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: increasing the original price of a certain item by 25 percent and then increasing the new price by 30 percent is equivalent to increasing the original price by what percent ?
Options: a. 31.25, b. 37.5, c. 50.0, d. 52.5, e. 62.5

Output: e


Input: Consider Input: Problem: in n is a positive integer less than 200, and 14 n / 60 is an integer, then n has how many different positive prime factors s ?
Options: a. 2, b. 3, c. 5, d. 6, e. 8

Output: b


Input: Consider Input: Problem: if 2 ^ 5, 3 ^ 3, and 13 ^ 2 are all factors of the product of 936 and w where w is a positive integer, what is the smallest possible value of w ?
Options: a. 26, b. 39, c. 42, d. 65, e. 156


Output: e