`altalt1ltbltc`
`{:("Quantity A","Quantity B"),((c^(2))/(a),(bc)/(ab)):}`

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 of comparing Quantity A and Quantity B, we will follow these steps:

### Step 1: Define the quantities
- **Quantity A:** \( \frac{c^2}{a} \)
- **Quantity B:** \( \frac{bc}{ab} \)

### Step 2: Substitute values for \( a \), \( b \), and \( c \)
Given the conditions:
- \( 0 < a < 1 \)
- \( 1 < b < c \)

We can choose:
- Let \( a = 0.5 \)
- Let \( b = 2 \)
- Let \( c = 3 \) (since \( c \) must be greater than \( b \))

### Step 3: Calculate Quantity A
Using the chosen values:
\[ \text{Quantity A} = \frac{c^2}{a} = \frac{3^2}{0.5} = \frac{9}{0.5} = 18 \]

### Step 4: Calculate Quantity B
Using the chosen values:
\[ \text{Quantity B} = \frac{bc}{ab} = \frac{2 \cdot 3}{0.5 \cdot 2} = \frac{6}{1} = 6 \]

### Step 5: Compare Quantity A and Quantity B
Now we compare the two quantities:
\[ \text{Quantity A} = 18 \quad \text{and} \quad \text{Quantity B} = 6 \]

Since \( 18 > 6 \), we conclude that:
\[ \text{Quantity A} > \text{Quantity B} \]

### Final Conclusion
Thus, Quantity A is greater than Quantity B.

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