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Question

There is one number which is formed by writing one digit 6 times, such number is always divisible by:
(e.g., 0.111111,0.444444 etc)


A
7
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B
11
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C
13
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D
all of these
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Solution

The correct option is D all of these
Let the number is $$111111$$
A number is divisible by 7 if we double the last digit and subtract it from the remaining leading truncated number and  the result is divisible by 7
so in 111111$$11111-2=11109$$which is divisible by 7
so 111111 is also divisible by 7
A number is divisible by 11 if we subtract the sum of odd digit number with sum of even digit number, we get 0 or any number that is divisible by 11 
In 111111 $$(1+1+1)-(1+1+1)=0$$
so 111111 is divisible by 11
A number is divisible by 13 if add four times the last digit to the remaining leading truncated number and  the result is divisible by 13
in 111111$$11111+4=11115$$which is divisible by 13
so 111111 is also divisible by 13
Hence any number like$$ 555555=5(111111)$$
is also divisible by 7,11,13 
So option D is answer

Mathematics

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