## A reduction in the price of petrol by 10% enables a motorist

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### A reduction in the price of petrol by 10% enables a motorist

by guerrero » Wed Jun 19, 2013 2:11 pm
A reduction in the price of petrol by 10% enables a motorist to buy 5 gallons more for $180. Find the original price of petrol? A.$11
B. $5 C.$45
D. $400 E.$4

OAE

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by sparkles3144 » Wed Jun 19, 2013 2:21 pm
Original:

x gallons * $n = 180 Reduced New: (x+5) gallons *$(1-0.1)n = 180

(x+5)(0.9n) = 180

0.9xn + 4.5n = 180

Substitute original equation xn = 180

0.9xn + 4.5n = 180
0.9(180) + 4.5n = 180
162 + 4.5n = 180
4.5n = 180 - 162 = 18
n = 18/4.5 = $4 ### GMAT/MBA Expert GMAT Instructor Posts: 16207 Joined: Mon Dec 08, 2008 6:26 pm Location: Vancouver, BC Thanked: 5254 times Followed by:1268 members GMAT Score:770 by Brent@GMATPrepNow » Wed Jun 19, 2013 2:34 pm guerrero wrote:A reduction in the price of petrol by 10% enables a motorist to buy 5 gallons more for$180. Find the original price of petrol?

A. $11 B.$5
C. $45 D.$400
E. $4 OAE Let P = the original price per gallon. So, if the price is reduced 10%, the new price is 0.9P IMPORTANT: # of gallons purchased = ($ spent)/(price per gallon)

(# of gallons purchased for $180 at original price) + 5 = (# of gallons purchased for$180 at reduced price)
So, ($180/P) + 5 = ($180/0.9P)
At this point, you might choose to plug in the answer choices, or you can solve the equation. Let's solve the equation. . .
Given: ($180/P) + 5 = ($180/0.9P)
Eliminate the fractions by multiplying both sides by 9P: (180)(9) + 45P = (180)(10)
So, 45P = 180
P = 4

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by GMATGuruNY » Wed Jun 19, 2013 3:00 pm
guerrero wrote:A reduction in the price of petrol by 10% enables a motorist to buy 5 gallons more for $180. Find the original price of petrol? A.$11
B. $5 C.$45
D. $400 E.$4

OAE
We can plug in the answers, which represent the original price.
The correct answer choice is almost certainly a factor of $180 -- B, C, or E. The price in answer choice C --$45 per gallon -- seems way too high.

Number of gallons that can be purchased at the original price = 180/5 = 36.
Discounted price = 5 - .1(5) = 4.5.
Number of gallons that can be purchased at the discounted price = 180/4.5 = 40.
Increase in purchasing power = 40-36 = 4 gallons.
Doesn't work: the increase in purchasing power must be 5 gallons.
Eliminate B.

Number of gallons that can be purchased at the original price = 180/4 = 45.
Discounted price = 4 - .1(4) = 3.6.
Number of gallons than can be purchased at the discounted price = 180/3.6 = 1800/36 = 50.
Increase in purchasing power = 50-45 = 5 gallons.
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