ardz24 wrote:What is the value of K?
(1) (-k)^5 = -k^5
(2) (-k)^4 = -k^4
What's the best way to determine whether statement 1 is sufficient? Can any experts help?
(1) (-k)^5 = -k^5
Case 1: Say k = 0; then at k = 0, we have (-k)^5 = -k^5 => (-0)^5 = -0^5 => 0 = 0. Thus k = 0.
Case 2: Say k > 0, then replacing the value of k with |k|, we have (-k)^5 = -k^5 => [(-1)^5]*|k|^5 = -|k|^5 => -|k|^5 = -|k|^5. Thus, k can be a positive number.
Case 3: Say k < 0, then replacing the value of k with -|k|, we have (-k)^5 = -k^5 => |k|^5 = |k|^5 => -|k|^5 = -|k|^5. Thus, k can be a negative number.
(2) (-k)^4 = -k^4
Case 1: Say k = 0; then at k = 0, we have (-k)^4 = -k^4 => (-0)^4 = -0^4 => 0 = 0. Thus k = 0.
Case 2: Say k > 0, then replacing the value of k with |k|, we have (-k)^4 = -k^4 => [(-1)^4]*|k|^4 = -|k|^4 => |k|^5 = -|k|^5. This is not a valid case, thus, k cannot be a positive number.
Case 3: Say k < 0, then replacing the value of k with -|k|, we have (-k)^4 = -k^4 => |k|^4 = -1*(-|k|)^4 => |k|^4 = -|k|^4. This is not a valid case, thus, k cannot be a negative number.
Thus, k = 0. Sufficient.
The correct answer:
B
Hope this helps!
-Jay
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