This DS question can be solved with a variety of Number Properties and TESTing VALUES:
We're asked for the value of X.
Fact 1: X^4 = |X|
While this certainly looks "scary", there can't be that many values that will "fit" this equation.
X = 0 is fairly obvious. Since we have a "fourth power" and an absolute value, I'd be looking for other solutions that are fairly close to 0 and possibly negative.
X = 1 and X = -1 also fit.
Fact 1 is INSUFFICIENT
Fact 2: X^2 > X
Here we can use a Number Property to our advantage - EVERY negative number, when squared, becomes positive.
So, X = ANY negative.
This is enough to prove that Fact 2 is INSUFFICIENT on its own, but I want to add a bit more detail to what X^2 > X means.
X CANNOT be 1, since 1^2 is NOT > 1.
X CANNOT be 0, since 0^2 is NOT > 0
X CANNOT be between 0 and 1 either (because of another Number Property - positive fractions, when squared, get SMALLER).
C CANNOT be 1/2, since (1/2)^2 is NOT > 1/2.
X CAN be > 1 though (choose any value greater than 1 and you can prove it).
Fact 2 is INSUFFICIENT
Combined, we know...
X = -1, 0 or 1
X CANNOT BE 0 OR 1
Thus, X can ONLY be -1
GMAT assassins aren't born, they're made,