The logic here is solely in the fact that:
A number and its positive powers will be odd or even at the same time
Meaning, if you take the number 2 (which is even), any power of 2 will also be even. Why, you might ask? Just think of it this way: a power of 2 automatically contains at least one 2. This makes it odd or even.
The same goes for odd numbers. 7^15 = 7*7*..*7 fifteen times and it's plain to see that there are no 2s in there.
Now, back to the problem at hand:
Neither statement says anything about x or its roots, in terms of odd/even.
For all we know, for stmt 1, x could be either 4 or 9. Same goes for stmt 2: x could be either 8 or 27.
Put the two together and you get that x is the square of an integer and the cube of another integer. So? Pick some numbers: 64 is the square of 8 but also the cube of 4; similarly, 3^6 = 729 is the square of 81 and the cube of 9. There is no way of distinguishing between the two.
