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I'm solving a problem in the Manhattan GRE 5 pound book.

When Mark fills his car with regular gasoline, he gets 20 miles/gallon. When he fills his car with premium gasoline, he gets 25 miles/gallon. If the price of regular gasoline is \$4.00 per gallon and the price of premium gas is $6.25 per gallon, then the cost efficiency of regular gasoline, in miles/dollar, is what percent greater than the cost efficiency of premium gasoline?

I find that regular gas gives 5 Miles/Dollar and Premium gives 4 Miles/Dollar, which means the difference is 1 Mile/Dollar. Now, in order to calculate the percentage- should I divide it by 5 or by 4 ? I have the same doubt with most of these percentage and profit/loss problems. Which is the 'original amount' that I should divide by ?

anon_16
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1 Answers1

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You should divide it by $4$, giving us a percentage of $25\%$. That way, we can say the following sentence:

"The cost efficiency of regular gasoline is $25\%$ greater than the cost efficiency of premium gasoline."

Indeed, we can check our work. What is $25\%$ greater than $4$? Well $25\%$ of $4$ is $1$, and the cost efficiency of regular gasoline is indeed $4 + 1 = 5$. So we picked the right number!

In general, the number that you want to divide by is the second quantity that you are comparing the first quantity against.

Adriano
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  • I'm not sure I understand. What if I rephrase the question as "The cost efficiency of premium gasoline, in miles/dollar, is what percent lesser than the cost efficiency of regular gasoline?" ? Should I divide by 5 in that case ? – anon_16 Aug 07 '14 at 09:47
  • Yes, giving us a percentage of $20%$. That way, we can say: "The cost efficiency of premium gasoline is $20%$ less than the cost efficiency of regular gasoline." Indeed, we can check our work. What is $20%$ less than $5$? Well $20%$ of $5$ is $1$, and the cost efficiency of premium gasoline is indeed $5 - 1 = 4$. So we picked the right number! – Adriano Aug 07 '14 at 17:38
  • That clears up my confusion. Thanks, Adriano! – anon_16 Aug 08 '14 at 06:22