SOLUTION: Which is the difference between sum of two 2-digit odd number and sum of two 2-digit even number. a)45 b)54 c)35 d)53

What you need to know are all the facts
about the results of operations with even 
and odd numbers.  They are:

even + even = even

even + odd = odd

odd + odd = even

even - even = even

even - odd = odd

odd - even = odd

odd - odd = even

even × even = even

even × odd = even

odd × odd = odd

You have here a case of this:

(odd + odd) - (even + even) =

We can replace "(odd + odd)" by "even"
and have this: 

       even - (even + even) =

And we can replace "(even + even)" by "even"
and have this:
                even - even =

Then we can replace "even - even" by "even",
and we end up with this:

                       even

So the answer has to be an even number.
Of the choices you have, which are 

a)45 b)54 c)35 d)53

only "b)54" is an even number.  So that is
the only possible choice.

There are lots of possibilities of that resulting in 54.
For instance, here are some:

(11 + 65) - (10 + 12) = 54

(67 + 29) - (28 + 14) = 54

(47 + 79) - (20 + 52) = 54

(99 + 97) - (98 + 44) = 54
 
Edwin