Question

In 3*8071,replace (*) by the smallest number to make it divisible by 11.​

Answer 1

Answer. 6

(3+8+7)-(x+0+1)

Smallest value of x is 6 because (3+8+7)-(6+0+1)=18-7=11 which is the smallest factor of ll.

Answer 2

Let us try if filling the blank by one digit solves the problem.  Let that digit be x.  If it is not possible by a single digit then we take two digits later.

3*8071 be divisible by 11.  It means the sum of odd digits and the sum of even digits differ by a multiple of 11.

So  (3+7+1) - (*+8+0) = 11 * n  for some integer n

    11 - * + 8 = 11 * n 

     19 - * = 11 * n 

  the smallest value of * for which this happens is  * =6.

so  answer is 8 and the number is  368071.

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