FatemehAsgarinejad wrote:

answer: E

ab is an integer which a is the tens digit and b is a unit digit. It is divisible by c so:

ab / c = x and (c * x) = ab

now we try to find a condition for each of the options to be true

A: a= 30 and c = 3. Then a is divisible by c.

B: a= 12 and c=4. Then a is not divisible by c.

C: a= even and c=2. Then c is prime.

D: ab=30 and c=3. Then both ab+c=33 and c are odd. In the other words:

(ab+c)= (c*x+c)= c*(x+1) if x is even and c is odd then ab+c is odd and it’s possible.

F: as said in D, ab+c = c*(x+1). If ab+c is odd then c*(x+1) is odd. It means that c is odd and x is even. So it is impossible for c to be even when ab+c is odd.

Could you please explain it more clearly?