If q and r are both odd numbers, which of the following must also be odd? Answers.
A) q – r  B) (q + r)^2  C) q(q + r)  D) (qr)^2  E) q/r
Since q and r are odd numbers we can put q and r as q=2*Q+1 and r=2*R+1, for some integers Q, R.   A. q-r2* +1= 
<gadget id="calculator">2* +1</gadget>
<output>2</output>
2*R+1, for some integers Q, R.   A. q-r=(2*Q+1)-(2*R+1)=2*(Q-R) ---&gt; must be an even number.   B. (q + r)^2 =(2Q+2R+2)^2= 4*(Q+R+1)^2 ---&gt; must be an even number.   C. q(q+r) = (2Q+1)(2Q+2R+2)= 2*(2Q+1)(Q+R+1) ---&gt; must be an even number.   D. (qr)^2 = ((2Q+1)(2R+1))^2 = (4QR +2Q +2R +1)^2   by putting 2QR+Q+R = T we have (2T+1)^2= 4T^2 + 4T +1=2(2T^2 +2T)+1 ---&gt; must be an odd number.   E. q/r cannot be an integer   The answer is, therefore, ((qr)^2)
<result>D</result>
If q and r are both odd numbers, which of the following must also be odd?