Direction: In the question given below, if the given mathematical symbols are changed from '+' to '\div', '-' to '\times', '\div' to '-' and from '\times' to '+', then choose your answers form the following options. Solve $67 \times 119 + 17 - 27 \div 259 = x$

### Concept & Formula This problem requires evaluating an expression after performing character-based operator substitutions. Once the operators are replaced, evaluation must follow the standard **BODMAS** rule hierarchy: 1. **B**rackets 2. **O**rders (Powers/Roots) 3. **D**ivision / **M**ultiplication (left-to-right) 4. **A**ddition / **S**ubtraction (left-to-right) ### Step-by-Step Solution * **Given:** The original expression is $67 \times 119 + 17 - 27 \div 259$. * **Step 1:** Apply the symbol transformations: * $\times \rightarrow +$ * $+ \rightarrow \div$ * $- \rightarrow \times$ * $\div \rightarrow -$ The new expression becomes: $$67 + 119 \div 17 \times 27 - 259$$ * **Step 2:** Perform division according to BODMAS ($119 \div 17 = 7$): $$67 + 7 \times 27 - 259$$ * **Step 3:** Perform multiplication ($7 \times 27 = 189$): $$67 + 189 - 259$$ * **Step 4:** Perform addition ($67 + 189 = 256$): $$256 - 259$$ * **Step 5:** Complete the subtraction: $$-3$$ ### Exam Strategy & Shortcut **Rapid Substitution & Mental Division:** Write the operational signs directly above or below the original question to save time rewriting the digits. Immediately calculate $119 \div 17 = 7$. Next, evaluate $7 \times 27 = 189$. Finally, use units-digit tracking or quick rounding: $67 + 189 = 256$, and $256 - 259 = -3$. ### Common Pitfall * **Ignoring Order of Operations:** A frequent mistake is performing the calculations linearly from left to right (e.g., executing $67 + 119$ first). Always follow the mandatory BODMAS precedence table. ### Final Answer **Therefore, the correct answer is -3.**