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: to deliver an order on time, a company has to make 25 parts a day. after making 25 parts per day for 3 days, the company started to produce 5 more parts per day, and by the last day of work 100 more parts than planned were produced. find how many parts the company made and how many days this took.
Options: a. 600, b. 500, c. 575, d. 655, e. 675
[EX A]: e

[EX Q]: Problem: the h. c. f. of two numbers is 30 and the other two factors of their l. c. m. are 15 and 12. the larger of the two numbers is
Options: a. 476, b. 399, c. 450, d. 322, e. none
[EX A]: c

[EX Q]: Problem: a prize of $ 1200 is to be distributed among 40 winners, each of whom must be awarded at least $ 40. if 2 / 5 of the prize will be distributed to 3 / 5 of the winners, what is the greatest possible individual award ?
Options: a. $ 100, b. $ 120, c. $ 280, d. $ 300, e. $ 360
[EX A]:
b