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: by selling 15 pencils for a rupee a man loses 20 %. how many for a rupee should he sell in order to gain 20 % ?
Options: a. 8, b. 7, c. 6, d. 4, e. 10

Output: e

Input: Consider Input: Problem: the denominator of a fraction is 7 greater than the numerator. if the numerator and the denominator are increased by 4, the resulting fraction is equal to 5 " 6. what is the value of the original fraction ?
Options: a. 23 / 30, b. 25 / 32, c. 31 / 38, d. 37 / 44, e. 47 / 54

Output: c

Input: Consider Input: Problem: if 4 xz + yw = 10 and xw + yz = 20, what is the value of the expression ( 2 x + y ) ( 2 z + w ) ?
Options: a. 9., b. 12., c. 15., d. 50., e. 18.
Output: d