Asample of crystalline compound when heated in an open test tube, produced several droplets of water on the upper region of the tube. the residue dissolved in water forming a yellow brown solution. why should you conclude that the compound is not a true hydrate

Answer is: If the compound were a true hydrate it would form aqueous solutions of identical color both before and after heating.

For example, copper(II) sulfate pentahydrate (CuSO₄·5H₂O) form aqueous solutions of bright blue both before and after heating.

Hydrate is a substance that contains water or its constituent elements.

The difference in color shows that there has been a chemical change on heating so the water formed could be produced in that chemical change. Alternatively the material could still be a true hydrate and the anhydrous material may have undergone a change on heating so you can't really conclude anything.