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: 6 / 9 of the population of the country of venezia lives in montague province, while the rest lives in capulet province. in the upcoming election, 80 % of montague residents support romeo, while 70 % of capulet residents support juliet; each resident of venezia supports exactly one of these two candidates. rounded if necessary to the nearest percent, the probability that a juliet supporter chosen at random resides in capulet is
Options: a. 64 %, b. 41 %, c. 45 %, d. 72 %, e. 78 %
[EX A]: a

[EX Q]: Problem: the l. c. m of two numbers is 495 and their h. c. f is 5. if the sum of the numbers is 100, then their difference is
Options: a. 19, b. 10, c. 28, d. 27, e. 29
[EX A]: b

[EX Q]: Problem: if a, b, and c are positive real numbers such that a ( b + c. = 152, b ( c + a. = 162, and c ( a + b. = 170, then abc is
Options: a. a. 672, b. b. 688, c. c. 704, d. d. 720, e. e. 750
[EX A]:
d