Understand the Divisibility Rule of 11

A number is divisible by 11 if the difference between the sum of its digits at odd places and the sum of its digits at even places is either 0 or divisible by 11.

$\text{Diff} = |\text{Sum(Odd positions)} - \text{Sum(Even positions)}| = 0 \text{ or } 11k$

Test Option C ($9246864$)

Let's take the number $9246864$. Counting positions from right to left:

• Odd positions (1st, 3rd, 5th, 7th): $4 + 8 + 4 + 9 = 25$
• Even positions (2nd, 4th, 6th): $6 + 6 + 2 = 14$ Difference = $25 - 14 = 11$. Since 11 is divisible by 11, the number $9246864$ is divisible by 11.

$25 - 14 = 11 \implies \text{Divisible by } 11$

Verify Other Options

• Option A ($9248164$): Odd = $4+1+4+9 = 18$, Even = $6+8+2 = 16$, Difference = $18 - 16 = 2$ (Not divisible).
• Option B ($7247564$): Odd = $4+5+4+7 = 20$, Even = $6+7+2 = 15$, Difference = $20 - 15 = 5$ (Not divisible).
• Option D ($8245964$): Odd = $4+9+4+8 = 25$, Even = $6+5+2 = 13$, Difference = $25 - 13 = 12$ (Not divisible).

$9246864 \text{ is the only number meeting the criteria}$