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: p has $ 32 more than what q and r together would have had if both b and c had 1 / 6 of what p has. how much does p have ?
Options: a. $ 44, b. $ 48, c. $ 52, d. $ 56, e. $ 60
[EX A]: b

[EX Q]: Problem: if each participant of a chess tournament plays exactly one game with each of the remaining participants, then 276 games will be played during the tournament. find the number of participants.
Options: a. 20, b. 22, c. 24, d. 26, e. 28
[EX A]: c

[EX Q]: Problem: when 17 is divided by positive integer x, the remainder is 1. for how many values of x is this true ?
Options: a. 1, b. 2, c. 3, d. 4, e. 5
[EX A]:
d