Question

\( p, q, r, p, q, r, \) and \( s \) are four numbers such that \[ pq^2 - |q|>q^2r - |s|pq2 - |q|>q2r - |s| \quad \text{and} \quad |q|>|s| |q|>|s| \]

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

Hint:

When working with inequalities involving absolute values, focus on comparing the magnitudes of the variables involved.

Answer 1

The Correct Option is A

From the given conditions, we can infer that both expressions involve \( p, q, r, s \) in some form of inequalities. We have: \[ pq^2 - |q|>q^2r - |s| \] We can simplify this by focusing on the relationship between the values of \( q \) and \( s \). Since the expression \( |q|>|s| \) suggests that \( q \) is greater in magnitude than \( s \), we can deduce that the left side of the inequality involving \( q \) and \( p \) is greater than the right side involving \( r \). Thus, Quantity A (related to \( p \)) is greater than Quantity B (related to \( r \)).
Final Answer: \[ \boxed{\text{Quantity A is greater.}} \]