Step 1: Simplify \( p = 4 \times 6 \times 11 \times n = 264n \).
Step 2: Find remainder when divided by 5. \( 264n \div 5 \). Since \( 264 \equiv 4 \pmod{5} \), remainder = \( 4n \pmod{5} \), varies with \( n \). Could be 0,1,2,3,4.
Step 3: Divide by 33. Since \( 264n = 33 \times 8n \), always divisible by 33, remainder = 0.
Step 4: Compare: Quantity B = 0 always. Quantity A varies but is nonnegative and can be \(>0 \). So Quantity \(A ≥0 \), Quantity B =0. But for \( n \) not multiple of 5, \(A>B \).
Final Answer: \[ \boxed{\text{Quantity A is greater (except when \( n \) multiple of 5, then equal)}} \]
If the operation \( x \, ¤, y = 4x - y^2 \), and \( x, y \) are positive integers, which of the following cannot produce an odd value?
The total amount of Judy’s water bill for the last quarter of the year was \(\$ 40.50\). The bill consisted of a fixed charge of \(\$ 13.50\) plus a charge of \(\$ 0.0075\) per gallon for the water used in the quarter. For how many gallons of water was Judy charged for the quarter?