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: the number of the members of a club is more than 50 and less than 80. when 4 people sit at a table, other people exactly divided to 8 - people groups ( 8 people sit at a table. or 7 - people groups ( 7 people sit at a table.. if the members are divided to 9 - people groups, how many people will be left ?
Options: a. 0, b. 2, c. 4, d. 6, e. 8

A: d
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Q: Problem: two clocks are set correctly at 1 0 ' clock in the afternoon. one keeps correct time. the other gains 5 seconds per minute. that evening, when the fast clock shows 6: 20, what does the correct clock show ?
Options: a. 4.0, b. 5.0, c. 6.0, d. 7.2, e. 3.5

A:
c
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