I used the following approach

S1: \(x = \frac{a}{b}\) and \(b\) is odd.

This means, b is a factor of a. This also means

\(x = \frac{(n) * b}{b}\). Here n = some positive integer. =>

\(x = n\). if n is even, x is even.

If n is odd, x is odd. Two different answer for x. Insufficient.

S2: \(x = \frac{a}{b}\) and \(a\) is odd.

By same reasoning, this means, b is a factor of a.

\(x = \frac{(n) * b}{b}\). Here n = some positive integer. =>

\(x = n\).

However, n cannot be odd even since a is odd. Hence, x = odd. Sufficient

Final Answer : B

Not sure if I am able to clearly convey what I intend to say.

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