If `x div y` yields an odd integer, what is x?

Answer

To solve the problem, we need to analyze the condition given: `x div y` yields an odd integer. This means that when we divide `x` by `y`, the result is an odd integer. Let's break down the steps to understand what `x` could be.

### Step-by-Step Solution:

1. **Understanding the Division**:
- The expression `x div y` means `x` divided by `y`. We denote this as \( \frac{x}{y} \).
- We know that \( \frac{x}{y} \) is an odd integer.

2. **Setting Up the Equation**:
- Let’s denote the odd integer result as \( k \). Therefore, we can write:
\[ \frac{x}{y} = k \]
- Rearranging gives us:
\[ x = k \cdot y \]

3. **Analyzing the Odd Integer**:
- Since \( k \) is an odd integer, it can be represented as \( k = 2m + 1 \) where \( m \) is an integer (this is the general form of odd integers).
- Substituting this back into our equation for \( x \):
\[ x = (2m + 1) \cdot y \]

4. **Considering Values of y**:
- The value of \( y \) can be either odd or even.
- If \( y \) is odd, then \( x \) will also be odd because the product of two odd numbers is odd.
- If \( y \) is even, then \( x \) will be even because the product of an odd number and an even number is even.

5. **Conclusion**:
- From the above analysis, we can conclude that `x` can either be odd or even depending on the value of `y`.
- Therefore, we cannot definitively determine the exact value of `x` based solely on the information given.

### Final Answer:
Thus, `x` cannot be determined uniquely from the information that `x div y` yields an odd integer.