Given that `a` and `b` are integers and `a + a^2 b^3` is odd, which one of the following statements is correct?

a and b are both odd
a and b are both even
a is even and b is odd
a is odd and b is even

Correct answer: a is odd and b is even

Solution

For `a + a^2 b^3` to be odd, the first term `a` must be odd; otherwise the sum would be even. Also, `a^2 b^3` must be even, which happens when `b` is even. Therefore `a` is odd and `b` is even.

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