24 = 2*3*4, if x² is divisible by 24, x² must have factors of 2 and 3.
1) only, x does not have factor of 3, so x² does not have factor of 3, x² cannot be divisible by 24, sufficient.
2) only, x is odd, so x does not have factor of 2, so x² does not have factor of 2, x² cannot be divisible by 24, sufficient.