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twixit's explanation is good...we know, x,y,z are not equal to zero...all we need to check for is, if y+z is not equal to zero...statement I doest that.

(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.