Stores \(X, Y,\) and \(Z\) each sell a certain item that has a given list price. Stores \(X\) and \(Y\) are located in

[M7MBA]

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 the 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. \(y<z<x\)

Answer: B

Source: GMAT Prep

[Brent@GMATPrepNow]

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 the 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. \(y<z<x\)

Answer: B

Source: GMAT Prep

Let $100 = the list price for all 3 stores

Store X
$100 plus 5% sales tax = $105
$105 minus 5% discount = (0.95)($105) = $99.75
Aside: a 5% discount means the buyer is paying 95% of the cost (thus 95% of $105)

Store Y
$100 minus 5% discount = $95
$95 plus 5% sales tax = (1.05)($95) = $99.75

Store Z
$100

We can see that $99.75 = $99.75 < $100
In other words, x = y < z

Answer: B

Cheers,
Brent