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.

Example Input: Problem: x does a work in 20 days. y does the same work in 40 days. in how many days they together will do the same work ?
Options: a. 10, b. 12, c. 20, d. 30, e. 13.33
Example Output: e

Example Input: Problem: how many integers v are prime numbers in the range 200 < v < 220 ?
Options: a. 1, b. 2, c. 3, d. 4, e. 5
Example Output: a

Example Input: Problem: in a circuit board factory, all circuit boards that pass a verification process are certified. every board that fails the verification process is indeed faulty, but 1 / 8 of those that pass are also faulty. approximately how many faulty circuit boards exist in a group of 3,200 circuit boards where 64 fail inspection ?
Options: a. 72, b. 192, c. 456, d. 256, e. 264
Example Output:
c