earth@work has it down.

here's a possibly more intuitive way to handle statement (2):

your first two numbers are "-x" and "x", since they must be opposites if they sum to zero (remember that any pair sums to zero, so we don't have to pick two "special" numbers for this to happen).

if this is the case, then your third number must be x (so that it adds to -x to give zero), but it must ALSO be -x (so that it adds to x to give zero). the only way that x can equal -x is if x is zero - which means that all three numbers are zero.

therefore, everything must be zero.
so (2) is sufficient.

ans (b)