For the gaseous reactions (I) and (II), the equilibrium constants are $X$ and $Y$ respectively.

(I) $\frac{1}{2}\text{N}_2(g) + \text{O}_2(g) \rightleftharpoons \text{NO}_2(g)$

(II) $2\text{NO}_2(g) \rightleftharpoons \text{N}_2\text{O}_4(g)$

Using the above reactions, the equilibrium constant $Z$ for the reaction (III) given below is

(III) $\text{N}_2\text{O}_4(g) \rightleftharpoons \text{N}_2(g) + 2\text{O}_2(g)$