An even number can be divided by 2 evenly. An odd number will have a remainder of 1 when divided by 2. Even plus odd is odd.
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The sum of two odd numbers is always even.
Because the sum of two odd numbers is always even and the sum of that even number plus another odd number is always odd.
Any set of three odd integers must be odd - for example, 3 + 5 + 7 = 15. Similarly, the sum of an even number of odd integers added together will always be an even integer.
The sum of two odd numbers is always even.
all even numbers can be written in the form 2k where, k is an integer. all odd numbers can be written in the form 2j+1, where j is an integer. 2k + 2j + 1 = 2(k+j) + 1. You can see that this is in the form of an odd number. hence, the sum of an odd number and an even number is always odd. Test the theory. Pick any even and any odd number. Add them. The total will always be odd.