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0ltpltqltr {:("Quantity A",,"Quantity ...

`0ltpltqltr`
`{:("Quantity A",,"Quantity B"),((q)/(r),"(?)",(r)/(q)):}`

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.

Text Solution

AI Generated Solution

The correct Answer is:
To solve the problem, we need to compare Quantity A and Quantity B based on the given conditions. Let's break it down step by step. ### Given: - \( p < q < r \) - \( p > 0 \) ### Step 1: Assign values to p, q, and r To make calculations easier, we can assign specific values to \( p \), \( q \), and \( r \) that satisfy the inequalities. - Let \( p = 1 \) (since \( p > 0 \)) - Since \( q > p \), let \( q = 2 \) - Since \( r > q \), let \( r = 4 \) ### Step 2: Calculate Quantity A Quantity A is defined as: \[ \text{Quantity A} = \frac{q}{r} \] Substituting the values of \( q \) and \( r \): \[ \text{Quantity A} = \frac{2}{4} = 0.5 \] ### Step 3: Calculate Quantity B Quantity B is defined as: \[ \text{Quantity B} = \frac{r}{q} \] Substituting the values of \( r \) and \( q \): \[ \text{Quantity B} = \frac{4}{2} = 2 \] ### Step 4: Compare Quantity A and Quantity B Now we compare the two quantities: - Quantity A = 0.5 - Quantity B = 2 Since \( 2 > 0.5 \), we conclude that: \[ \text{Quantity B} > \text{Quantity A} \] ### Final Conclusion The correct answer is that Quantity B is greater than Quantity A.
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