Answer
Element Y: Magnesium
Element X: Calcium
Work Step by Step
Element Y: Magnesium
Element Y is also a group 2 element . Since ionization energy increases as you go up a group, element Y should be higher in the periodic table than magnesium (lower atomic number).
Element X: Calcium
Element X should be a group 2 element because there is a big jump between the second and third ionization energies. The big jump is because after the second ionization, the ion will have a stable, full outer shell, and removing another electron would require a lot more energy.
Element X: calcium, strontium, barium, radium
Note that this solution is only one of the possible answers. Element X can be any group 2 element calcium and below, element Y can be any element above element X.