`0ltpltqltr`
`{:("Quantity A",,"Quantity B"),({:(" "q-p),(" +q"),(" "bar(2q-p)):},"(?)",{:(r-q),(" -q"),(bar(r-2q)):}):}`

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 analyze the two quantities given:

**Quantity A:** \( q - p + q = 2q - p \)

**Quantity B:** \( r - q - q = r - 2q \)

Given the conditions \( 0 < p < q < r \), we will evaluate these quantities step by step.

### Step 1: Express Quantity A
We start with Quantity A:
\[ \text{Quantity A} = q - p + q = 2q - p \]

### Step 2: Express Quantity B
Next, we express Quantity B:
\[ \text{Quantity B} = r - q - q = r - 2q \]

### Step 3: Compare the Two Quantities
Now we need to compare \( 2q - p \) and \( r - 2q \).

To do this, we can rearrange the comparison:
\[ 2q - p \quad \text{and} \quad r - 2q \]
We want to see if \( 2q - p > r - 2q \), \( 2q - p < r - 2q \), or if they are equal.

### Step 4: Rearranging the Inequality
Rearranging gives us:
\[ 2q - p > r - 2q \implies 2q + 2q > r + p \implies 4q > r + p \]
\[ 2q - p < r - 2q \implies 2q + 2q < r + p \implies 4q < r + p \]

### Step 5: Analyze the Relationships
Given the constraints \( 0 < p < q < r \):
- If \( p \) is very small compared to \( r \), it is possible that \( 4q > r + p \).
- Conversely, if \( r \) is very large compared to \( q \), it could be that \( 4q < r + p \).

### Step 6: Conclusion
Since we have seen that depending on the values of \( p, q, \) and \( r \), either quantity A or quantity B can be greater, we conclude that we cannot definitively determine the relationship between the two quantities based on the information given.

Thus, the answer is:
**Option 4: The relationship cannot be determined from the information given.**