$(46351 - 36418 - 4505) \div x = 1357$

### Concept & Strategy This question evaluates your ability to resolve multi-term brackets following the BODMAS rule, followed by transposing variables in a division equation. Grouping numbers with the same sign simplifies the bracket resolution. $$ \text{If } \frac{A}{x} = B, \text{ then } x = \frac{A}{B} $$ ### Step-by-Step Solution * **Given:** The equation $(46351 - 36418 - 4505) \div x = 1357$. * **Step 1:** Simplify the expression inside the parentheses. Sum the negative numbers first to avoid sequential subtraction. $-(36418 + 4505) = -40923$ * **Step 2:** Subtract this sum from the primary positive number. $46351 - 40923 = 5428$ * **Step 3:** Substitute the resolved bracket back into the main equation. $5428 \div x = 1357$ * **Step 4:** Rearrange the equation to solve for $x$. $x = \frac{5428}{1357}$ * **Step 5:** Perform the division to find the final value. $x = 4$ ### Exam Strategy & Shortcut Use **Unit Digit Tracking** combined with mental math to solve this in seconds. 1. Find the unit digit of the bracket: $1 - 8 - 5$. Borrow to make it positive: $11 - 8 = 3$, and $3 - 5 \rightarrow 13 - 5 = 8$. The bracket evaluates to a number ending in $8$. 2. Set up the unit digit equation: $8 \div x = 7 \implies 8 = 7 \times x$. 3. What unit digit multiplied by $7$ yields a number ending in $8$? $7 \times 4 = 28$. So, $x$ must end in $4$. 4. Look at the options: only option (c) is $4$. Verify mentally: $1350 \times 4 \approx 5400$, which matches our magnitude. ### Common Pitfall Students often subtract sequentially ($46351 - 36418$, then subtract $4505$), which increases the chance of borrowing errors. Grouping the negatives ($36418 + 4505$) is structurally safer. ### Final Answer Therefore, the correct answer is **4**.