$(800 \div 64) \times (1296 \div 36) = x$

Concept & Strategy This question tests the simplification of bracketed division operations followed by multiplication (BODMAS). Recognizing perfect squares makes the second bracket much faster to solve. Step-by-Step Solution * The given expression is: $$(800 \div 64) \times (1296 \div 36) = x$$ * Simplify the first bracket by writing it as a fraction and reducing: $$\frac{800}{64} = \frac{100 \times 8}{8 \times 8} = \frac{100}{8} = 12.5$$ * Simplify the second bracket. Notice that $1296$ is the square of $36$ ($36 \times 36 = 1296$): $$\frac{1296}{36} = 36$$ * Multiply the simplified terms together: $$x = 12.5 \times 36$$ * To calculate this easily, treat $12.5$ as $\frac{100}{8}$: $$x = \frac{100}{8} \times 36$$ $$x = 100 \times \frac{36}{8}$$ $$x = 100 \times 4.5$$ $$x = 450$$ * Review the given options: (a) $420$, (b) $460$, (c) $500$, (d) $540$. The calculated answer $450$ is not present. Exam Strategy & Shortcut Memorizing squares up to $40$ is crucial for banking exams; knowing $36^2 = 1296$ instantly turns the second bracket into $36$. For the first bracket, $800 \div 64 \rightarrow \frac{100}{8}$. Multiplying $\frac{100}{8}$ by $36$ gives $\frac{3600}{8}$, which easily divides into $450$. Checking the options immediately confirms that "None of these" is required. Common Pitfall Converting $\frac{100}{8}$ into the decimal $12.5$ and then performing long decimal multiplication by $36$ is slower and increases the chance of placing the decimal point in the wrong position. Always keep it as a fraction when multiplying by another whole number. Final Answer **Therefore, the correct answer is None of these.**