{100}\right)\right)$ $\displaystyle S=P\left(1-\left(1-\frac{D}{100}\right)\cdot \left(1-\frac{E}{100}\right)\right)$

Correct answer:

$S=P\left(1-\left(1-\frac{D}{100}\right)\cdot \left(1-\frac{E}{100}\right)\right)$ $\displaystyle S=P\left(1-\left(1-\frac{D}{100}\right)\cdot \left(1-\frac{E}{100}\right)\right)$

Explanation:

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

$Q=P\left(1-\frac{D}{100}\right)\cdot \left(1-\frac{E}{100}\right)$ $\displaystyle Q=P\left(1-\frac{D}{100}\right)\cdot \left(1-\frac{E}{100}\right)$

The 100 represents the conversion from % to decimal.

The savings, $\displaystyle S$, is the difference between the price charged and the list price. So,

$S=P\left(1-\left(1-\frac{D}{100}\right)\cdot \left(1-\frac{E}{100}\right)\right)$ $\displaystyle S=P\left(1-\left(1-\frac{D}{100}\right)\cdot \left(1-\frac{E}{100}\right)\right)$

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Example Question #101 : Word Problems

A lawn-mower is initially listed as $\displaystyle P$ in dollars $(\$)$ $\displaystyle (\$)$ but then discounted $D\%$ $\displaystyle D\%$. A customer wants to know how much she will save.

In terms of $\displaystyle P$ in dollars, and the discount $\displaystyle D$ in percent, what is the formula for savings, $\displaystyle S$ in dollars?

Possible Answers:

$S= P\cdot (1-D)$ $\displaystyle S= P\cdot (1-D)$

$S= 100\cdot P\cdot (1-D/100)$ $\displaystyle S= 100\cdot P\cdot (1-D/100)$

$S=P\cdot D/100$ $\displaystyle S=P\cdot D/100$

$S= P\cdot (1-D/100)$ $\displaystyle S= P\cdot (1-D/100)$

$S= P\cdot D$ $\displaystyle S= P\cdot D$

Correct answer:

$S=P\cdot D/100$ $\displaystyle S=P\cdot D/100$

Explanation:

When a single discount applies, the savings in dollars is the product of the discount, $\displaystyle D$ in $\%$ $\displaystyle \%$ and the list price, $\displaystyle P$ in dolalrs:

$S=P\cdot D/100$ $\displaystyle S=P\cdot D/100$

The factor of 100 $\displaystyle 100$ represents the conversion from $\%$ $\displaystyle \%$ to decimal.

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Example Question #11 : Dsq: Calculating Discounts

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:

Statement (1) ALONE is sufficient, but Statement (2) ALONE is not sufficient.

Both statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

Each Statement ALONE is sufficient.

Statements (1) and (2) TOGETHER are not sufficient.

Statement (2) ALONE is sufficient, but Statement (1) ALONE is 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

x=1.2y $\displaystyle x=1.2y$

Statement (2) alone is not sufficient.

Combining both statements:

$\displaystyle y=x-4000$

$\displaystyle x=1.2(x-4000)$

We can calculate the original price as:

$\displaystyle x=1.2x-4800$

$\displaystyle -0.2x=-4800$

x=24000 $\displaystyle x=24000$

So we can find the new price:

$\displaystyle y=24000-4000=20000$

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GMAT Math : DSQ: Calculating discounts

Study concepts, example questions & explanations for GMAT Math

All GMAT Math Resources

Example Questions

Example Question #91 : Data Sufficiency Questions

Example Question #2211 : Gmat Quantitative Reasoning

Example Question #2212 : Gmat Quantitative Reasoning

Example Question #2213 : Gmat Quantitative Reasoning

Example Question #101 : Word Problems

Example Question #11 : Dsq: Calculating Discounts

All GMAT Math Resources

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