`119 div [ 22 - { 90 div ( 23 - 105 div bar(7 xx 3) ) } = ? `

Options

A. 7
B. 12
C. 3
D. 4

Answer

To solve the expression \( 119 \div [ 22 - \{ 90 \div ( 23 - 105 \div \text{bar}(7 \times 3) ) \} ] \), we will follow the order of operations (BODMAS/BIDMAS rules). Let's break it down step by step.

### Step 1: Calculate the value inside the bar
First, we need to calculate \( 7 \times 3 \):
\[ 7 \times 3 = 21 \]

### Step 2: Substitute the value back into the expression
Now, we substitute this back into the expression:
\[ 119 \div [ 22 - \{ 90 \div ( 23 - 105 \div 21 ) \} ] \]

### Step 3: Calculate \( 105 \div 21 \)
Next, we calculate \( 105 \div 21 \):
\[ 105 \div 21 = 5 \]

### Step 4: Substitute this value into the expression
Now, we substitute this value back into the expression:
\[ 119 \div [ 22 - \{ 90 \div ( 23 - 5 ) \} ] \]

### Step 5: Calculate \( 23 - 5 \)
Now, we calculate \( 23 - 5 \):
\[ 23 - 5 = 18 \]

### Step 6: Substitute this value into the expression
Now, we substitute this value back into the expression:
\[ 119 \div [ 22 - \{ 90 \div 18 \} ] \]

### Step 7: Calculate \( 90 \div 18 \)
Next, we calculate \( 90 \div 18 \):
\[ 90 \div 18 = 5 \]

### Step 8: Substitute this value into the expression
Now, we substitute this value back into the expression:
\[ 119 \div [ 22 - 5 ] \]

### Step 9: Calculate \( 22 - 5 \)
Now, we calculate \( 22 - 5 \):
\[ 22 - 5 = 17 \]

### Step 10: Substitute this value into the expression
Now, we substitute this value back into the expression:
\[ 119 \div 17 \]

### Step 11: Calculate \( 119 \div 17 \)
Finally, we calculate \( 119 \div 17 \):
\[ 119 \div 17 = 7 \]

### Final Answer
Thus, the final answer is:
\[ \boxed{7} \]