Final answer:
When N is an even number, dividing it by 2 gives an even result, and both N/2 + 1 and N/2 + 3 are always odd. Options A (N/2 + 1) and C (N/2 + 3) are correct answers.
Step-by-step explanation:
If N is an even number, we need to determine which of the following is always odd: A. N/2 +1 B. N/2+2 C. N/2+3 D. None of these. When you divide an even number by 2, the result is always an even number since even numbers are multiples of 2. Now, let's break down the options:
- A. If you add 1 to an even number, the result is always odd. Therefore, N/2 + 1 is always odd.
- B. Adding 2 to an even number results in another even number. So, N/2 + 2 is even.
- C. Adding 3 to an even number results in an odd number. However, since N/2 is even, N/2 + 3 is also odd.
- D. None of these is not a correct option because options A and C do result in odd numbers.
Thus, both options A and C are correct indicating that when N is an even number, both N/2 + 1 and N/2 + 3 are always odd.