Evaluate: $(923 - 347) / x = 32$

### Concept & Logic This is a straightforward arithmetic equation relying on basic **Subtraction and Division**. The strategy is to resolve the brackets first as dictated by BODMAS, and then rearrange the resulting simple linear equation to isolate the unknown variable $x$. ### Step-by-Step Solution **Given:** $$ \frac{923 - 347}{x} = 32 $$ **Calculation:** Step 1: Evaluate the expression inside the parentheses. $$ 923 - 347 = 576 $$ The equation is now: $$ \frac{576}{x} = 32 $$ Step 2: Rearrange to solve for $x$. Multiply both sides by $x$ and divide by $32$: $$ x = \frac{576}{32} $$ Step 3: Perform the division. You can simplify by breaking it down: $32 \times 10 = 320$. Remaining: $576 - 320 = 256$. $32 \times 8 = 256$. Therefore, $10 + 8 = 18$. $$ x = 18 $$ ### Exam Strategy & Shortcut **Unit Digit Tracking:** Once you have $\frac{576}{x} = 32$, this means $32 \times x = 576$. Look purely at the unit digits. $2 \times (\text{unit digit of } x) = (\text{ends in } 6)$. What single digit multiplied by 2 gives a number ending in 6? It must be either 3 (since $2 \times 3 = 6$) or 8 (since $2 \times 8 = 16$). Look at the given options: 35, 20, 18, 15, 40. The only option ending in a 3 or an 8 is 18. You can select it immediately without actually dividing 576 by 32! ### Common Pitfall A common unforced error is messing up the initial subtraction due to carrying digits poorly. $923 - 347$ might be mistakenly calculated as $586$ if a student forgets to borrow properly from the tens and hundreds columns, which throws off the entire subsequent division. ### Final Answer **Therefore, the correct answer is 18.**