For non-negative integers \(x, y,\) and \(z,\) is \(x^z\) odd?

[Gmat_mission]

For non-negative integers \(x, y,\) and \(z,\) is \(x^z\) odd?

(1) The product \(xz\) is odd.
(2) \(x = 2^y\)

Answer: A

Source: Veritas Prep

[ravimani]

For non-negative integers \(x, y,\) and \(z,\) is \(x^z\) odd?

(1) The product \(xz\) is odd.
(2) \(x = 2^y\)

Answer: A

Source: Veritas Prep

x, y and z are >= 0

\(x^z\ \) can only ODD if x is ODD.

So from (1) it is given that xz is ODD. The multiplication of two numbers can only be ODD if both are ODD. Hence, x and z should be ODD. There (1) is enough

from (2), we know that x can be EVEN or ODD. If y = 1 or more then x is EVEN. But if y = 0 then x is ODD. Hence, (2) is not alone sufficient.

Hence choose (A)