Here the total number of ionization energy values of element X is
So the total number of electrons in X atom should be 4 and the electronic configuration will be
Hence the number of valance electron in the atom is
The question is not clear enough and data given here is not realistic.e.g IE1>>>than IE2 etc.
I assumed that only 4 ionisation energy values of the atom are possible.
Another view of the same question given in the site.