Question

\( \oplus \) and \( \odot \) are two operators on numbers \( p \) and \( q \) such that 
\( p \odot q = p - q\) and \(p \oplus q = p \times q. \) 
Then, \( (9 \odot (6 \oplus 7)) \odot (7 \oplus (6 \odot 5)) = ? \)

• A. 40
• B. -26
• C. -33
• D. -40

Hint:

When dealing with composite operations, start by solving the innermost operations and proceed outward. Be careful with the order of operations and operator precedence.

Answer 1

The Correct Option is D

We are given two operators \( \oplus \) and \( \circ \), and we need to evaluate the expression: \[ (9 \circ (6 \oplus 7)) \circ (7 \oplus (6 \circ 5)). \] Step 1: Calculate the inner operations first.
First, calculate \( 6 \oplus 7 \), which is: \[ 6 \oplus 7 = 6 \times 7 = 42. \] Now calculate \( 6 \circ 5 \), which is: \[ 6 \circ 5 = 6 - 5 = 1. \] Step 2: Substitute the results into the main expression.
Substitute the results back into the original expression: \[ (9 \circ 42) \circ (7 \oplus 1). \] Now calculate \( 9 \circ 42 \), which is: \[ 9 \circ 42 = 9 - 42 = -33. \] Next, calculate \( 7 \oplus 1 \), which is: \[ 7 \oplus 1 = 7 \times 1 = 7. \] Step 3: Final calculation.
Now calculate \( -33 \circ 7 \), which is: \[ -33 \circ 7 = -33 - 7 = -40. \] Final Answer: \[ \boxed{-40}. \]