How to find the sale price - GRE Quantitative Reasoning
Card 1 of 120
A winter shirt is regularly priced at $50. At the end of the Christmas season, it is marked down by 40%. A month after this initial markdown, it is marked back up by 50%.
Quantity A
The initial cost of the shirt.
Quantity B
The final cost of the shirt, after it is marked up.
A winter shirt is regularly priced at $50. At the end of the Christmas season, it is marked down by 40%. A month after this initial markdown, it is marked back up by 50%.
Quantity A
The initial cost of the shirt.
Quantity B
The final cost of the shirt, after it is marked up.
Tap to reveal answer
There are two ways to consider the value of B. First, you can subtract 40% from the initial $50 dollars: $50 – 0.4 * $50 = $30. This gives you the value after the markdown. Then to mark up the price, add 50% of $30 to the $30: $30 + 0.5 * $30 = $45.
A shorter way to do this problem is to consider the first markdown as reducing the price to 60% of the original, then considering the markup as making it 150% of the new price. This can be done in one set of multiplications: $50 * 0.6 * 1.5 = $45. Either way, the answer is the same. A is the larger quantity.
There are two ways to consider the value of B. First, you can subtract 40% from the initial $50 dollars: $50 – 0.4 * $50 = $30. This gives you the value after the markdown. Then to mark up the price, add 50% of $30 to the $30: $30 + 0.5 * $30 = $45.
A shorter way to do this problem is to consider the first markdown as reducing the price to 60% of the original, then considering the markup as making it 150% of the new price. This can be done in one set of multiplications: $50 * 0.6 * 1.5 = $45. Either way, the answer is the same. A is the larger quantity.
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The price of a laptop is reduced by 
. During a markdown sale, the price is reduced by another 
. What is the total percentage discount?
The price of a laptop is reduced by
Tap to reveal answer
To solve this problem, imagine that the original price of the laptop is $100. After the first 20% discount, the price of the laptop becomes $80. With the additional 10% reduction, we discount from $80, not $100. 10% of 80 is 8 so we must deduct $8 from $80. This gives $72 as the final price of the laptop after both reductions. Since we started at $100, the total discount is 28%.
To solve this problem, imagine that the original price of the laptop is $100. After the first 20% discount, the price of the laptop becomes $80. With the additional 10% reduction, we discount from $80, not $100. 10% of 80 is 8 so we must deduct $8 from $80. This gives $72 as the final price of the laptop after both reductions. Since we started at $100, the total discount is 28%.
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A store puts a $200 dress on a 70% discount and then takes an additional 15% off the reduced price. How much of the original price was removed?
A store puts a $200 dress on a 70% discount and then takes an additional 15% off the reduced price. How much of the original price was removed?
Tap to reveal answer
If we multiply $200 by 0.7, we find the dress has been reduced by $140 on the first discount. Since the dress now costs $60, we multiply that by 0.15 and find the dress has been discounted by an additional $9. The final sale of the dress is $51, with $149 of the original price removed.
If we multiply $200 by 0.7, we find the dress has been reduced by $140 on the first discount. Since the dress now costs $60, we multiply that by 0.15 and find the dress has been discounted by an additional $9. The final sale of the dress is $51, with $149 of the original price removed.
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In a local store, pens that normally sell for 49 cents each are on sale at 3 for 99 cents. How much can be saved by purchasing 12 of these pens at the sale price?
In a local store, pens that normally sell for 49 cents each are on sale at 3 for 99 cents. How much can be saved by purchasing 12 of these pens at the sale price?
Tap to reveal answer
Normally, 3 pens cost 3 * .49 = $1.47. Thus, on each set of 3 pens, the sale price saves the customer $1.47 - 99 = 48 cents. Multiply this by 4 to get the savings for 12 pens, and you get .48 * 4 = $1.92.
Normally, 3 pens cost 3 * .49 = $1.47. Thus, on each set of 3 pens, the sale price saves the customer $1.47 - 99 = 48 cents. Multiply this by 4 to get the savings for 12 pens, and you get .48 * 4 = $1.92.
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A department store sells a set of hand weights for $X. If the store offers a 20% discount on the original price of the weights, and then an additional 10% employee discount, what will be the price of the weights if an employee purchases them?
A department store sells a set of hand weights for $X. If the store offers a 20% discount on the original price of the weights, and then an additional 10% employee discount, what will be the price of the weights if an employee purchases them?
Tap to reveal answer
This is a straightforward percentage problem. After the first discount, the price of the weights is $0.8X. This price is then further reduced by 10% for the employee discount. 90% of 0.8X = 0.9(0.8X) = 0.72X.
This is a straightforward percentage problem. After the first discount, the price of the weights is $0.8X. This price is then further reduced by 10% for the employee discount. 90% of 0.8X = 0.9(0.8X) = 0.72X.
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A shirt is originally $20 and marked down 30%. After this it is marked up by 40% then marked down again by 10%. What is its final price?
A shirt is originally $20 and marked down 30%. After this it is marked up by 40% then marked down again by 10%. What is its final price?
Tap to reveal answer
The easiest way to solve this is to note that a 30% markdown reduces the cost to 70% of the original cost. Likewise, a 40% markup is the same as making the price 140% of its current value. Using this, we can solve our problem in one string of multiplications:
New cost = Original * 0.7 * 1.4 * 0.9
New cost = 20 * 0.7 * 1.4 * 0.9 = 17.64
The easiest way to solve this is to note that a 30% markdown reduces the cost to 70% of the original cost. Likewise, a 40% markup is the same as making the price 140% of its current value. Using this, we can solve our problem in one string of multiplications:
New cost = Original * 0.7 * 1.4 * 0.9
New cost = 20 * 0.7 * 1.4 * 0.9 = 17.64
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A dress originally costs $50 but is on sale for 25% off. In addition, you have a 10% off coupon. How much will the dress cost after these discounts?
A dress originally costs $50 but is on sale for 25% off. In addition, you have a 10% off coupon. How much will the dress cost after these discounts?
Tap to reveal answer
To find 25% of $50 you multiply 50 and 0.25. This gives you 12.50. This means the dress is $12.50 cheaper, so it now costs 50 – 12.50 = $37.50. You have an additional 10% off, so you multiply 37.50 by 0.10 to get 3.75. 37.50 – 3.75 = $33.75. This is the cost of the dress. NOTE: You CANNOT add 25% and 10% and take 35% off of the $50 dress. You will get the wrong answer.
To find 25% of $50 you multiply 50 and 0.25. This gives you 12.50. This means the dress is $12.50 cheaper, so it now costs 50 – 12.50 = $37.50. You have an additional 10% off, so you multiply 37.50 by 0.10 to get 3.75. 37.50 – 3.75 = $33.75. This is the cost of the dress. NOTE: You CANNOT add 25% and 10% and take 35% off of the $50 dress. You will get the wrong answer.
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A retail chain wishes to make at least a 
profit on a new item. If it can only sell its items for integer values, what is the lowest price it can sell the item for if it costs the chain 
to purchase it?
A retail chain wishes to make at least a
Tap to reveal answer
Let's begin by finding the absolute amount necessary for a 27% profit. Following that, we will adjust for the needs of having a whole number price. If the sale price is S, we can set up the following equation:
(S – 23)/23 = 0.27
S – 23 = 6.21
S = 29.21
The product must, however, be sold for at least $30 because it has to be an integer value.
Let's begin by finding the absolute amount necessary for a 27% profit. Following that, we will adjust for the needs of having a whole number price. If the sale price is S, we can set up the following equation:
(S – 23)/23 = 0.27
S – 23 = 6.21
S = 29.21
The product must, however, be sold for at least $30 because it has to be an integer value.
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Product X costs $27 to manufacture at the rate of 50 per hour. Production can only be increased in groups of 10 units per hour. For each such increase, the production cost increases 30% of its previous amount. If the output is to be doubled, for how much must each unit be sold to make at least a 25% profit?
Product X costs $27 to manufacture at the rate of 50 per hour. Production can only be increased in groups of 10 units per hour. For each such increase, the production cost increases 30% of its previous amount. If the output is to be doubled, for how much must each unit be sold to make at least a 25% profit?
Tap to reveal answer
To calculate a 30% increase in cost, you can multiply the base cost by 1.3; therefore, if we are going to increase the rate five times, we will multiply by 1.3 five times, which is the same as 1.35. The cost of creating 100 units per hour is 27 * 1.35 = 100.25.
If we want to make a 25% profit, we can set up the equation:
Price = 1.25 * 100.25 or 125.3125. To make at least a 25%, this will be $125.32.
To calculate a 30% increase in cost, you can multiply the base cost by 1.3; therefore, if we are going to increase the rate five times, we will multiply by 1.3 five times, which is the same as 1.35. The cost of creating 100 units per hour is 27 * 1.35 = 100.25.
If we want to make a 25% profit, we can set up the equation:
Price = 1.25 * 100.25 or 125.3125. To make at least a 25%, this will be $125.32.
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To promote a new ice cream flavor, an ice cream parlor is selling their $1.29 cones at 70% of the original price. Approximately how much will be saved by buying 4 of their cones?
To promote a new ice cream flavor, an ice cream parlor is selling their $1.29 cones at 70% of the original price. Approximately how much will be saved by buying 4 of their cones?
Tap to reveal answer
First let's calculate what 70% of $1.29 is: .7(1.29) = .9
Next, calculate how much 4 cones would have cost at the original price vs. the sale price:
4(1.29) = 5.16
4(.9) = 3.60
5.16 – 3.60 = $1.56 saved
First let's calculate what 70% of $1.29 is: .7(1.29) = .9
Next, calculate how much 4 cones would have cost at the original price vs. the sale price:
4(1.29) = 5.16
4(.9) = 3.60
5.16 – 3.60 = $1.56 saved
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Betty buys a sweater for $36. The next week, Alice buys the same sweater on sale for 25% off. The week after that, Chelsea buys the same sweater that is now 15% off the sale price. How much did Chelsea spend on the sweater?
Betty buys a sweater for $36. The next week, Alice buys the same sweater on sale for 25% off. The week after that, Chelsea buys the same sweater that is now 15% off the sale price. How much did Chelsea spend on the sweater?
Tap to reveal answer
The sweater price starts at $36. Alice pays $36 – (.25 * $36) = $27. Chelsea then pays $27 – (.15 * $27) = $22.95, which is the correct answer.
When solving percentage questions such as this one, do NOT try to add up the discounts and find the final sale price all in one step. If you tried to do that here, the answer would have been $36 – (.25 + .15) * $36 = $21.60. This is an answer choice, but the wrong answer! Most GRE percentage questions will always give you this as one of your answer choices to try and trick you!
The sweater price starts at $36. Alice pays $36 – (.25 * $36) = $27. Chelsea then pays $27 – (.15 * $27) = $22.95, which is the correct answer.
When solving percentage questions such as this one, do NOT try to add up the discounts and find the final sale price all in one step. If you tried to do that here, the answer would have been $36 – (.25 + .15) * $36 = $21.60. This is an answer choice, but the wrong answer! Most GRE percentage questions will always give you this as one of your answer choices to try and trick you!
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How much does a sweater cost that is 18% more than a $50 dress?
How much does a sweater cost that is 18% more than a $50 dress?
Tap to reveal answer
18% of the dress is .18 * 50 = $9. Then the sweater costs $50 + $9 = $59.
18% of the dress is .18 * 50 = $9. Then the sweater costs $50 + $9 = $59.
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Jenny is at a store and would like to buy a shirt. The shirt is labelled 20% off, and the store is having a store-wide sale where everything is 15% off. What percent of the original price does Jenny have to pay?
Jenny is at a store and would like to buy a shirt. The shirt is labelled 20% off, and the store is having a store-wide sale where everything is 15% off. What percent of the original price does Jenny have to pay?
Tap to reveal answer
Based on the shirts label, Jenny should pay 80% of the full price. With the store's discount, she will pay 85% of this. Thus, she will pay .8times .85=.68 of the full price. This is equivalent to 68%.
Based on the shirts label, Jenny should pay 80% of the full price. With the store's discount, she will pay 85% of this. Thus, she will pay .8times .85=.68 of the full price. This is equivalent to 68%.
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A car dealer purchased a used truck, marked it up to make a 30% profit, then sold it at a 30% discount from the sticker price.
Quantity A: The amount that the dealer paid for the truck
Quantity B: The amount for which the dealer sold the truck
A car dealer purchased a used truck, marked it up to make a 30% profit, then sold it at a 30% discount from the sticker price.
Quantity A: The amount that the dealer paid for the truck
Quantity B: The amount for which the dealer sold the truck
Tap to reveal answer
Since no price is given, you can pick $100 as the starting point for the value of the truck. $100 marked up 30% is $130, and the 30% discount brings it to $91.
Since no price is given, you can pick $100 as the starting point for the value of the truck. $100 marked up 30% is $130, and the 30% discount brings it to $91.
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A car dealer sold two trucks for 
each, resulting in a 
profit on one truck and a 
loss on the other.
Quantity A: The dealer's net gain
Quantity B: The dealer's net loss
A car dealer sold two trucks for
Quantity A: The dealer's net gain
Quantity B: The dealer's net loss
Tap to reveal answer
For the profitable truck, the dealer bought it for 
, where 
. Therefore, 
.
For the unprofitable truck, the dealer bought it for 
, where 
. Therefore, 
.
Thus, the dealer's net profit is $8,000, and the dealer's net loss is $10,000.
His loss is greater than his profit, so Quantity B is larger.
For the profitable truck, the dealer bought it for
For the unprofitable truck, the dealer bought it for
Thus, the dealer's net profit is $8,000, and the dealer's net loss is $10,000.
His loss is greater than his profit, so Quantity B is larger.
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A winter shirt is regularly priced at $50. At the end of the Christmas season, it is marked down by 40%. A month after this initial markdown, it is marked back up by 50%.
Quantity A
The initial cost of the shirt.
Quantity B
The final cost of the shirt, after it is marked up.
A winter shirt is regularly priced at $50. At the end of the Christmas season, it is marked down by 40%. A month after this initial markdown, it is marked back up by 50%.
Quantity A
The initial cost of the shirt.
Quantity B
The final cost of the shirt, after it is marked up.
Tap to reveal answer
There are two ways to consider the value of B. First, you can subtract 40% from the initial $50 dollars: $50 – 0.4 * $50 = $30. This gives you the value after the markdown. Then to mark up the price, add 50% of $30 to the $30: $30 + 0.5 * $30 = $45.
A shorter way to do this problem is to consider the first markdown as reducing the price to 60% of the original, then considering the markup as making it 150% of the new price. This can be done in one set of multiplications: $50 * 0.6 * 1.5 = $45. Either way, the answer is the same. A is the larger quantity.
There are two ways to consider the value of B. First, you can subtract 40% from the initial $50 dollars: $50 – 0.4 * $50 = $30. This gives you the value after the markdown. Then to mark up the price, add 50% of $30 to the $30: $30 + 0.5 * $30 = $45.
A shorter way to do this problem is to consider the first markdown as reducing the price to 60% of the original, then considering the markup as making it 150% of the new price. This can be done in one set of multiplications: $50 * 0.6 * 1.5 = $45. Either way, the answer is the same. A is the larger quantity.
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The price of a laptop is reduced by . During a markdown sale, the price is reduced by another . What is the total percentage discount?
The price of a laptop is reduced by
Tap to reveal answer
To solve this problem, imagine that the original price of the laptop is $100. After the first 20% discount, the price of the laptop becomes $80. With the additional 10% reduction, we discount from $80, not $100. 10% of 80 is 8 so we must deduct $8 from $80. This gives $72 as the final price of the laptop after both reductions. Since we started at $100, the total discount is 28%.
To solve this problem, imagine that the original price of the laptop is $100. After the first 20% discount, the price of the laptop becomes $80. With the additional 10% reduction, we discount from $80, not $100. 10% of 80 is 8 so we must deduct $8 from $80. This gives $72 as the final price of the laptop after both reductions. Since we started at $100, the total discount is 28%.
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A store puts a $200 dress on a 70% discount and then takes an additional 15% off the reduced price. How much of the original price was removed?
A store puts a $200 dress on a 70% discount and then takes an additional 15% off the reduced price. How much of the original price was removed?
Tap to reveal answer
If we multiply $200 by 0.7, we find the dress has been reduced by $140 on the first discount. Since the dress now costs $60, we multiply that by 0.15 and find the dress has been discounted by an additional $9. The final sale of the dress is $51, with $149 of the original price removed.
If we multiply $200 by 0.7, we find the dress has been reduced by $140 on the first discount. Since the dress now costs $60, we multiply that by 0.15 and find the dress has been discounted by an additional $9. The final sale of the dress is $51, with $149 of the original price removed.
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In a local store, pens that normally sell for 49 cents each are on sale at 3 for 99 cents. How much can be saved by purchasing 12 of these pens at the sale price?
In a local store, pens that normally sell for 49 cents each are on sale at 3 for 99 cents. How much can be saved by purchasing 12 of these pens at the sale price?
Tap to reveal answer
Normally, 3 pens cost 3 * .49 = $1.47. Thus, on each set of 3 pens, the sale price saves the customer $1.47 - 99 = 48 cents. Multiply this by 4 to get the savings for 12 pens, and you get .48 * 4 = $1.92.
Normally, 3 pens cost 3 * .49 = $1.47. Thus, on each set of 3 pens, the sale price saves the customer $1.47 - 99 = 48 cents. Multiply this by 4 to get the savings for 12 pens, and you get .48 * 4 = $1.92.
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A department store sells a set of hand weights for $X. If the store offers a 20% discount on the original price of the weights, and then an additional 10% employee discount, what will be the price of the weights if an employee purchases them?
A department store sells a set of hand weights for $X. If the store offers a 20% discount on the original price of the weights, and then an additional 10% employee discount, what will be the price of the weights if an employee purchases them?
Tap to reveal answer
This is a straightforward percentage problem. After the first discount, the price of the weights is $0.8X. This price is then further reduced by 10% for the employee discount. 90% of 0.8X = 0.9(0.8X) = 0.72X.
This is a straightforward percentage problem. After the first discount, the price of the weights is $0.8X. This price is then further reduced by 10% for the employee discount. 90% of 0.8X = 0.9(0.8X) = 0.72X.
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