Data Sufficiency (DS) | Is (a^2 - b^2)/2 an odd integer?

(1) a-b is odd. We are not given that a/b are integers. If we assume that a/b are integers, then a-b will be odd if one of a/b is odd and the other is even. So in this case a^2 - b^2 will also be odd, and thus not divisible by 2. This would make (a^2 - b^2)/2 a decimal, and thus not an integer. So the answer to the question asked would be NO.

But it is also possible that a/b are not integers, rather decimals. Eg, a=4.5
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