`162 div [ 51 - { 29 - ( 9 - bar( 6 + 7 ) ) } ] = ? `

Options

A. 18
B. 14
C. 7
D. 9

Answer

To solve the expression \( 162 \div [ 51 - \{ 29 - ( 9 - \text{bar}( 6 + 7 ) ) \} ] \), we will follow the order of operations (parentheses, exponents, multiplication and division from left to right, addition and subtraction from left to right).

### Step-by-step Solution:

1. **Calculate the innermost expression**:
\[ 6 + 7 = 13 \]
So, we replace \(\text{bar}(6 + 7)\) with \(13\).

2. **Substitute back into the expression**:
\[ 162 \div [ 51 - \{ 29 - ( 9 - 13 ) \} ] \]

3. **Calculate \(9 - 13\)**:
\[ 9 - 13 = -4 \]
Now substitute this back:
\[ 162 \div [ 51 - \{ 29 - (-4) \} ] \]

4. **Calculate \(29 - (-4)\)**:
\[ 29 + 4 = 33 \]
Now substitute this back:
\[ 162 \div [ 51 - 33 ] \]

5. **Calculate \(51 - 33\)**:
\[ 51 - 33 = 18 \]
Now substitute this back:
\[ 162 \div 18 \]

6. **Perform the division**:
\[ 162 \div 18 = 9 \]

### Final Answer:
\[ \text{The answer is } 9. \]