$74844 \div x = 54 \times 63$

Concept & Formula This problem tests simplification and the relationship between multiplication and division. You need to simplify the right side of the equation and then isolate the divisor $x$. Step-by-Step Solution * The equation is: $$74844 \div x = 54 \times 63$$ * First, compute the product on the right-hand side (RHS): $$54 \times 63 = 3402$$ * Substitute this back into the equation: $$\frac{74844}{x} = 3402$$ * Rearrange the formula to solve for $x$: $$x = \frac{74844}{3402}$$ * Perform the final division. Notice that $3402 \times 20 = 68040$, so the answer is slightly more than $20$. * Let's test $22$: $$3402 \times 22 = 3402 \times (20 + 2) = 68040 + 6804 = 74844$$ * Thus, $x = 22$. Exam Strategy & Shortcut Use the unit digit concept. Let's look at the equation $\frac{74844}{x} = 54 \times 63$. The unit digit of the RHS ($54 \times 63$) is $4 \times 3 = 12$, so it ends in $2$. This means $74844 = x \times (\text{a number ending in } 2)$. The unit digit of the LHS is $4$. For $x \times 2$ to end in $4$, the unit digit of $x$ must be either $2$ or $7$. Looking at the options, only $22$ and $42$ end in $2$. By quickly estimating $\frac{74000}{3400} \approx 22$, we can confirm the answer is $22$ without doing full multiplication. Common Pitfall Students often waste time trying to divide $74844$ by $54$ and then by $63$ sequentially, which can be prone to calculation errors, rather than evaluating the RHS as a single block first. Final Answer **Therefore, the correct answer is 22.**