Question
Let x = (726)245 – (437)458 +
(333)335. What is the unit digit of x?Solution
Given, x = (726)245 – (437)458 + (333)335 Unit digit of 6n is always equal to 6 where ‘n’ is positive integer. Cyclicity of ‘7’ and ‘3’ is ‘4’ So, unit digit of (6)245 = 6 Unit digit of (437)458 = Unit digit of (7)458 = unit digit of 7(4 × 114 + 2) = unit digit of 72 = unit digit of 49 = 9 Unit digit of (333)335 = Unit digit of 3335 = unit digit of 7(4 × 83 + 3) = unit digit of 33 = unit digit of 27 = 7 Required answer = 6 – 9 + 7 = 4
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