GRE - Percentage Question?

Question

A full glass of juice is a mixture of 20% grape juice and 80% apple juice. The contents of the glass are poured into a pitcher that is 200 percent larger than the glass. The remainder of the pitcher is filled with 16 ounces of water. What was the original volume of grape juice in the mixture? I have approached the following problem as follows. Let x represent the capacity of original color. Since we know the new glass is 200% larger than the original we can do 2x. We also know that in the new glass 16 ounces of water is added in addition to the original juice so we can setup the equation as follows: 2x = x + 16. Solving for x gives me 16. Then I find 20% of 16 and get 3.6. However the answer is wrong. Can anyone correct my approach?

Answer 1

Think about it this way: if the glass was 10 ounces, and the pitcher was 100% larger than the glass, would the pitcher be 10 ounces? No. It would be 20 ounces. So 200% larger than the glass means the glass PLUS 200%. We are conditioned to think 200% OF the glass, which would be what you did, but 200% larger than the glass means we have to add in the volume of the glass. So I think it should be 3x=x +16 so x=8, 20% is 1.6ounces. Good luck.

Answer 2

I think your approach is right, but the math is wrong.

20% of 16 is 3.2, not 3.6

Try 3.2 and see if that's right