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: points a, b, c, and d, in that order, lie on a line. if ab = 3 cm, ac = 4 cm, and bd = 8 cm, what is cd, in centimeters ?
Options: a. 7, b. 2, c. 3, d. 4, e. 5

Answer: a


Question: Problem: a rope of which a calf is tied is increased from 12 m to 23 m, how much additional grassy ground shall it graze ?
Options: a. 2989, b. 2789, c. 1210, d. 1288, e. 1211

Answer: c


Question: Problem: running at the same constant rate, 6 identical machines can produce a total of 270 bottles per minute. at this rate, how many bottles could 8 such machines produce in 4 minutes ?
Options: a. 648, b. 1800, c. 2700, d. 1440, e. none of these

Answer:
d