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Stores X, Y, and Z each sell a certain item that has a given

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Stores X, Y, and Z each sell a certain item that has a given list price. Stores X and Y are located in a state with a 5 percent sales tax, and both sell the item at a 5 percent discount off list price, while Store Z is located in a state with no sales tax and gives no discounts. Store X applies its discounts first and then charges sales tax on the discounted price, while Store Y adds the tax first and then applies the discount to the price with tax. If x and y are the prices, with tax and discount, charged by Stores X and Y, respectively, and z is the price charged by Store Z, which of the following statements correctly describes the relationship among x, y, and z?

A. x=y=z
B. x=y<z
C. x<y<z
D. x<z<y
E. y<z<x
[Reveal] Spoiler: OA

Last edited by Bunuel on 14 Oct 2013, 06:55, edited 1 time in total.
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bulletpoint wrote:
Stores X, Y, and Z each sell a certain item that has a given list price. Stores X and Y are located in a state with a 5 percent sales tax, and both sell the item at a 5 percent discount off list price, while Store Z is located in a state with no sales tax and gives no discounts. Store X applies its discounts first and then charges sales tax on the discounted price, while Store Y adds the tax first and then applies the discount to the price with tax. If x and y are the prices, with tax and discount, charged by Stores X and Y, respectively, and z is the price charged by Store Z, which of the following statements correctly describes the relationship among x, y, and z?

A. x=y=z
B. x=y<z
C. x<y<z
D. x<z<y
E. y<z<x


Say the price of the item is 100. Then:

x = (100*0.95)*1.05 < 100.
y = (100*1.05)*0.95 < 100.
z = 100.

So, we have that x=y<z.

Answer: B.
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Re: Stores X, Y, and Z each sell a certain item that has a given [#permalink]

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Hi Bunuel,

I tried this on a spreadsheet. I took a common number (100) and did 2 sets of operations for 2 options:
option 1 (Store Y) added X% and subtracted Y% from the result of the first operation
option 2 (Store X) subtracted Y% and added X% from the result of the first operation
Attachment:
Capture.PNG
Capture.PNG [ 1.74 KiB | Viewed 13854 times ]

I always got the same answer. Is this a property that we can by heart?
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Stores X, Y, and Z each sell a certain item that has a given [#permalink]

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joseph0alexander wrote:
Hi Bunuel,

I tried this on a spreadsheet. I took a common number (100) and did 2 sets of operations for 2 options:
option 1 (Store Y) added X% and subtracted Y% from the result of the first operation
option 2 (Store X) subtracted Y% and added X% from the result of the first operation
Attachment:
Capture.PNG

I always got the same answer. Is this a property that we can by heart?


Yes, increasing a quantity by x% and then decreasing the result by y% is the same as decreasing by y% and then increasing the result by x%:

[p*(1 + x/100)]*(1 - y/100) = [p*(1 - y/100)]*(1 + x/100)
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Re: Stores X, Y, and Z each sell a certain item that has a given [#permalink]

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@Bunnel, looks like there is a small typo. It should be

increasing a quantity by x% and then decreasing the result by y% is the same as decreasing by y% and then increasing the result by x

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Re: Stores X, Y, and Z each sell a certain item that has a given [#permalink]

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New post 28 Jul 2015, 16:30
Thought process: We're dealing with percents. Increase and decrease.
Strategy: Pick numbers and plow through the calculations. Choose 100 or another easy round number.

See that x=y<z
CHOOSE B

ON TO THE NEXT

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Re: Stores X, Y, and Z each sell a certain item that has a given [#permalink]

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New post 29 Sep 2016, 03:02
Bunuel Can you please explain if this is correct - If we used the formula instead of successive discounts ie A + B + AB/100 (where A and B are successive discounts/percentages applied to the same quantity) then the ans for final list price value is:

X: (-5) + 5 -25/100 (X) => X is the list price
Y: 5 - 5 -25/100 (Y) => Y is the list price

But seems like the final list price value is different using this formula. Is it incorrect to use it here?

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Re: Stores X, Y, and Z each sell a certain item that has a given [#permalink]

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New post 09 Oct 2016, 08:03
Hi Bunnel,


I tried solving this question by taking the value of the product as 100. A 5% decrease results 95 (discounted price) after we add the tax to this value it is equal to 99.3. If the sales tax is added and then discounted its 101.5. Can you please explain what am i missing here ?

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New post 09 Oct 2016, 08:50
nikitamitra wrote:
Bunuel Can you please explain if this is correct - If we used the formula instead of successive discounts ie A + B + AB/100 (where A and B are successive discounts/percentages applied to the same quantity) then the ans for final list price value is:

X: (-5) + 5 -25/100 (X) => X is the list price
Y: 5 - 5 -25/100 (Y) => Y is the list price

But seems like the final list price value is different using this formula. Is it incorrect to use it here?


Yes, using the formula also we will get the same result. Note that List price of the product is same. So, Try taking the value of each product 'a' and then substutitute in your formula. You will get the result.

anuj11 wrote:
Hi Bunnel,


I tried solving this question by taking the value of the product as 100. A 5% decrease results 95 (discounted price) after we add the tax to this value it is equal to 99.3. If the sales tax is added and then discounted its 101.5. Can you please explain what am i missing here ?


You are making a calculation mistake.

List price 100.

Case 1 : 5% increase then 5% discount. = 105 * 0.95

Case 2 : 5% discount the n 5% increase = 95 *1.05

Both will be equal.
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Re: Stores X, Y, and Z each sell a certain item that has a given [#permalink]

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New post 04 Jun 2017, 20:29
Bunuel wrote:
bulletpoint wrote:
Stores X, Y, and Z each sell a certain item that has a given list price. Stores X and Y are located in a state with a 5 percent sales tax, and both sell the item at a 5 percent discount off list price, while Store Z is located in a state with no sales tax and gives no discounts. Store X applies its discounts first and then charges sales tax on the discounted price, while Store Y adds the tax first and then applies the discount to the price with tax. If x and y are the prices, with tax and discount, charged by Stores X and Y, respectively, and z is the price charged by Store Z, which of the following statements correctly describes the relationship among x, y, and z?

A. x=y=z
B. x=y<z
C. x<y<z
D. x<z<y
E. y<z<x


Say the price of the item is 100. Then:

x = (100*0.95)*1.05 < 100.
y = (100*1.05)*0.95 < 100.
z = 100.

So, we have that x=y<z.

Answer: B.


Hi, I understand that Y<Z, but could you please explain why X equals to Y<Z?

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Re: Stores X, Y, and Z each sell a certain item that has a given [#permalink]

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New post 04 Jun 2017, 22:43
nielsenn wrote:
Bunuel wrote:
bulletpoint wrote:
Stores X, Y, and Z each sell a certain item that has a given list price. Stores X and Y are located in a state with a 5 percent sales tax, and both sell the item at a 5 percent discount off list price, while Store Z is located in a state with no sales tax and gives no discounts. Store X applies its discounts first and then charges sales tax on the discounted price, while Store Y adds the tax first and then applies the discount to the price with tax. If x and y are the prices, with tax and discount, charged by Stores X and Y, respectively, and z is the price charged by Store Z, which of the following statements correctly describes the relationship among x, y, and z?

A. x=y=z
B. x=y<z
C. x<y<z
D. x<z<y
E. y<z<x


Say the price of the item is 100. Then:

x = (100*0.95)*1.05 < 100.
y = (100*1.05)*0.95 < 100.
z = 100.

So, we have that x=y<z.

Answer: B.


Hi, I understand that Y<Z, but could you please explain why X equals to Y<Z?


Hi

x=y<z simply means that x and y are equal to each other, and both are less than z.

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Re: Stores X, Y, and Z each sell a certain item that has a given [#permalink]

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New post 06 Jun 2017, 16:46
bulletpoint wrote:
Stores X, Y, and Z each sell a certain item that has a given list price. Stores X and Y are located in a state with a 5 percent sales tax, and both sell the item at a 5 percent discount off list price, while Store Z is located in a state with no sales tax and gives no discounts. Store X applies its discounts first and then charges sales tax on the discounted price, while Store Y adds the tax first and then applies the discount to the price with tax. If x and y are the prices, with tax and discount, charged by Stores X and Y, respectively, and z is the price charged by Store Z, which of the following statements correctly describes the relationship among x, y, and z?

A. x=y=z
B. x=y<z
C. x<y<z
D. x<z<y
E. y<z<x


We are given that Stores X and Y are located in a state with a 5 percent sales tax, and both sell an item at a 5 percent discount off list price, while Store Z is located in a state with no sales tax and gives no discounts.

We are also given that Store X applies its discounts first and then charges sales tax on the discounted price, while Store Y adds the tax first and then applies the discount to the price with tax.

Let’s determine the prices, x, y, and z and let the original price of the item = 100.

Price at Store X:

(100)(0.95)(1.05) = $99.75

Price at Store Y:

(100)(1.05)(0.95) = $99.75

Price at Store Z:

$100

Thus, x = y < z

Answer: B
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Re: Stores X, Y, and Z each sell a certain item that has a given   [#permalink] 06 Jun 2017, 16:46
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