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PS Computing Unknowns

by Striver » Sat Sep 22, 2012 12:24 pm
In a certain state, gasoline stations compute the price per gallon p, in dollars, charged at the pump by adding a 4 percent sales tax to the dealer's price per gallon d, in dollars, and then adding a gasoline tax of $0.18 per gallon. Which of the following gives the dealer's price per gallon d in terms of the price per gallon p charged at the pump?

A) d= p-0.22
B) d= p/1.22
C) d= p/1.04 - 0.18
D) d= p-0.18 / 1.04
E) d= p-0.04 / 1.18

Answer = D. Why?
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by GMATGuruNY » Sat Sep 22, 2012 4:13 pm
Striver wrote:In a certain state, gasoline stations compute the price per gallon p, in dollars, charged at the pump by adding a 4 percent sales tax to the dealer's price per gallon d, in dollars, and then adding a gasoline tax of $0.18 per gallon. Which of the following gives the dealer's price per gallon d in terms of the price per gallon p charged at the pump?

A) d= p-0.22
B) d= p/1.22
C) d= p/1.04 - 0.18
D) d= p-0.18 / 1.04
E) d= p-0.04 / 1.18
Dealer's cost:
Let d=1.

Selling price:
If d=1, then p = d + 4% tax + .18 = 1 + .04 + .18 = 1.22.

Since the problem asks for the value of d, our target is d=1.
Now we plug p=1.22 into the answers to which yields our target of d=1.

Only D works:
d = (p - 0.18)/(1.04) = (1.22 - 0.18)/(1.04) = (1.04)/(1.04) = 1.

The correct answer is D.
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by Brent@GMATPrepNow » Sat Sep 22, 2012 10:07 pm
Striver wrote:In a certain state, gasoline stations compute the price per gallon p, in dollars, charged at the pump by adding a 4 percent sales tax to the dealer's price per gallon d, in dollars, and then adding a gasoline tax of $0.18 per gallon. Which of the following gives the dealer's price per gallon d in terms of the price per gallon p charged at the pump?

A) d= p-0.22
B) d= p/1.22
C) d= (p/1.04) - 0.18
D) d= (p-0.18)/1.04
E) d= (p-0.04)/1.18

Answer = D. Why?
Note: The answer choices needed some brackets to avoid confusion, so I added them.

Here's the algebraic approach:

Dealer's price per gallon = d
When we add a 4% sales tax, we get a new price of 1.04d
When we add a gasoline tax of $0.18 per gallon, we get a final price of 1.04d + 0.18
In other words, p = 1.04d + 0.18

The question asks us to represent d in terms of p. In other words, solve the equation for d.
p = 1.04d + 0.18
p - 0.18 = 1.04d
(p - 0.18)/1.04 = d

Answer = D

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