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: the h. c. f. of two numbers is 30 and the other two factors of their l. c. m. are 15 and 12. the larger of the two numbers is
Options: a. 476, b. 399, c. 450, d. 322, e. none
Example Output: c

Example Input: Problem: how many positive integer solutions does the equation 8 x + 2 y = 100 have ?
Options: a. 50, b. 84, c. 16, d. 35, e. 14
Example Output: b

Example Input: Problem: in a group of cows and chickens, the number of legs was 12 more than twice the number of heads. the number of cows was :
Options: a. 6, b. 7, c. 10, d. 12, e. 14
Example Output:
a