Solve the following quantitative comparison problem by plugging in the number 0,1,2, -2, and `1//2` in that order - when possible.
`{:("Column A", -1 < x < 0,"Column B"),(x,,1//x):}`

Options

A. If column A is larger
B. If column B is larger
C. If the columns are equal
D. If there is not enough information to decide

Answer

To solve the quantitative comparison problem, we need to evaluate the expressions in Column A and Column B for values of \( x \) within the range \( -1 < x < 0 \). The expressions are:

- Column A: \( x \)
- Column B: \( \frac{1}{x} \)

We will plug in the values \( 0, 1, 2, -2, \) and \( \frac{1}{2} \) in that order, but we must remember that \( x \) must be in the range \( -1 < x < 0 \). Therefore, we can only use negative fractions within this range.

### Step-by-Step Solution:

1. **Identify valid values for \( x \)**:
Since \( x \) must be between -1 and 0, the only valid number to plug in from the given options is \( -\frac{1}{2} \).

2. **Plug in \( x = -\frac{1}{2} \)**:
- For Column A:
\[ x = -\frac{1}{2} \]
- For Column B:
\[ \frac{1}{x} = \frac{1}{-\frac{1}{2}} = -2 \]

3. **Compare the values**:
- Column A: \( -\frac{1}{2} \)
- Column B: \( -2 \)

Now we compare \( -\frac{1}{2} \) and \( -2 \). On the number line, \( -\frac{1}{2} \) is to the right of \( -2 \), which means:
\[ -\frac{1}{2} > -2 \]

4. **Conclusion**:
Since \( -\frac{1}{2} \) is greater than \( -2 \), we can conclude that:
\[ \text{Column A is greater than Column B} \]

### Final Answer:
Column A is greater than Column B.