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",a < 0,"Column B"),(1//a,,a):}`

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 by substituting the given values in the order specified (0, 1, 2, -2, and 1/2), while keeping in mind that \( a < 0 \).

### Step-by-Step Solution:

1. **Identify the Columns:**
- Column A: \( \frac{1}{a} \)
- Column B: \( a \)

2. **Substituting \( a = 0 \):**
- Column A: \( \frac{1}{0} \) (undefined)
- Column B: \( 0 \)
- **Conclusion:** Not applicable since \( a \) cannot be 0.

3. **Substituting \( a = 1 \):**
- Column A: \( \frac{1}{1} = 1 \)
- Column B: \( 1 \)
- **Conclusion:** Both columns are equal.

4. **Substituting \( a = 2 \):**
- Column A: \( \frac{1}{2} = 0.5 \)
- Column B: \( 2 \)
- **Conclusion:** Column A (0.5) is less than Column B (2).

5. **Substituting \( a = -2 \):**
- Column A: \( \frac{1}{-2} = -0.5 \)
- Column B: \( -2 \)
- **Conclusion:** Column A (-0.5) is greater than Column B (-2).

6. **Substituting \( a = -\frac{1}{2} \):**
- Column A: \( \frac{1}{-\frac{1}{2}} = -2 \)
- Column B: \( -\frac{1}{2} \)
- **Conclusion:** Column A (-2) is less than Column B (-0.5).

### Summary of Results:
- For \( a = 1 \): Both columns are equal.
- For \( a = 2 \): Column A < Column B.
- For \( a = -2 \): Column A > Column B.
- For \( a = -\frac{1}{2} \): Column A < Column B.

### Final Conclusion:
Since we have different results depending on the values of \( a \) that we substituted, we cannot definitively say which column is larger overall. Therefore, the correct answer is that there is not enough information to decide.