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A simple and ELEGANT way of checking if one number is divisble by 11 is to sum the alternate digits of this number.

sum of digits starting with 7 =  7 + 9 + 2 + 2 = 20
Sum of digits starting with 8 =  8 + 5 + 7 = 20

Difference between these two sums = 0
Rule is that if this difference is divisible by 11, then the original number is divisible by 11.
Hence it is divisible by 11

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