IMO E

E is correct. But why not B?

I think the answer is E.

If you just plug in an even integer you can easily eliminate all the options but B and E.

Option B -- 3x/2 +1 ,

Since we are dividing by an even integer and then adding 1 to it. This option would lead to an even integer. Try pluggin in 2 in place of x you'll know what exactly I mean.

Option E -- 3x^2/2 +1

Here even when we are diving by 2 we are still left with even integer which is multiplied by an odd integer i.e. 3, therefore result will always be even. Then odd integer 1 is added to the result.

Therefore for option E no matter what the value (even) of x is, the result will always be an odd integer.

Let me know if you still have any doubts.

Brilliant stuff.I got it.Thnx

The way I found the answer is by plugging in numbers. I don't remember which book I found it in, but the book says that when plugging in numbers, if 2 or more answers give the same result try differnt numbers until only 1 choice is correct. EX:

if x=4
b)7
e)73

if x=6
b)10
e)163 => therefore e is always odd