If element x forms the oxides xo and x2o3 the oxidation numbers of element x are
a)+1 and +2
b)+2 and +3
c)+1 and +3
d)+2 and +4

b) +2 and +3.

Explanation:

Hello,

In this case, given the molecular formulas:

And:

We can relate the subscripts with the oxidation states by knowing that they are crossed when the compound is formed, for that reason, we notice that oxygen oxidation state should be -2 for both cases and the oxidation state of X in the first formula must be +2 since both X and O has one as their subscript as they were simplified:

Moreover, for the second case the oxidation state of X should be +3 in order to obtain 3 as the subscript of oxygen:

Thus, answer is b)+2 and +3

Best regards.

"the periodic table is arranged in order of atomic number."