Is x > y ? (1) x^2 > y^2 (2) xy < 0

It is perfectly fine to think of the question as "Is x bigger than y?", but remember that you can also rewrite the question to Is \(x-y>0\)? which is equivalent to "Is x to the right of y on the number line?".

Anyways, let us assess the statements.

Statement 1:
Remember that if you square any non-zero number, it becomes positive.
\(x^{2}>y^{2}\) is the same as saying that \(|x|>|y|\). (draw a number line, plot in values for x and y, and check this out for yourself)
So we still do not know if \(x\) is bigger than \(y\) and therefore we do not know where they are relative to each other on the number line.
INSUFFICIENT

Statement 2:
So from this we know that one of the variables has to be positive, and the other one has to be negative.
We do not know which is biggest or where they are relative to each other on the number line.
INSUFFICIENT

Statement 1 and 2 together:
So we know that \(|x|>|y|\) and that one variable is positive while the other is negative.
\(x\) could be \(10\) and \(y\) could be \(-5\), making the answer to the question YES.
\(x\) could be \(-10\) and \(y\) could be \(5\), making the answer to the question NO.
INSUFFICIENT