Data Sufficiency

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.

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

Veritas - Your answer is correct But explanation is little wrong. Please check below.

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.

y^m * y^K = y^m

y^m can be 0
y^k can be 1

Statement 1 - k is odd k can 1,3,5,7,9
y^K =1 means y =1 since 1^Odd number will retain the sign of 1 so y =1
y^m = 0 says y=0

so y = 1 or 0
so NOT SUFFICIENT.

Statement 2 = y is Odd -
y^k =1 y can be 1 or -1 since -1 raised to even number will result in 1

since 1 raised to odd number will result in 1
so y = 1 or -1

so NOT SUFFICIENT.

ANSWER is C - K is odd & y is odd leads to y =1