Anamika wants to form a positive odd integer Her number cannot be of the form_______.

Options

A. 8p+1
B. 8p + 5
C. 8p + 3
D. 8p + 6

Answer

To solve the problem, we need to determine which form cannot represent a positive odd integer. We will analyze the forms given in the options and identify which one results in an even number.

### Step-by-Step Solution:

1. **Understanding the Forms**:
The forms given in the question are:
- A) \(8p + 1\)
- B) \(8p + 5\)
- C) \(8p + 3\)
- D) \(8p + 6\)

2. **Identifying the Remainders**:
The expression \(8p + r\) represents numbers where \(r\) is the remainder when divided by 8. The possible values for \(r\) can be 0, 1, 2, 3, 4, 5, 6, or 7.

3. **Analyzing Each Option**:
- **Option A: \(8p + 1\)**:
- Here, \(8p\) is even (as it is a multiple of 8), and adding 1 makes it odd.
- **Option B: \(8p + 5\)**:
- Again, \(8p\) is even, and adding 5 makes it odd.
- **Option C: \(8p + 3\)**:
- \(8p\) is even, and adding 3 makes it odd.
- **Option D: \(8p + 6\)**:
- \(8p\) is even, and adding 6 also results in an even number.

4. **Conclusion**:
Since we are looking for a form that cannot represent a positive odd integer, we find that **Option D**: \(8p + 6\) is the only form that results in an even integer.

Thus, the answer is: **Anamika's number cannot be of the form \(8p + 6\)**.