Question of the week 03-Dec-2017

The remainder we get after dividing 555.... (twenty such 5s) with 7 is
a) 2              b) 3              c) 5                d) 6

I don't mind even if you use google for ideas or calculator as i am sure that you mayn't find the question or answer 😃. I am cautious that i have given here a CGL level question. This question and technique to solve is part of my upcoming book and it is solvable in less than 10 seconds. Your answer only with a logical explanation is welcomed in the comments section.

Solution (25-Dec-17):

It is almost three weeks since i ask this question and only a peron or two was able to solve this question correct. Actual tip involved in this question is that Any six digit number that has only one repeated digit is always divisible by 7.
Ex: 111111 is divisible by 7 and hence 222222, 333333 etc.. are all divisible by 7.

So, 555.... (18 such 5s) is exactly divisible by 7 as there are three sets of such six digits. So, our required remainder can be obtained by dividing the remaining last two digits i.e. 55. So, Remainder of 55/7 = 6. This is well explained in my upcoming book. Stay tuned for more questions and related tips.