Find the remainder when 711 + 7111 + 71111 is divided by 8.
Solution
Correct Answer: Option D
When, 7 is divided by 8 then remainder = 7
When, 72 is divided by 8 then remainder = 1
When, 73 is divided by 8 then remainder = 7
When, 74 is divided by 8 then remainder = 1
Odd exponents give remainder = 7
Even exponents give remainder = 1
In 1st term, exponent is 11, which is odd so remainder = 7
In 2nd term, exponent is 111, which is also odd so remainder = 7
In 3rd term, exponent is 1111, which is odd so remainder = 7
So, (711 + 7111 + 71111) mod 8 = (7 + 7 + 7) mod 8 = 21 mod 8 = 5
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