Question

The operation □ is defined as a □ b = a(b+1) - 3. 
Compare Quantity A and Quantity B. 
Quantity A: 1 □ 1 
Quantity B: 2 □ 0} 
 

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

Hint:

For problems with custom-defined operators, read the rule carefully. Substitute the numbers in the correct positions (the first number for 'a' and the second for 'b') and follow the order of operations (parentheses, multiplication, then subtraction).

Answer 1

The Correct Option is C

Step 1: Understanding the Concept:
This problem defines a new mathematical operation, □. To solve the problem, we must apply the given rule for this operation to evaluate both Quantity A and Quantity B, and then compare their values.
Step 2: Detailed Explanation:
The rule for the operation is given by: \(a \text{ □ } b = a(b+1) - 3\).
Calculate Quantity A:
For Quantity A, we have \(1 \text{ □ } 1\). Here, \(a=1\) and \(b=1\).
Substitute these values into the rule:
\[ \text{Quantity A} = 1(1+1) - 3 \] \[ \text{Quantity A} = 1(2) - 3 \] \[ \text{Quantity A} = 2 - 3 \] \[ \text{Quantity A} = -1 \] Calculate Quantity B:
For Quantity B, we have \(2 \text{ □ } 0\). Here, \(a=2\) and \(b=0\).
Substitute these values into the rule:
\[ \text{Quantity B} = 2(0+1) - 3 \] \[ \text{Quantity B} = 2(1) - 3 \] \[ \text{Quantity B} = 2 - 3 \] \[ \text{Quantity B} = -1 \] Compare the Quantities:
We found that Quantity A = -1 and Quantity B = -1.
Therefore, Quantity A and Quantity B are equal.
Step 3: Final Answer:
The two quantities are equal.