An even number
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Yes.
The sum of any two odd numbers is always even. This is because (a) any odd number can always be expressed as an even number plus 1, and (b) the sum of two even numbers is always even. So if X is even and Y is even then X+1 added to Y+1 will equal X+Y+2
5 odd numbers must always equal an odd number so can never equal 1000
Odd divided by even will always be a decimal. The answer will not be an integer.
Because the sum of two odd numbers is always even and the sum of that even number plus another odd number is always odd.