If \(x, y,\) and \(z\) are positive integers such that \(x^4y^3=z^2,\) is \(x^9-y^6\) odd?

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If \(x, y,\) and \(z\) are positive integers such that \(x^4y^3=z^2,\) is \(x^9-y^6\) odd?

(1) \(\dfrac{x^4y^3}{x^2+y^2}\) can be written in the form \(4k+3,\) where \(k\) is a positive integer.

(2) \(z=x+y\)

Answer: D

Source: e-GMAT