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

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14 Oct 2013, 06:24

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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?

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.

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

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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 [ 1.74 KiB | Viewed 7636 times ]

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

Cheers!!

JA If you like my post, let me know. Give me a kudos!

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%:

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

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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.

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

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02 Aug 2016, 10:00

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