Solve $\left(\frac{18}{4}\right)^2 \times \left(\frac{455}{19}\right) \div \left(\frac{61}{799}\right) = x$

### Concept & Logic This is a classic approximation problem found in banking exams. The numbers are deliberately designed to be slightly off from clean multiples. The strategy is to round the tricky fractions to the nearest whole numbers or simple ratios to execute the calculation quickly. ### Step-by-Step Solution * **Step 1:** Simplify the first term. * $\frac{18}{4} = 4.5$. * $(4.5)^2 = 20.25$. * **Step 2:** Approximate the second term. * Notice that $19 \cdot 24 = 456$. * Therefore, $\frac{455}{19}$ is extremely close to $\frac{456}{19} = 24$. * **Step 3:** Approximate the third term (the divisor). * Notice that $61 \cdot 13 = 793$. So $\frac{799}{61}$ is slightly more than $13$. * Alternatively, for an easier mental division inversion, $\frac{61}{799} \approx \frac{60}{800} = \frac{3}{40}$. * Let's use the exact inversion: $\div \left(\frac{61}{799}\right)$ becomes $\cdot \left(\frac{799}{61}\right)$. * As established, $\frac{799}{61} \approx 13.1$. * **Step 4:** Multiply the approximated values together. * $x \approx 20.25 \cdot 24 \cdot 13.1$ * $20.25 \cdot 24 = 486$. (Calculated easily as $20 \cdot 24 = 480$, and $0.25 \cdot 24 = 6$). * $486 \cdot 13.1 \approx 486 \cdot 13 + 486 \cdot 0.1$ * $486 \cdot 13 = 6318$. * $6318 + 48.6 = 6366.6$. * The closest option provided by the exam setter for this approximation is $6350$. (If calculated without any rounding, the exact value is roughly $6351.6$). ### Exam Strategy & Shortcut In approximation questions with options spread $30$-$50$ units apart, immediately replace ugly fractions with their closest clean integers. $\frac{455}{19} \rightarrow 24$. For $\frac{799}{61}$, flip it to multiplication: $\frac{800}{61} \approx 13.1$. Then execute $20.25 \cdot 24 \cdot 13.1$. ### Common Pitfall The biggest mistake is trying to calculate the exact decimal values of $\frac{455}{19}$ and $\frac{61}{799}$. This will consume minutes of your time and likely lead to an arithmetic error, whereas approximation takes seconds. ### Final Answer **Therefore, the correct answer is 6350.**