Hi Maysaa,

In a DS question, each statement is essentially factual information that you're supposed to use to answer the question.

In Fact 1, we're told that (X^2) > (Y^2).

Your example (X = 2, Y = -3) does NOT fit the given information, so you are NOT allowed to use that example. You COULD use (X = -3, Y = 2); these numbers will give you a YES answer to the given question. Any combination of values that fits the information in Fact 1 will also give you a YES answer to the question. The consistent answer is what makes Fact 1 SUFFICIENT.

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

Absolute value and squares are often related. Think about a square root: if we say that √4 is equal to 2 or -2, we could really say:
√4 = |2|

That's why when you see (√x)², you shouldn't just interpret that as x. You should interpret (√x)² = |x|.

If we know that x² > y², we don't know whether they are positive or negative, but it doesn't matter. If the square of one number is greater than the other, that number must be further from 0.