Find the multiple of 11 in the following numbers.

### Concept & Formula The rule for divisibility by $11$ states that the difference between the sum of digits at odd positions and the sum of digits at even positions must be either $0$ or a multiple of $11$. ### Step-by-Step Solution Let us systematically test each option by applying the divisibility rule: * **Option (a) 112144:** Sum of digits at odd places: $1 + 2 + 4 = 7$ Sum of digits at even places: $1 + 1 + 4 = 6$ Difference: $7 - 6 = 1$ (Not divisible by $11$) * **Option (b) 447355:** Sum of digits at odd places: $4 + 7 + 5 = 16$ Sum of digits at even places: $4 + 3 + 5 = 12$ Difference: $16 - 12 = 4$ (Not divisible by $11$) * **Option (c) 869756:** Sum of digits at odd places: $8 + 9 + 5 = 22$ Sum of digits at even places: $6 + 7 + 6 = 19$ Difference: $22 - 19 = 3$ (Not divisible by $11$) * **Option (d) 978626:** Sum of digits at odd places: $9 + 8 + 2 = 19$ Sum of digits at even places: $7 + 6 + 6 = 19$ Difference: $19 - 19 = 0$ (Divisible by $11$) ### Exam Strategy & Shortcut Do not write out the sums during the exam. Mentally track a running total by adding and subtracting alternating digits from left to right. For option (d): $9 - 7 + 8 - 6 + 2 - 6 = 0$. Since the final result is $0$, it is perfectly divisible by $11$. ### Common Pitfall A common error is grouping adjacent pairs of digits instead of correctly identifying strictly alternating positions, which leads to incorrect sums and false conclusions. ### Final Answer Therefore, the correct answer is **978626**.