1. ab is odd
Implies, both a and b are odd numbers. (In case even one of them is even, the product would also be even.)
when both numbers are odd, then a/b will also be either a odd integer or a decimal number, but can never be even integer.
Hence A is sufficient to determine.
2. a+b is even
Either both a and b are odd, or both even.
We cannot conclude that a/b would be odd or even
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