Data Sufficiency

Vincen wrote:If m and k are non-zero integers and if y^(m+k) = y^m, what is the value of y?

(1) k is odd.
(2) y is odd.

The OA is C.

I think answer should be B.

The only numbers that satisfy y^(m+k)=y^m are y=0 or y=1.

So, if y is odd then y=1. Am I wrong?

Your logic is almost perfect... but y could also equal -1, if (m + k) and (m) were either both odd or both even. Or in other words... if k was even.

Thus, statement (2) is not sufficient, because y = 1 and y = -1 could both work.

Together, though, we know that of (m + k) and (m), one of the exponents will be even and the other odd. And since (-1)^(even) = (-1)^(odd) can't work, then the base y must equal 1.