The sum of an odd and even number is always odd because there's always one left over. Think of any odd number as being any even number plus one. If you add two even numbers, the answer is always even. If you add an even and an odd (plus one), the answer is always odd.
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The sum of two odd numbers or two even numbers is an even number. The sum of an odd number and an even number is an odd number.
Two odd numbers always sum to an even number. Always. Two even numbers always sum to an even number, and an odd number and an even number always sum to an odd number.
Odd
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No. No matter what you use, the sum of an odd number and an even number will always be odd.