x and y are positive.
`{:("Quantity A","Quantity B"),(xy,(xy)^(2)):}`

Options

A. Quantity A is greater.
B. Quantity B is greater.
C. The two quantities are equal.
D. The relationship cannot be determined from the infromation given.

Answer

To solve the problem, we need to compare Quantity A and Quantity B, where:

- Quantity A = xy
- Quantity B = (xy)²

Given that x and y are positive numbers, we can analyze the relationship between these two quantities.

### Step-by-Step Solution:

1. **Understanding the quantities**:
- Quantity A is the product of x and y, denoted as xy.
- Quantity B is the square of the product of x and y, denoted as (xy)².

2. **Expressing Quantity B**:
- We can expand Quantity B:
\[ (xy)² = xy \cdot xy = x²y² \]

3. **Analyzing the relationship**:
- Since x and y are positive, we know that both xy and (xy)² are also positive.
- We want to compare xy and (xy)².

4. **Case 1**: Let’s assume specific values for x and y.
- Let x = 1 and y = 2.
- Then, Quantity A = xy = 1 * 2 = 2.
- Quantity B = (xy)² = (1 * 2)² = 2² = 4.
- Here, Quantity B (4) is greater than Quantity A (2).

5. **Case 2**: Let’s try different values for x and y.
- Let x = 1/2 and y = 1/4.
- Then, Quantity A = xy = (1/2) * (1/4) = 1/8.
- Quantity B = (xy)² = (1/8)² = 1/64.
- Here, Quantity A (1/8) is greater than Quantity B (1/64).

6. **Conclusion**:
- In the first case, Quantity B was greater than Quantity A.
- In the second case, Quantity A was greater than Quantity B.
- Since we have found instances where either quantity can be greater than the other, we conclude that the relationship between Quantity A and Quantity B cannot be determined from the given conditions.

### Final Answer:
The relationship between Quantity A and Quantity B cannot be determined.