Hi petud,

The "key" to this DS question is your ability to rewrite the given information and the question.

We're asked for the value of (X+Y)^2.

You might recognize this as one of the "Classic Quadratics", so you can rewrite the question to ask "what is the value of X^2 + 2XY + Y^2?"

Fact 1: X+Y+1 - 0

We can rewrite this Fact as....

X + Y = -1

With THAT value, we can now answer the question (by substituting the value into the question): (-1)^2 = 1
Fact 1 is SUFFICIENT

Fact 2: X^2 + Y^2 = 1 - 2XY

Here, we can add 2XY to both sides, which gives us...

X^2 + 2XY + Y^2 = 1

This ALSO answers the question (although you would have to rewrite the question to realize it).
Fact 2 is SUFFICIENT

Final Answer: D

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