Can you tell if sum of several numbers will be even or odd?

Yes, all you have to do is to count the number of ODD numbers in the list. If it is odd, then the sum will be odd; if even, so will the sum.

Knowing this can help you run a quick validity check when you sum up a list of numbers.

(The method works because:

a) the sum of two even numbers is even, and

b) the sum pf two odd numbers is even, but

c) the sum of an even number and an odd number is odd.

Hence, if you only determine whether there are any unpaired odd numbers, you know the answer.)