Is 10, a factor of n + 5 ?
I. n is odd and divisible by 9
II. n is even and divisible by 5

I.

Let say value of n is 9 which is divisible by 9.

So,$$n+5=9+5=14$$,10 is not a factor of 14.

But, if value of n is 45 which is also divisible by 9, gives $$n+5=45+5=50$$.

10 is a factor of 50.

So, from statement I ,we can not say that whether 10 is a factor n+5 or not.

II.

n is even and also divisible 5 , this statement is only possible when the last digit of the number is 0.

In that case 10 is never be a factor of n+5.

So, B is correct choice.