Which one of the following numbers is divisible by 11?

### Concept & Strategy To determine if a number is divisible by 11, we use the alternating sum method. Find the sum of digits in the odd positions (1st, 3rd, 5th, etc.) and the sum of digits in the even positions (2nd, 4th, 6th, etc.). The number is divisible by 11 if the difference between these two sums is 0 or a multiple of 11. ### Step-by-Step Solution Let us test the options systematically: * **Option (a) 4823718:** Odd places sum: $8 + 7 + 2 + 4 = 21$ Even places sum: $1 + 3 + 8 = 12$ Difference: $21 - 12 = 9$ (Not a multiple of 11) * **Option (b) 4832718:** Odd places sum: $8 + 7 + 3 + 4 = 22$ Even places sum: $1 + 2 + 8 = 11$ Difference: $22 - 11 = 11$ (This is a multiple of 11) Since we found the correct answer, there is no need to fully calculate the rest during an exam, but for completion: * Option (c) yields a difference of 17. * Option (d) yields a difference of 19. ### Exam Strategy & Shortcut Instead of writing out separate addition equations, use a mental "running difference" technique moving from right to left (or left to right). For option (b): $8 - 1 + 7 - 2 + 3 - 8 + 4 = 7 + 5 - 5 + 4 = 11$. This keeps numbers small and prevents arithmetic errors when dealing with large totals. ### Common Pitfall The most frequent error is misaligning the odd and even positions, especially in numbers with repeating digits or similar sequences. Always double-check your initial grouping before adding. ### Final Answer Therefore, the correct answer is **4832718**.