If r and s are positive integers, and r2 + r/s is an odd integer, which of the following cannot be even?	Select the correct option
A) 3r + 2s B) (r-1)(s+2) C) r^(s+1) + s^r D) D. r^3 +3 E) s^4 +4
r and s are positive integers.   r2+rsr2+rs is an odd integer. Since r2r2 is an integer, rsrs will also be an integer. So s is a factor of r.   To get an odd integer after adding two terms, one term must be odd and the other even.   Say r is even. Then r^2 is even. So r/s must be odd. This means that when we divide r by s, we are removing all the 2s that r has. So s must be even too. This is one possible case.   Say r is odd. Then r^2 is odd. So r/s must be even. But if you divide an odd integer by another integer, it will never become even because division takes away factors. It cannot introduce 2 as an additional factor. So r/s cannot be even. This case is not possible.   Hence, r and s both MUST BE EVEN.   In option (D), r^3 + 3 will be odd because Even + Odd = Odd. Hence option (D) can never be even.   ANSWER:D. r^3 +3
<result>D</result>
If r and s are positive integers, and r2 + r/s is an odd integer, which of the following cannot be even?