If 1!+3!+5!+7!+...+199! is divided by 24, what is the remainder?
- A. 3
- B. 6
- C. 7 ✓
- D. 9
Correct Answer: C. 7
Explanation
For n \geq 4, n! is a multiple of 24. Therefore, 5!, 7!, ..., 199! are all perfectly divisible by 24. We only need to find the remainder of 1! + 3! = 1 + 6 = 7 when divided by 24, which is 7.
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