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Playing with Numbers — Maths STD 8 — Question

Maharashtra BoardEnglish MediumSTD 8MathsPlaying with Numbers2 Marks
Question
Without performing actual division, find the remainder when 928174653 is divided by 11.
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Answer

Let n = 928174653
= A multiple of 11 + (9 + 8 + 7 + 6 + 3) - (2 + 1 + 4 + 5)
= A multiple of 11 + 33 - 12
= A multiple of 11 + 21
= A multiple of 11 + 11 + 10
= A multiple of 11 + 10
$\therefore$ Remainder = 10

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