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(I) means y and z have same sign, so that the absolute value of their sum is equal to the sum of their absolute values. In other words y+z can't be zero unless both are zero, but the question has xyz<>0. Therefore we would be able to determine that x(y+z)<>0.
This is why I is sufficient.
(II) By the same reason we get x+y<>0, but we don't know if y+z=0, so not sufficient to tell if x(y+z)=0.