$24.96^2 \div (34.11 \div 20.05) + 67.96 - 89.11 = x$

### Concept & Strategy This question is a classic test of **Approximation**. In banking and competitive exams, exact calculation of such convoluted decimals is mathematically punitive and entirely unnecessary. The strategy is to round every single term to its nearest whole number or highly compatible integer *before* performing any operations. ### Step-by-Step Solution **Calculation:** Step 1: Approximate all values to the nearest sensible integer. * $24.96 \approx 25$ * $34.11 \approx 34$ * $20.05 \approx 20$ * $67.96 \approx 68$ * $89.11 \approx 89$ Step 2: Rewrite the equation with approximated values. $$ 25^2 \div (34 \div 20) + 68 - 89 = x $$ Step 3: Solve using BODMAS. Focus on the division first. $$ 625 \div \left(\frac{34}{20}\right) + 68 - 89 $$ $$ 625 \times \left(\frac{20}{34}\right) + 68 - 89 $$ Step 4: Simplify the fraction block. $$ 625 \times \left(\frac{10}{17}\right) $$ Notice that $625 \div 17$ is roughly $36.7$ (since $17 \times 30 = 510$ and $17 \times 6 = 102$, $510+102 = 612$). So, $36.7 \times 10 \approx 367$. Step 5: Perform the final addition and subtraction. $$ 367 + 68 - 89 $$ $$ 435 - 89 = 346 $$ ### Exam Strategy & Shortcut **Fraction Scaling:** If doing $625 \times (\frac{10}{17})$ feels slow, you can quickly round the ratio itself. $34 \div 20 = 1.7$. So, $625 \div 1.7$. We know $17 \times 4 = 68$, so $625 \div 1.7$ is a little bit less than $680/1.7 = 400$. It is around 360-370. $370 + 68 - 89 = 349$. Looking at the options: 884, 346, 252, 424, 366. The only option solidly in this ballpark is 346. ### Common Pitfall The trap is attempting to calculate exact decimal values. Multiplying $24.96 \times 24.96$ will drain 3 minutes of your exam time and likely result in an arithmetic error, leading you to guess wildly. Always boldly round numbers in approximation questions. ### Final Answer **Therefore, the correct answer is 346.**