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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 + 21928174653= A multiple of 11 + (11 × 1 + 10)928174653= A multiple of 11 + 10Therefore, the remainder is 10.

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