Question 479594
<pre>

  I. {{{(a + b)/2}}} NO, because {{{(3+7)/2}}} = {{{10/2}}} = 5, which is ODD  

 II. {{{ab - 1}}} YES, because an ODD times an ODD is an ODD, 
so ab is always ODD, and then when we subtract 1 from that ODD, 
we will always get an EVEN.

or algebraically,

(2m+1)(2n+1)-1 = 4mn+2m+2n+1-1 = 2(2mn+m+n) = which is EVEN.

III. {{{(ab + 1)/2}}}  NO, because {{{(3x7+1)/2=(21+1)/2=22/2}}} = 11, which is ODD

Therefore only II is always even.  Answer b. 

Edwin</pre>