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Question
Without performing actual division, find the remainder when 928174653 is divided by 11.
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Solution
928174653 = A multiple of 11 + (Sum of its digits at odd places - Sum of its digits at even places)
928174653 = A multiple of 11 + {(9 + 8 + 7 + 6 + 3) - (2 + 1 + 4 + 5)}
928174653 = A multiple of 11 + (33 - 12)
928174653 = A multiple of 11 + 21
928174653 = A multiple of 11 + (11 x 1 + 10)
928174653 = A multiple of 11 + 10
Therefore, the remainder is 10.
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