YOU ARE PROVIDED WITH A SOLUTION OF SUBSTANCE "X". HOW WILL YOU TEST WHETHER IT IS SATURATED OR UNSATURATED WITH RESPECT TO "X" AT A GIVEN TEMPERATURE? WHAT HAPPENS WHEN A HOT SATURATED SOLUTION IS ALLOWED TO COOL?

At any particular temperature, a solution that has dissolved as much solute as it is capable of dissolving is said to be a saturated solution.

If you add more amount of X in the solution then :

(a) If it remain undissolved that means it is a saturated solution.

(b) If it dissolves then it is an unsaturated solution.

Usually For solids Solubility is a function of temperature, so on decreasing the temperature solubility decreases therefore if a  hot saturated solution of X is cooled then more and more amount of X (which is solute here) will precipitate out and settle down at the bottom.