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zaarathelab
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Statement 1: x+y=z, so x=z-y. Replacing x with z-y in the given: |z-y|=y-z. The expression on the left is always non-negative, so this would only by true if y>=z, which we don't know. INSUFFICIENT
Statement 2: This is obviously insufficient by itself since it gives no information about y and z.
Statements 1 & 2: With both statements, we know that x=z-y AND x<0, using substitution, we know z-y<0 or z<y or y>z. As discussed above, |z-y|=y-z whenever y>z, so this is sufficient.
Answer is C
