Integers \(x\) and \(y\) are each odd, and \(x > y.\) Which of the following represents the number of odd integers \(z\)

[Gmat_mission]

Integers \(x\) and \(y\) are each odd, and \(x > y.\) Which of the following represents the number of odd integers, \(z,\) that exist such that \(x > z > y ?\)

A. \(x-y-1\)

B. \(x-y\)

C. \(\dfrac{x-y}2\)

D. \(\dfrac{x-y-1}2\)

E. \(\dfrac{x-y-2}2\)

Answer: E

Source: Veritas Prep