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.

Ex Input:
Problem: 108 ã — 108 + 92 ã — 92 = ?
Options: a. 20120, b. 11500, c. 20128, d. 20660, e. 20228

Ex Output:
c


Ex Input:
Problem: for 2 consecutive yrs, my incomes are in the ratio of 4: 7 and expenses in the ratio of 3: 5. if my income in the 2 nd yr is rs. 42000 & my expenses in the first yr in rs. 23000, my total savings for the two - year is
Options: a. s. 8000, b. s. 9000, c. s. 9900, d. s. 9990, e. s. 10000

Ex Output:
a


Ex Input:
Problem: the function f ( n ) is defined as the product of all the consecutive positive integers between 3 and n ^ 2, inclusive, whereas the function g ( n ) is defined as the product of the squares of all the consecutive positive integers between 1 and n, inclusive. the exponent on 2 in the prime factorization of f ( 3 ) / g ( 3 ) is
Options: a. 1, b. 2, c. 3, d. 4, e. 5

Ex Output:

c