Calculating discounts - GMAT Quantitative Reasoning
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Vanessa purchased an mp3 player, originally priced at $290, but discounted by $27. Approximately what percent discount did Vanessa receive on the mp3 player?
Vanessa purchased an mp3 player, originally priced at $290, but discounted by $27. Approximately what percent discount did Vanessa receive on the mp3 player?
27 is a little less than 29, which is 10% of $290. Therefore, 9% is the closest approximation.
27 is a little less than 29, which is 10% of $290. Therefore, 9% is the closest approximation.
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Wally has a $500 gift card that he wants to spend at the store where he works. He gets a 25% employee discount, and the sales tax rate is 6.45%. How much can Wally spend before the discount and tax using only his gift card? (Round to the nearest cent.)
Wally has a $500 gift card that he wants to spend at the store where he works. He gets a 25% employee discount, and the sales tax rate is 6.45%. How much can Wally spend before the discount and tax using only his gift card? (Round to the nearest cent.)
Let 
be the price of the merchandise before discount and tax are figured in.
A 25% discount means that the price Wally pays is 
of the retail price. This can be written as 
.
A 6.45% sales tax means that 
of that discounted price is being paid.
We can combine the discount and sales rate as 
.
As the maximum purchase price after discount and tax is $500, we set up the following equation:
Wally can purchase up to $626.27 in merchandise.
Let
A 25% discount means that the price Wally pays is
A 6.45% sales tax means that
We can combine the discount and sales rate as
As the maximum purchase price after discount and tax is $500, we set up the following equation:
Wally can purchase up to $626.27 in merchandise.
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A refrigorator is on sale for 20% off the original price. A store-wide sale results in an additional reduction of 25%. What is the total discount based on the original price?
A refrigorator is on sale for 20% off the original price. A store-wide sale results in an additional reduction of 25%. What is the total discount based on the original price?
Let 
equal the original price.
First discount: 
(sale price).
Second discount: 
(final sale price)
Therefore, the final price is 60% of the original price. To calculate the discount:
or 40%
Let
First discount:
Second discount:
Therefore, the final price is 60% of the original price. To calculate the discount:
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Carolyn won a $450 gift card, and she wants to spend it at the store where she works. Normally, she gets a 10% employee discount, but in one week, her store will be having an "Employee Appreciation Day" during which a 25% employee discount will apply. If, as an employee, she does not have to pay sales tax, how much more worth of merchandise (in terms of price before discount) will she be able to purchase by holding out to that day (nearest cent, if applicable)?
Carolyn won a $450 gift card, and she wants to spend it at the store where she works. Normally, she gets a 10% employee discount, but in one week, her store will be having an "Employee Appreciation Day" during which a 25% employee discount will apply. If, as an employee, she does not have to pay sales tax, how much more worth of merchandise (in terms of price before discount) will she be able to purchase by holding out to that day (nearest cent, if applicable)?
Let 
be the price before discount of the merchandise Carolyn can purchase now using her 10% discount. Then Carolyn will pay 90% of that price, or 
. Set up and solve the equation:
So Carolyn can use that gift card to purchase $500 worth of merchandise now.
Now let 
be the price before discount of the merchandise Carolyn can purchase during Employee Appreciation Day using a 25% discount. Then Carolyn will pay 75% of that price, or 
. Set up and solve the equation:
So Carolyn can use that gift card to purchase $600 worth of merchandise on Employee Appreciation Day.
Carolyn can save $100 by holding out.
Let
So Carolyn can use that gift card to purchase $500 worth of merchandise now.
Now let
So Carolyn can use that gift card to purchase $600 worth of merchandise on Employee Appreciation Day.
Carolyn can save $100 by holding out.
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The following is a partial menu at Moonbucks Coffee.
Today, Moonbucks is running a special - buy one drink and get one of equal or lesser value free.
Charles is buying drinks for his family. He orders three lattes, two cappucinos, two espressos, and a Turkish coffee. How much will he pay for the drinks, disregarding tax?
The following is a partial menu at Moonbucks Coffee.
Today, Moonbucks is running a special - buy one drink and get one of equal or lesser value free.
Charles is buying drinks for his family. He orders three lattes, two cappucinos, two espressos, and a Turkish coffee. How much will he pay for the drinks, disregarding tax?
List the prices of the drinks in descending order:
With the most expensive drink, Charlie will get the second-most expensive drink free; with the third-most expensive drink, he will get the fourth-most expensive drink free; and so forth.
Charlie will only pay for the first, third, fifth, and seventh most expensive drinks. Add their prices.
List the prices of the drinks in descending order:
With the most expensive drink, Charlie will get the second-most expensive drink free; with the third-most expensive drink, he will get the fourth-most expensive drink free; and so forth.
Charlie will only pay for the first, third, fifth, and seventh most expensive drinks. Add their prices.
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A restaurant owner allows employees to purchase meals for 28% off list price. An employee purchases a meal with a list price of $16.50. What does she pay for the meal?
A restaurant owner allows employees to purchase meals for 28% off list price. An employee purchases a meal with a list price of $16.50. What does she pay for the meal?
If she gets a 28% discount, she pays 72% of the list price:
If she gets a 28% discount, she pays 72% of the list price:
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A stereo system costs 
after applying a 
discount and adding the 
sales tax.
What was the original price of the stereo system?
A stereo system costs
What was the original price of the stereo system?
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 
:
A
We can now write an equation and solve for
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The above is the menu at Monorail Sandwich Shop.
Kyle works at Monorail and is therefore allowed to buy up to four sandwiches and four sodas a day with his 25% employee discount. If he buys more than the allowed number with any one purchase, he can take 25% off the four highest-priced sandwiches and the four highest-priced sodas.
Kyle is buying three turkey sandwiches, three ham sandwiches, and six large sodas. If this is Kyle's first purchase of the day, how much will he pay, disregarding tax?
The above is the menu at Monorail Sandwich Shop.
Kyle works at Monorail and is therefore allowed to buy up to four sandwiches and four sodas a day with his 25% employee discount. If he buys more than the allowed number with any one purchase, he can take 25% off the four highest-priced sandwiches and the four highest-priced sodas.
Kyle is buying three turkey sandwiches, three ham sandwiches, and six large sodas. If this is Kyle's first purchase of the day, how much will he pay, disregarding tax?
Kyle is buying six sandwiches and six large sodas, so his discount will apply to four of the sodas and the four highest-priced sandwiches - namely, the three turkey sandwiches and one ham sandwich.
The price of those eight items, before discount, is
.
A 25% discount means that Kyle will pay 75% of this, or
.
The items for which Kyle will pay full price - two ham sandwiches and two large sodas - cost
.
The total cost to Kyle:
Kyle is buying six sandwiches and six large sodas, so his discount will apply to four of the sodas and the four highest-priced sandwiches - namely, the three turkey sandwiches and one ham sandwich.
The price of those eight items, before discount, is
A 25% discount means that Kyle will pay 75% of this, or
The items for which Kyle will pay full price - two ham sandwiches and two large sodas - cost
The total cost to Kyle:
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The following is a partial menu at Moonbucks Coffee:
Jim is allowed to use his 20% employee discount on up to four drinks per day. Assuming he has not used the discount yet today, Jim wants to purchase three Americanos, a Turkish coffee, and a latte. After the discount, what will the drinks cost him? (Disregard tax).
The following is a partial menu at Moonbucks Coffee:
Jim is allowed to use his 20% employee discount on up to four drinks per day. Assuming he has not used the discount yet today, Jim wants to purchase three Americanos, a Turkish coffee, and a latte. After the discount, what will the drinks cost him? (Disregard tax).
The 20% discount will apply to the four most expensive drinks, presumably, so he will pay 20% less - or 80% - for the Turkish coffee, the latte, and two of the Americanos, and full price for the third Americano.
The price he will pay is as follows:
He will pay $11.26 for the drinks.
The 20% discount will apply to the four most expensive drinks, presumably, so he will pay 20% less - or 80% - for the Turkish coffee, the latte, and two of the Americanos, and full price for the third Americano.
The price he will pay is as follows:
He will pay $11.26 for the drinks.
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A clothing store offers a dress initally at $100. Then one week later, the store offers the dress at 15% off. The dress still doesn't sell, so after another week, the store reduces its new price by 20%. How much does the dress cost now?
A clothing store offers a dress initally at $100. Then one week later, the store offers the dress at 15% off. The dress still doesn't sell, so after another week, the store reduces its new price by 20%. How much does the dress cost now?
For the first discount, we have 
. So the dress is worth $85
After the second discount, we have 
So the final dress price is $68
For the first discount, we have
After the second discount, we have
So the final dress price is $68
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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 
. What is the employee discount?
A lawn-mower is initially listed at
The relationship between the list price, 
, price rung up at the register, 
, the listed discount 
and the unknown employee discount, 
is
Substituting values
Solving for 
, 
The relationship between the list price,
Substituting values
Solving for
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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?
A hat is discounted
Let 
be the price of the hat, before discount and tax.
Taking 
percent off the price of the hat is equivalent to charging 
percent of the price of the hat, or multiplying the price of the hat by 
.
Analogously, adding 
percent to the amount paid as tax is the same as multiplying the amount paid by 
percent, or 
.
Therefore, the amount paid is
To find 
in terms of the other variables:
Let
Taking
Analogously, adding
Therefore, the amount paid is
To find
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A lawn-mower is initially listed at 
. Its price is discounted 
off the full price. An employee uses their 
discount at the register. How much did the employee save relative to the initial list price?
A lawn-mower is initially listed at
If the initial price is 
and two discounts 
and 
are applied, the final sale price can be computed using
Inserting values this is:
The savings off list price is
.
If the initial price is
Inserting values this is:
The savings off list price is
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Julie has a choice between purchasing a hat at Stacy's or purchasing an identical hat at Gumble's. The hat at Stacy's costs $350. The hat at Gumble's normally costs $425, but it is on sale at 20% off. The sales tax is 7.5% for both stores. At which store can Julie get the hat cheaper, and how much will she save?
Julie has a choice between purchasing a hat at Stacy's or purchasing an identical hat at Gumble's. The hat at Stacy's costs $350. The hat at Gumble's normally costs $425, but it is on sale at 20% off. The sales tax is 7.5% for both stores. At which store can Julie get the hat cheaper, and how much will she save?
If Julie purchases the hat at Stacy's, she will spend $350 plus 7.5% of this as tax - that is, she will spend 1.075 times $350:
.
If Julie purchases the hat at Gumble's, her price before tax will be 20% off of the price of $425 - this is 80% of, or 0.80 times, $425:
Adding 7.5% tax, Julie will spend 1.075 times $340:
.
By going to Gumble's, she saves
If Julie purchases the hat at Stacy's, she will spend $350 plus 7.5% of this as tax - that is, she will spend 1.075 times $350:
If Julie purchases the hat at Gumble's, her price before tax will be 20% off of the price of $425 - this is 80% of, or 0.80 times, $425:
Adding 7.5% tax, Julie will spend 1.075 times $340:
By going to Gumble's, she saves
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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 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?
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
buying at Costless.
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
buying at Costless.
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The price of a hat after a 15% discount is 
. In terms of 
, what was the price before the discount?
The price of a hat after a 15% discount is
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 
Call
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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.
The price of a dress after a 15% store discount and a 15% employee discount is
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 
Call
Similarly, the price after the employee discount will be
So
and, consequently,
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After a 20% employee discount and 5% sales tax, Catherine pays 
dollars for a dress. What is the regular price of the dress before tax or discounts, in terms of 
?
After a 20% employee discount and 5% sales tax, Catherine pays
Call the price before discount or tax. The amount of the discount is 20% of this, so the price after discount but before tax is 
of this, or 
of 
; this is 
.
Similarly, the amount paid will be this price plus 5% of this as tax, or 
of 
. 105% is 
, so the final amount paid is
Therefore,
and
Call
Similarly, the amount paid will be this price plus 5% of this as tax, or
Therefore,
and
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A style of chair that Brian wants to purchase can be found in five different stores in town. Brian wants to buy the chair this weekend, and, as luck would have it, four of the stores are running specials this weekend:
Carter Brothers Furniture is discounting the price of the chair, which normally sells for $600, by 30%.
Edison Furniture is discounting the price of the chair, which normally sells for $575, by 20%.
General Grant Furniture is discounting the price of the chair, which normally sells for $560, by 10%.
Irving Furniture is discounting the price of the chair, which normally sells for $720, by 40%.
King of Furniture is not running any specials; the chair will sell for its normal price of $540.
To get the chair for the lowest price, where should Brian go?
NOTE: Assume all sales tax and other charges are equal.
A style of chair that Brian wants to purchase can be found in five different stores in town. Brian wants to buy the chair this weekend, and, as luck would have it, four of the stores are running specials this weekend:
Carter Brothers Furniture is discounting the price of the chair, which normally sells for $600, by 30%.
Edison Furniture is discounting the price of the chair, which normally sells for $575, by 20%.
General Grant Furniture is discounting the price of the chair, which normally sells for $560, by 10%.
Irving Furniture is discounting the price of the chair, which normally sells for $720, by 40%.
King of Furniture is not running any specials; the chair will sell for its normal price of $540.
To get the chair for the lowest price, where should Brian go?
NOTE: Assume all sales tax and other charges are equal.
At Carter Brothers Furniture, the chair sells for 30% off the normal price of $600. This is 70% of $600, or
At Elm Street Furniture, the chair sells for 20% off the normal price of $575. This is 80% of $575, or
At General Grant Furniture, the chair sells for 10% off the normal price of $560. This is 90% of $560, or
At Irving Furniture, the chair sells for 40% off the normal price of $720. This is 60% of $720, or
At King of Furniture the chair sells for $540.
Carter Brothers Furniture is selling the chair for the lowest price, and it is where Brian should go.
At Carter Brothers Furniture, the chair sells for 30% off the normal price of $600. This is 70% of $600, or
At Elm Street Furniture, the chair sells for 20% off the normal price of $575. This is 80% of $575, or
At General Grant Furniture, the chair sells for 10% off the normal price of $560. This is 90% of $560, or
At Irving Furniture, the chair sells for 40% off the normal price of $720. This is 60% of $720, or
At King of Furniture the chair sells for $540.
Carter Brothers Furniture is selling the chair for the lowest price, and it is where Brian should go.
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After a 
discount, a shirt costs 
. What is the original price of the shirt? (Round your answer to the nearest cent.)
After a
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:
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
Another approach is to think as the new price as
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