If \(r\) and \(s\) are integers, is \(r^2+s\) even?

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If \(r\) and \(s\) are integers, is \(r^2+s\) even?

(1) The product of \(rs\) is odd.
(2) \(r\) is odd.

Answer: A

Source: GMAT Paper Tests

Junior | Next Rank: 30 Posts
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The product rs can be odd only when both r and s are odd.
In such a case, \(r^2\) + s would be even, as the sq. of an odd number added to an odd number would be an even number
Thus A is sufficient
2nd option only mentions r is odd and nothing about s. Not sufficient.

Correct answer is thus A.