GMAT Math : Calculating discounts

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Example Questions

Example Question #31 : Calculating Discounts

A lawn-mower is initially listed at $\$600$ . Its price is discounted $10\%$ off the full price. An employee uses their discount at the register and is charged $\$400$ . What is the employee discount?

Possible Answers:

$25.9\%$

$10.0\%$

$12.2\%$

$40.0\%$

$15\%$

Correct answer:

$25.9\%$

Explanation:

The relationship between the list price, $L=\$600$ , price rung up at the register, $S=\$400$ , the listed discount $D=10\%$ and the unknown employee discount, is

$(1-E/100) =\frac{S}{L(1-D/100)}$

Substituting values

$(1-E/100) =\frac{400}{600\cdot(1-10/100)}$

Solving for , $E=25.9\%$

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Example Question #32 : Calculating Discounts

A lawn-mower is initially listed at $\$400$ . Its price is discounted $40\%$ off the full price. An employee uses their $10\%$ discount at the register. How much did the employee save relative to the initial list price?

Possible Answers:

$\$108.00$

$\$216.00$

$\$92.00$

$\$54.00$

$\$184.00$

Correct answer:

$\$184.00$

Explanation:

If the initial price is $L=\$400$ and two discounts $D=40\%$ and $E=10\%$ are applied, the final sale price can be computed using

$L\cdot (1-D/100)\cdot (1-E/100)) = S$

Inserting values this is:

$\$400\cdot(1-40/100)\cdot(1-10/100))\% =\$216=S$

The savings off list price is

$L-S=\$400- \$216=\$184$ .

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Example Question #101 : Problem Solving Questions

A store is offering a discount on clothing purchases made today. It is giving a 10% discount on purchases that total $50.00 to $99.99, a 20% discount on purchases totalling $100.00 to $199.99, and a 30% discount on purchases totaling $200.00 or more. The discount applies only to clothing items; no other items are discounted today.

Paris decides to purchase the following: Two bottles of perfume, one for $32 and one for $42; one handbag for $128; and one dress for $89. Disregarding tax, how much will she pay for these items?

Possible Answers:

$\$261.90$

$\$ 282.10$

$\$264.30$

$\$203.70$

$\$291.00$

Correct answer:

$\$ 282.10$

Explanation:

The only item of clothing among Paris's items is the dress. It costs $89, so Paris will get a 10% discount - that is, she will pay 90% of the price, or

$\$89 \cdot 0.90 = \$80.10$

She will pay full price for the other items, so she will pay a total of

$\$80.10 + \$32.00 + \$42.00 + \$128.00 = \$282.10$ .

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Example Question #102 : Word Problems

A hat is discounted percent; the sales tax on the hat is percent. If is the amount of money paid at the register, what was the price of the hat before discount and tax?

Possible Answers:

$Y = X \cdot \frac{100}{100-D}\cdot \frac{100}{100+T}$

$Y = X \cdot \left ( 100-D \right ) \cdot \left ( 100+T \right )$

$Y = X \cdot \frac{1}{1-D}\cdot \frac{1}{1+T}$

$Y = X \cdot \left ( 100+D \right ) \cdot \left ( 100-T \right )$

$Y = X \cdot \frac{100+D}{100}\cdot \frac{100-T}{100}$

Correct answer:

$Y = X \cdot \frac{100}{100-D}\cdot \frac{100}{100+T}$

Explanation:

Let be the price of the hat, before discount and tax.

Taking percent off the price of the hat is equivalent to charging 100-D percent of the price of the hat, or multiplying the price of the hat by $\frac{100-D}{100}$ .

Analogously, adding percent to the amount paid as tax is the same as multiplying the amount paid by 100+T percent, or $\frac{100+T}{100}$ .

Therefore, the amount paid is

$X = Y \cdot \frac{100-D}{100}\cdot \frac{100+T}{100}$

To find in terms of the other variables:

$Y \cdot \frac{100-D}{100}\cdot \frac{100+T}{100} = X$

$Y \cdot \frac{100-D}{100}\cdot \frac{100+T}{100} \cdot \frac{100}{100-D}\cdot \frac{100}{100+T}= X \cdot \frac{100}{100-D}\cdot \frac{100}{100+T}$

$Y = X \cdot \frac{100}{100-D}\cdot \frac{100}{100+T}$

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Example Question #101 : Gmat Quantitative Reasoning

A bag is normally $\$12.82$ but is on sale by $20\%$ . What is the purse's price to the nearest penny before tax?

Possible Answers:

$\$15.38$

$\$11.54$

$\$10.26$

$\$12.82$

Correct answer:

$\$10.26$

Explanation:

To calculate a $20\%$ discount, simply multiply the total by .2 and then subtract it from the original price.

$\$12.82\cdot.2=\$2.56$

$\$12.82-\$2.56=\$10.26$

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Example Question #101 : Problem Solving Questions

A store is offering a discount on clothing purchases made today. It is giving a $10\%$ discount on purchases that total $\$50.00$ to $\$99.99$ , a $20\%$ discount on purchases totalling $\$100.00$ to $\$199.99$ , and a $30\%$ discount on purchases totaling $\$200.00$ or more. The discount applies only to clothing items; no other items are discounted today.

Bryan decides to purchase the following: Two pairs of jeans that cost $\$45$ each, two shirts that cost $\$32$ each, and a bottle of cologne that costs $\$18$ . Disregarding tax, how much will Bryan pay for his items?

Possible Answers:

$\$125.80$

$\$141.20$

$\$ 137.60$

$\$156.60$

$\$ 120.40$

Correct answer:

$\$141.20$

Explanation:

The discount will apply to the jeans and the shirts, which, together, cost

$\$45 + \$45 + \$32 + \$32 = \$154$

Clothing purchases between $\$100$ and $\$199.99$ are discounted 20%, so Bryan will pay $80\%$ of the price of the items, or

$\$154 \cdot 0.80 = \$123.20$

Add to this the $18 cologne, which is not discounted:

$\$123.20 + \$18.00 = \$141.80$ .

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Example Question #32 : Discount

A store is offering a discount on all purchases made today, except for clothing items. It is giving a 10% discount on purchases that total $50.00 to $99.99, a 20% discount on purchases totaling $100.00 to $199.99, and a 30% discount on purchases totaling $200.00 or more.

Harvey purchases three shirts that cost $49 each, a bottle of cologne that costs $19, and a watch that costs $69. Disregarding tax, what will Harvey pay for the items?

Possible Answers:

$\$226.20$

$\$235.00$

$\$164.50$

$\$205.60$

$\$188.00$

Correct answer:

$\$226.20$

Explanation:

Harvey will receive a discount on the watch and the cologne; their prices total, before discount,

$\$19 + \$69 = \$ 88$ .

Since this purchase totals under $100, he will receive 10% off - that is, he will pay 90% of the original price, or

$\$ 88 \cdot 0.90 = \$ 79.20$ .

Add to this the price of the shirts, for which he will pay full price:

$\$ 79.20 + \$49.00 + \$49. 00+ \$49. 00 = \$226.20$

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GMAT Math : Calculating discounts

Study concepts, example questions & explanations for GMAT Math

All GMAT Math Resources

Example Questions

Example Question #31 : Calculating Discounts

Example Question #32 : Calculating Discounts

Example Question #101 : Problem Solving Questions

Example Question #102 : Word Problems

Example Question #101 : Gmat Quantitative Reasoning

Example Question #101 : Problem Solving Questions

Example Question #32 : Discount

All GMAT Math Resources

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