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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 [#permalink]

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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.
Moved to PS forum.
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New post 14 Oct 2013, 06:58
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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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New post 24 Nov 2014, 03:18
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 7636 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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Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

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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 08 Jan 2015, 13:53
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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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Kudos [?]: 79800 [0], given: 10022

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

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New post 09 Jan 2015, 03:47
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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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Re: Stores X, Y, and Z each sell a certain item that has a given   [#permalink] 02 Aug 2016, 10:00
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