Find the number which is nearest to 3105 and is exactly divisible by 21.

### Concept & Strategy To find the nearest divisible number, you must calculate both the nearest lower multiple (by subtracting the remainder) and the nearest upper multiple (by adding the difference between the divisor and remainder), then compare which is closer. ### Step-by-Step Solution - **Given:** Target number = 3105, Divisor = 21. - **Calculation / Deduction:** Divide 3105 by 21 to find the remainder. - $3105 \div 21$ gives a remainder of 18. - Option 1 (Subtract): Subtract the remainder to find the lower multiple: $3105 - 18 = 3087$. The distance is 18. - Option 2 (Add): Add $(\text{Divisor} - \text{Remainder})$ to find the upper multiple: $3105 + (21 - 18) = 3105 + 3 = 3108$. The distance is 3. - Comparing distances, 3 is strictly less than 18, so 3108 is nearer to 3105. ### Exam Strategy & Shortcut Compare the remainder to half of the divisor. If the remainder is greater than half the divisor ($18 > 10.5$), the *upper* multiple is closer, so add $(\text{Divisor} - \text{Remainder})$. If it is less, the *lower* multiple is closer, so subtract the remainder. ### Common Pitfall A frequent mistake is automatically subtracting the remainder and picking that number (3087) without checking if the next multiple is physically closer on the number line. Always evaluate both directions. ### Final Answer Therefore, the correct answer is 3108.