Is |x| = y - z?
(1) x + y = z
(2) x < 0
Statement 1: x = z-y
Case 1: x = z-y = 0, which case y-z = 0.
In this case, |x| = y-z.
Case 2: x = z-y = 1, in which case y-z = -1.
In this case, |x| ≠y-z.
INSUFFICIENT.
Statement 2: x < 0
No information about y-z.
INSUFFICIENT.
Statements combined:
Case 3: x = z-y = -1, in which case y-z = 1.
In this case, |x| = y-z.
Case 4: x = z-y = -10, in which case y-z = 10.
In this case, |x| = y-z.
Case 5: x = z-y = -1/2, in which case y-z = 1/2.
In this case, |x|= y-z.
Since |x|= y-z in every case, SUFFICIENT.
The correct answer is
C.
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