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.

Input: Consider 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

Output: b


Input: Consider Input: Problem: of the 20 members of a kitchen crew, 17 can use the meat - cutting machine, 18 can use the bread - slicing machine, and 15 can use both machines. if one member is chosen at random, what is the probability that the member chosen will be someone who can not use either machine ?
Options: a. 0, b. 1 / 10, c. 1 / 7, d. 1 / 4, e. 1 / 3

Output: a


Input: Consider Input: Problem: in an office, 50 percent of the workers have at least 5 years of service, and a total of 16 workers have at least 10 years of service. if 90 percent of the workers have fewer than 10 years of service, how many of the workers have at least 5 but fewer than 10 years of service ?
Options: a. 8, b. 64, c. 50, d. 144, e. 160


Output: a