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: if n is a positive integer and n ^ 2 is divisible by 36, then the largest positive integer that must divide n is
Options: a. 6, b. 12, c. 24, d. 36, e. 48
[EX A]: a

[EX Q]: Problem: cathy and jim begin running at the same time and they start at the same place on a straight path. cathy runs at 10 miles per hour, and jim runs at 6 miles per hour. after 18 minutes, cathy stops to stretch. if it takes cathy 27 minutes to stretch and jim continues to run during this time, how many minutes will it take cathy to catch up to jim ?
Options: a. 20.5, b. 21.5, c. 22.5, d. 23.5, e. 24.5
[EX A]: c

[EX Q]: Problem: one night 17 percent of the female officers on a police force were on duty. if 204 police officers were on duty that night and half of these were female officers, how many female officers were on the police force ?
Options: a. 420, b. 480, c. 540, d. 600, e. 660
[EX A]:
d