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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