Source: Revised GRE PDF 2nd Ed. Section 5; #19 (p. 81)

7

In 2000 the amount of Germany’s gasoline tax

In 2000 the amount of Germany’s gasoline tax revenue was approximately what percent less than the amount of its income tax revenue? 10%, 20%, 30%, 40%, 50%

2 Explanations

2

Abhiram Ravikumar

Why do we need to divide by 28.6 again? Shouldn't it be just the difference of the percentages themselves?

Jun 16, 2017 • Comment

Cydney Seigerman, Magoosh Tutor

Excellent question, Abhiram!

In this question, we need to calculate the percent difference. The formula for percent difference is

[new - original] / [original] x 100%

For this question, it's a little confusing because we're dealing with percents themselves. However, we can think of "percent" as the unit, and the unit doesn't change the equation itself. By dividing by the original amount, we're finding the fraction of the change compared to the original amount. Then, to find the percent change, we need to multiply by 100%. :)

I hope this helps!

how do we know which is "new" and which is "original"?

David Recine

Great question! When calculating percent difference, we're looking at the difference between the bigger number and the smaller number. Since that difference needs to be positive (we don't deal with negatives in the final answer to a percent change question), the larger amount will always be treated as "new."

Victoria H Davis

Hi, I am confused by what you just said -- "the larger amount will always be treated as 'new'" -- the equation for percent increase is new - old / old x100. The denominator should be the old or the original value. From this perspective and your answer, shouldn't it be divided by the "old" AKA smaller amount? Any help is appreciated! Thank you!

Hey Victoria! Using that formula, (new - old)/old × 100 , will give you the change from the old to the new, that is, the percent difference from 20.4 to 28.6. And that's a 40% increase. However, we want to know the decrease from 28.6 down to 20.4, not the increase from 20.4 to 28.6. This is why I don't rely on formulas when working with percents. They can easily confuse you. I like to make things as clear as possible by rephrasing the question: 28.6 minus what percent of 28.6 will equal 20.4? Written as an equation:

28.6 - (x/100)(28.6) = 20.4

Solve for x and we get x = 28.67, which is close enough.

1

Chris Lele

Sep 27, 2012 • Comment