instruction:
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.
question:
Problem: there are 15 balls in a jar. you take out 3 blue balls without putting them back inside, and now the probability of pulling out a blue ball is 1 / 3. how many blue balls were there in the beginning ?
Options: a. 12., b. 9., c. 8., d. 7., e. 6.
answer:
d

question:
Problem: four bells commence tolling together and toll at intervals of 2, 4, 6, 8 seconds respectively. in 18 minutes, how many times do they toll together ?
Options: a. 43, b. 44, c. 45, d. 46, e. 47
answer:
c

question:
Problem: how many different positive integers are factors of 20 ?
Options: a. 6, b. 8, c. 4, d. 10, e. 12
answer:
c