Let us say two odd numbers are p and q. And we know that sum of two odd numbers is always even. But the average of two odd numbers is not always even.
Average of p and q = (p+q)/2 = even number/2 = odd or even.
Two examples will make it clear.
e.g. Average of 5 and 1 = (5+1)/2 = 6/2 = 3(odd number)
Average of 3 and 5 = (3+5)/2 = 8/2 = 4(even number)
So, average of two odd numbers can be even or odd.
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The product of two odd numbers is always odd.
The sum of two odd numbers is always even.
There are no two consecutive odd numbers.
The sum of two whole numbers is odd when one but not both of them is odd.
Multiply two odd numbers Add an even and an odd Subtract an odd and an even