Metal chloride solubility characteristics:
x must be water soluble at room temperature, y must be sparingly soluble at room temperature, and z must be soluble in hot water but not in cold water.
is highly soluble in water (x).
AgCl is notoriously insoluble in water and sparingly soluble at any temperature, classifying it as sparingly soluble (y).
exhibits unusual solubility behavior-it is sparingly soluble in cold water but its solubility increases with temperature, making it soluble in hot water (z).

This combination perfectly matches all three criteria.