Oil and Water Proportion

[ErikaG895]

Source: Manhattan GMAT CAT Exam Review Question for Quant.

A mixture of oil, water, and vinegar contains 10% oil. After all of the water evaporates, what percent of the mixture is oil?

(1) Before the water evaporated, the mixture exactly filled a one liter bottle.

(2) Before the water evaporated, vinegar accounted for forty percent of the mixture.

I undertstsand why statement 1 is insufficient. I do not understand why statment 2 is suffiencient.

For statatement 2, I undertstand the proportion of oil to vinager. I do not understand how oil after water was evaporated was calculated.

[jlucero]

Source: Manhattan GMAT CAT Exam Review Question for Quant.

A mixture of oil, water, and vinegar contains 10% oil. After all of the water evaporates, what percent of the mixture is oil?

(1) Before the water evaporated, the mixture exactly filled a one liter bottle.

(2) Before the water evaporated, vinegar accounted for forty percent of the mixture.

I undertstsand why statement 1 is insufficient. I do not understand why statment 2 is suffiencient.

For statatement 2, I undertstand the proportion of oil to vinager. I do not understand how oil after water was evaporated was calculated.

The original information is that 10% of the mixture is oil. Statement two says that 40% of the mixture is vinegar. Which allows us to infer that 50% of the mixture is water. Since we know the original ratio, after the water is gone, we are left with a oil to vinegar ratio of 10 to 40 or 1 to 4.

Notice the question doesn't ask about absolute amounts, but simply what percent of the mixture leftover is oil.

[RonPurewal]

after the water is gone, we are left with a oil to vinegar ratio of 10 to 40 or 1 to 4.

... which means that the answer to the actual question is 20%.

Because it's a data sufficiency problem, you don't actually have to calculate this answer——it's enough to know that fixed percentages can be found from a fixed ratio (and vice versa), as long as the ratio contains everything in the mixture.
If you were to see this sort of thing in a multiple-choice problem, though, you'd want to be able to go back and forth between "A:B = 1:4" and "20% A and 80% B".