Question 340872
{{{(x+3)/2}}} is an integer
<pre><b>
First we look at the 2 denominator.  In order for {{{(x+3)/2}}}
to end up being an integer the numerator {{{x+3}}} must
be divisible by 2, which means that the whole numerator {{{x+3}}} 
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 {{{x+3}}} to end up an even integer.

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

Therefore the correct answer is E.

Edwin</pre>