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 Q]: 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
[EX A]: b

[EX Q]: Problem: there are 7 pairs of socks and 2 socks are worn from that such that the pair of socks worn are not of the same pair. what is the number of pair that can be formed.
Options: a. 40, b. 49, c. 41, d. 56, e. 42
[EX A]: e

[EX Q]: Problem: a, b and c are partners. a receives 2 / 3 of profits, b and c dividing the remainder equally. a ' s income is increased by rs. 400 when the rate to profit rises from 5 to 7 percent. find the capital of c ?
Options: a. 3377, b. 2899, c. 5000, d. 2778, e. 1991
[EX A]:
c