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 ?
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.