(1)|x-|x^2||=2

Since x^2>=0 it redueces to |x-x^2|=2

(x-x^2) is always less than zero if x is an integer (very easy to prove)

So it reduces to

x^2-x-2=0

x=2 or x=-1

Insufficient

(2)|x^2-|x||=2

If x>0

|x^2-x|=2

x=2 (solve as (1))

If x<0

x=-2 (by symmetry. You can solve it too like before)

Insufficient

Combined:

x=2

sufficient

I disagree this is too hard for GMAT. I say it is a perfect GMAT question.

_________________

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