If \(x\) and \(y\) are positive integers and \(xy\) is divisible by \(4,\) which of the following must be true?

[Gmat_mission]

If \(x\) and \(y\) are positive integers and \(xy\) is divisible by \(4,\) which of the following must be true?

A) If \(x\) is even then \(y\) is odd.
B) If \(x\) is odd then \(y\) is a multiple of \(4.\)
C) If \(x+y\) is odd then \(\dfrac{y}{x}\) is not an integer.
D) If \(x+y\) is even then \(\dfrac{x}{y}\) is an integer.
E) \(x^y\) is even.

Answer: B

Source: GMAT Club Tests