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It is an odd number.
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 even.
Count how many of the numbers are odd. If an odd number of them are odd, then their sum is odd. If an even number of them are odd, then their sum is even.
Any odd number can be written as an even number plus one. Any even number plus any other even number makes an even number. Add one makes an odd number. So an odd number plus an even number is always an odd number. Algebraically, any odd number can be written as 2a+ 1 where a is a whole number. Any even number can be written as 2b, where b is a whole number. Add them together, the sum is 2(a + b) + 1, which is odd.
If the number (count) of odd values to sum is odd, then the answer is odd.If the number (count) of odd values to sum is even, then the answer is even.