If r and s are positive integers, and r^2 + r/s is an odd integer, which of the following cannot be even?
Choose the correct choice from the following choices.
A) 3r + 2s
B) (r-1)(s+2)
C) r^(s+1) + s^r
D) r^3 +3
E) s^4 +4
Given: r and s are positive integers, and r2r2 + r/s is an odd integer   What are some "nice" values that make this true?   How about r = 2 and s = 2. We get: 2222 + 2/2 = 4 + 1= 
<gadget id="calculator">4 + 1</gadget>
<output>5</output>
5, which IS an odd integer   Great, now let's plug r= 2 and s = 2 into each answer choice.   A. 3(2) + 2(2) = 10, which is even. so ELIMINATE A   B. (2 - 1)(2 + 2) = 4, which is even. so ELIMINATE B   C. 2^(2+1) + 2^2 = 12, which is even. so ELIMINATE C   D. 23+323+3 = 11, which is odd. so KEEP D for now   E. 24+424+4 = 20, which is even. so ELIMINATE E   By the process of elimination, the answer must be r^3 +3
<result>D</result>
If r and s are positive integers, and r^2 + r/s is an odd integer, which of the following cannot be even?