Question

If $a * b$ denote the bigger among a and b and $a \cdot b = a + b + 3(a*b)$, then $4 \cdot 7$ is equal to

• A. $4$
• B. $31$
• C. $10$
• D. $8$

Hint:

Follow the definition carefully.

Answer 1

The Correct Option is B

Given the operations defined as follows:

• \(a * b\) denotes the bigger among \(a\) and \(b\).
• The operation \(a \cdot b\) is defined as \(a + b + 3(a * b)\).

We need to calculate \(4 \cdot 7\) using these definitions.

1. First, determine \(4 * 7\), which is the bigger of 4 and 7. Since 7 is larger, \(4 * 7 = 7\).
2. Now use the formula for \(a \cdot b\):

\(4 \cdot 7 = 4 + 7 + 3 \times (4 * 7)\)

Substituting \(4 * 7 = 7\) into the expression:

\(4 \cdot 7 = 4 + 7 + 3 \times 7\)

Calculate each part:

• \(4 + 7 = 11\)
• \(3 \times 7 = 21\)

1. The final result is \(32\).

Therefore, the answer is \(32\).