There are certain rules to the mathematical operation of Odd and Even numbers.
The followings rules illustrate the point:
1) Odd + Odd = Even number
2) Odd x Odd = Odd number
3) Even + Even = Even number
4) Even x Even = Even number
5) Even x Odd = Even number
6) Even + Odd = Odd number
Though they are basic mathematical concepts, they may trick the mind when one is not careful.
It is a form of self-checking too.