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If x = 2, z-y = 4-2 and y-z will not be equal to |x| If x = -2, z-y = 2-4 and y-z will be equal to |x|.

Insufficient.

2) x < 0. It doesn't mean a thing. x could be -3, and so |x| = 3 but y-z could be any value. Insufficient.

Using both, we know it's sufficient. y-z must be equal to |x|

Ans C

Aren't we out to prove that |x| = y-z and not that x =/ <> y-z. Correct me if my understanding is incorrect. I feel that if x = z-y the |x| = y-x, thus A.

Still confused
If x = 2 or -2; |x| will always be 2.
thus if y-z = 2 then (y = 4; z =2) x =2==> |x| = true
if y-z = -2 (y =2; z=4) then x=-2; even though |x| = 2; y-z <> 2

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