A reduction in the price of petrol by 10% enables...

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BTGmoderatorLU: Moderator; Posts: 2505; Joined: Sun Oct 15, 2017 1:50 pm; Followed by:6 members

A reduction in the price of petrol by 10% enables...

by BTGmoderatorLU » Thu Feb 22, 2018 5:40 am

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

The OA is E.

I'm really confused by this PS question. Experts, any suggestion about how can I solve it? Thanks in advance.

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Source: Beat The GMAT — Problem Solving | Thu Feb 22, 2018 5:40 am

DavidG@VeritasPrep: Legendary Member; Posts: 2663; Joined: Wed Jan 14, 2015 8:25 am; Location: Boston, MA; Thanked: 1153 times; Followed by:128 members; GMAT Score:770

by DavidG@VeritasPrep » Thu Feb 22, 2018 8:38 am

LUANDATO wrote:A motorist spends $180 on gas. If the cost per gallon had been 10% less, then for the same $180, the motorist would have been able to purchase 5 more gallons of gas than he had purchased initially. What was the original cost per gallon of gas?

A. $11
B. $5
C. $45
D. $400
E. $4

The OA is E.

I'm really confused by this PS question. Experts, any suggestion about how can I solve it? Thanks in advance.

Aside: I cleaned up the wording of the question to make it clearer.

Note that the unit cost and quantity will have a reciprocal relationship. If the unit cost were to double, you could buy half as much gas for the same total outlay.

Thus, if the cost decreased by 10%, the new cost would be .9, or 9/10 of the old cost.
If cost and quantity have a reciprocal relationship, then the new quantity of gas would be 10/9, or 1 + 1/9 of the old quantity. Put another way, the old quantity was increased by 1/9.
If 5 gallons represents a 1/9 increase, and we call the old quantity 'q' then (1/9)q = 5 --> q = 45.
If the old quantity was 45 gallons, and the motorist paid $180, the old cost was 180/45 = 4. The answer is E

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DavidG@VeritasPrep: Legendary Member; Posts: 2663; Joined: Wed Jan 14, 2015 8:25 am; Location: Boston, MA; Thanked: 1153 times; Followed by:128 members; GMAT Score:770

by DavidG@VeritasPrep » Thu Feb 22, 2018 8:45 am

A motorist spends $180 on gas. If the cost per gallon had been 10% less, then for the same $180, the motorist would have been able to purchase 5 more gallons of gas than he had purchased initially. What was the original cost per gallon of gas?

A. $11
B. $5
C. $45
D. $400
E. $4

The OA is E.

I'm really confused by this PS question. Experts, any suggestion about how can I solve it? Thanks in advance.

And there's always good-old-fashioned back-solving.

Test B. If the old price were $5, the old quantity would have been 180/5 = 36 gallons.
If the price decreased by 10%, the new price would be $4.50, and the new quantity would be 180/4.5 = 40 gallons.
Thus, the motorist could have purchased 40-36 = 4 more gallons. It should actually be 5. So B is out.

(Notice now that you're close to the correct answer. The only other answer choice that makes sense is E. You don't really need to test it.

But for fun....

If old cost were $4, the old quantity would have been 180/4 = 45 gallons
If the cost decreased by 10%, the new cost would be $3.60, and the new quantity would be 180/3.6 = 50
50 -45 = 5 gallons. And we're done. The answer is E

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Scott@TargetTestPrep: GMAT Instructor; Posts: 8086; Joined: Sat Apr 25, 2015 10:56 am; Location: Los Angeles, CA; Thanked: 43 times; Followed by:29 members

by Scott@TargetTestPrep » Sun Jun 23, 2019 10:19 am

BTGmoderatorLU 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

The OA is E.

We can let n = the number of gallons normally purchased, and p = the normal price and create the equations:

p x n = 180

n = 180/p

and

0.9p x (n + 5) = 180

0.9p x (180/p + 5) = 180

162 + 4.5p = 180

4.5p = 18

p = 4

Answer: E

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