The least number more than 5000 which is divisible by 73 is

### Concept & Strategy Finding a number "more than" a base value that is perfectly divisible by a divisor is mathematically identical to finding the least number to *add* to that base value. We find the remainder of the base value, then calculate the difference needed to step up to the next perfect multiple. $$ \text{Required} = \text{Base} + (\text{Divisor} - \text{Remainder}) $$ ### Step-by-Step Solution * **Step 1:** Set up long division for $5000 \div 73$. * **Step 2:** Execute the division steps. $500 \div 73 \approx 6$. ($73 \times 6 = 438$) Remainder $= 500 - 438 = 62$. Bring down the $0$ to make $620$. $620 \div 73 \approx 8$. ($73 \times 8 = 584$) Remainder $= 620 - 584 = 36$. * **Step 3:** Calculate the amount required to reach the next multiple. Amount to add $= \text{Divisor} - \text{Remainder}$ Amount to add $= 73 - 36 = 37$. * **Step 4:** Add this amount to the original base. $5000 + 37 = 5037$. ### Exam Strategy & Shortcut **Approximation via Multiplication:** Rather than performing long division, use base-10 estimations. We need a multiple of $73$ near $5000$. $73 \times 100 = 7300$ (Too high) $73 \times 50 = 3650$ (Too low) Let's try $73 \times 70 = 5110$. $5110$ is very close to $5000$. Now, step backward by subtracting $73$ to find the first multiple just above $5000$. $5110 - 73 = 5037$. This matches option (b) directly. This method is often faster and less prone to subtraction errors than standard long division. ### Common Pitfall Students often subtract the remainder directly from the base number ($5000 - 36 = 4964$). While $4964$ is perfectly divisible by $73$, the question explicitly asks for a number *more than* $5000$. Subtracting drops you into the range below the target base. ### Final Answer **Therefore, the correct answer is 5037.**