If m and k are non-zero integers and y^(m+k) = y^m, what is the value of y?
(1) k is odd.
(2) y is odd.
Let's rephrase: y^(m+k) = y^m can be rewritten as y^m * y^k = y^m.
Now there are two possibilities. First, is that y = 0.
Alternatively, if y is not 0, we divide both sides of y^m * y^k = y^m by y^m to get y^k = 1.
If y^k = 1. y is either 1 or -1. 1^k will be 1 for all non-zero values of k. (-1)^k will be 1 for all non-zero EVEN values of k.
Pre-statement summary: y can be -1, 0, or 1.
Statement 1: k is odd. In this case, y could be 0 or 1. (If y = 0 , y^m * y^k = y^m, will be true for all non-zero values of k and m. If y = 1, then y^k = 1 will be true for all non-zero values of k. Not sufficient. )
Statement 2: y is odd. Now y could be -1 or 1. Not Sufficient.
Together: If y is odd, it can no longer be 0. If k is odd, y can no longer be -1. (-1 raised to an ODD, will not give us 1.) Therefore y =1. Sufficient. Answer is
C
