Question
The unit digit in the expression written as {(348)216 + (579)135 + (642)227} is:
Solution
Cyclicity of ‘8’ = 4 i.e. 8, 4, 2 and 6
Cyclicity of ‘9’ = 2 i.e. 9 and 1
Cyclicity of ‘2’ = 4 i.e. 2, 4, 8 and 6
Unit digit of (348)216 = unit digit of 8216 = unit digit of 8(54 × 4) = 6
Unit digit of (579)135 = unit digit of 9135 = unit digit of 9(67 × 2 + 1) = 9
Unit digit of (642)227 = unit digit of 2227 = unit digit of 2(56 × 4 + 3) = unit digit of 23 = 8
Required unit digit = Unit place value of (6 + 9 + 8) = 3
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