Given a math problem with context and a question and 5 answer choices, the task is to provide the correct answer choice based on the problem. You must choose one of the given answer choices by letter: a, b, c, d, or e; anything else is invalid.

Q: Problem: what is the smallest number which, when increased by 7, is divisible by 8, 11, and 24 ?
Options: a. 264, b. 257, c. 269, d. 270, e. 282

A: b
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Q: Problem: if 7 a = 8 b and ab ≠ 0, what is the ratio of a / 8 to b / 7 ?
Options: a. 16 / 14, b. 8 / 7, c. 1, d. 7 / 8, e. 64 / 49

A: c
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Q: Problem: for all real numbers v, an operation is defined by the equation v * = v - v / 3. if ( v * ) * = 16, then v =
Options: a. 30, b. 33, c. 36, d. 39, e. 42

A:
c
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