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 units digit of 32 ! + 50 ! + 4 ! + 4 ! ?
Options: a. 0, b. 2, c. 4, d. 6, e. 8

A: e
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Q: Problem: set s consists of integers { 7, 8, 10, 12, 13 }. if integer n is included in the set, the average ( arithmetic mean ) of set s will increase by 10 %. what is the value of integer n ?
Options: a. 10, b. 12, c. 16, d. 22, e. 24

A: c
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Q: Problem: arjun started a business with rs. 10,000 and is joined afterwards by anoop with rs. 40, 000. after how many months did anoop join if the profits at the end of the year are divided equally ?
Options: a. 3, b. 4, c. 5, d. 6, e. 9

A:
e
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