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: if a certain coin is flipped, the probability that the coin will land heads is 1 / 2. if the coin is flipped 6 times, what is the probability that it will land heads up on the first 4 flips but not on the last 2 flips ?
Options: a. 1 / 8, b. 1 / 16, c. 1 / 32, d. 1 / 64, e. 1 / 128
answer:
d

question:
Problem: two trains travel in opposite directions at 36 kmph and 45 kmph and a man sitting in slower train passes the faster train in 8 seconds. the length of the faster train is
Options: a. 80 m, b. 100 m, c. 120 m, d. 180 m, e. 160 m
answer:
b

question:
Problem: a certain experimental mathematics program was tried out in 2 classes in each of 38 elementary schools and involved 44 teachers. each of the classes had 1 teacher and each of the teachers taught at least 1, but not more than 3, of the classes. if the number of teachers who taught 3 classes is n, then the least and greatest possible values of n, respectively, are
Options: a. 0 and 13, b. 0 and 14, c. 0 and 16, d. 1 and 9, e. 2 and 8
answer:
c