Hi ollapodrida,

This DS question is perfect for TESTing Values.

We're asked if |x^2 + y^2| > |x^2 - y^2|? This is a YES/NO question. We are told nothing about x and y.

Fact 1: x > y

Let's TEST Values and track the results:
x = 1
y = 0
Is |1| > |1|? The answer to the question is NO.

x = 2
y = 1
Is |5| > |3|? The answer to the question is YES.
Fact 1 is INSUFFICIENT

Fact 2: x > 0

The same two examples from Fact 1 can be applied here.
We have a NO and a YES answer.
Fact 2 is INSUFFICIENT

Combined, we have the same TEST Cases for both Facts.
We have a NO and a YES answer.
Combined, INSUFFICIENT.

Final Answer: E

GMAT assassins aren't born, they're made,
Rich

Both x^2 and y^2 must be either positive or 0. The absolute value of |pos + pos| will always be greater than |pos - pos|. The only time |x^2 + y^2| will not be greater than |x^2 - y^2| is if either x or y is 0, in which case the quantities will be equal.

Target question: is either x or y equal to 0?

Statement 1: x > y

This tells us nothing about whether either quantity is 0. Insufficient.

Statement 2: x > 0

This tells us that x is not equal to 0, but it doesn't tell us whether y is. Insufficient.

Together: The statements tell us nothing about whether either quantity equals 0. Insufficient.

The answer is E.