Answer
$a-c$ is odd.
Work Step by Step
Since $a-b$ is odd and $b-c$ is even and odd+even=odd, adding the two to yield $a-c$ results in an odd number.
You can help us out by revising, improving and updating this answer.
Update this answerAfter you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.