If x=8y+11 then which of the following cannot be a divisor

I think the answer is Option D "12".

Reasoning :-

A quick way to approach this problem is to see the x=8y + 11 equation & trying to quickly substituting values for "y"; If you plug in y=-1, -2, 3 you can easily see they are respectively divisible by 3, 5 & 7. But in each case, the final value of "x" will be odd due to the addition of 11 to a multiple of 8 (due to 8y). Hence, you can never have an even divisor for "x".

Thus option D (12) is the one that can not be a possible divisor for x. In hindsight, you can see that this boils down to a simple remainder problem, one where you can easily guess the answer based on the fact that x will always be "odd" and hence not divisible by an even number.

Hope it helps!