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.

Q: Problem: what is the greatest positive integer n such that 3 ^ n is a factor of 36 ^ 100 ?
Options: a. 100, b. 200, c. 300, d. 600, e. 900

A: b
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Q: Problem: what is the smallest number by which 2880 must be divided in order to make it into a perfect square ?
Options: a. 3, b. 4, c. 5, d. 6, e. 7

A: c
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Q: Problem: a motorcyclist goes from bombay to pune, a distance of 160 kms at an average of 32 kmph speed. another man starts from bombay by car 2 ½ hours after the first, and reaches pune ½ hour earlier. what is the ratio of the speed of the motorcycle and the car ?
Options: a. 1: 2, b. 2: 5, c. 1: 4, d. 1: 1, e. 1: 6

A:
b
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