First we look at the 2 denominator.  In order for 
to end up being an integer the numerator  must
be divisible by 2, which means that the whole numerator  
must end up being an even integer.

Now we remember the rules for adding even and odd integers

1. even + even = even
2. even + odd = odd
3. odd + odd = even

We want  to end up an even integer.

Now since  is odd, in order for  to be an
even integer we must have the 3rd case.  That is, the only way 
to get an even integer for  is to add an odd integer 
to the odd integer 3.

Therefore the correct answer is E.

Edwin