The capacity of glass X is 80 percent of the...

[swerve]

The capacity of glass X is 80 percent of the capacity of glass Y. Glass X contains how many more ounces of punch than glass Y?

(1) Glass X contains 6 ounces of punch and is half-full, while glass Y is full.
(2) Glass X is 70 percent full, and glass Y is 30 percent full.

The OA is A.

Please, can any expert explain this DS question for me? I have many difficulties to understand why that is the correct answer. Thanks.

[ErikaPrepScholar]

We start knowing that Glass X has 80% the capacity of Glass Y. In other words X = 0.8Y.

Statement 1:

If Glass X contains 6 ounces of punch and is half full, Glass X must have a total capacity of 12 ounces. Plugging this into our initial equation gives

12 = 0.8Y
15 = Y

So the total capacity of Glass Y is 15 ounces. We also know that Glass Y is full, so Glass Y contains 15 ounces of punch. This is 15 - 6 = 9 ounces more punch that Glass X contains. Sufficient.

Statement 2:

This statement tells us nothing about the number of ounces in each glass, just how the volumes compare. This means that Glass X could contain 7 ounces of punch, giving a total capacity of 10 ounces of punch, meaning that Glass Y has a total capacity of 12.5 ounces and currently contains 3.75 ounces of punch. This gives a difference of 3.25 ounces of punch. HOWEVER, Glass X could contain 14 ounces of punch, giving a total capacity of 20 ounces of punch, meaning that Glass Y has a total capacity of 25 ounces and currently contains 7.5 ounces of punch. This gives a difference of 6.5 ounces of punch. Depending on how large the glasses are, the difference changes. Insufficient.

However, I'm curious where this question comes from, as we saw that given statement 1, Glass Y actually contained more punch than Glass X, where the question asked how many more ounces Glass X contained than Glass Y. We also see that the two statements aren't compatible - Statement 1 claims that Glass X is half full and Glass Y is full, whereas Statement 2 claims that Glass X is 70% full and Glass Y is 30% full. These two statements cannot both be true. In a real GMAT Data Sufficiency problem, the two statements should be compatible.