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.
--------
Question: 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

Answer: b


Question: Problem: virginia, adrienne, and dennis have taught history for a combined total of 96 years. if virginia has taught for 9 more years than adrienne and for 12 fewer years than dennis, for how many years has dennis taught ?
Options: a. 23, b. 32, c. 35, d. 41, e. 42

Answer: e


Question: Problem: what is the prime factors ’ number of 12 ?
Options: a. 2, b. 3, c. 4, d. 5, e. 6

Answer:
b