Correct Option (D)
The problem states that n > 3, n is divisible by 3, and n is not divisible by 6. These conditions imply that n must be an odd multiple of 3. Examples of such numbers include 9, 15, 21, and so on. For the purpose of evaluating the options, we can use the smallest such integer, n = 9.
Evaluating option (D):
- 3n + 1 = 3(9) + 1 = 27 + 1 = 28.
- Since 28 is divisible by 4 (28 ÷ 4 = 7), option (D) is the correct answer.
Incorrect Options:
Using n = 9, we evaluate the other options:
- For option (A): 2n = 2(9) = 18. 18 is not divisible by 4.
- For option (B): 3n = 3(9) = 27. 27 is not divisible by 4.
- For option (C): 2n + 4 = 2(9) + 4 = 18 + 4 = 22. 22 is not divisible by 4.