The smallest 1-digit number to be added to the 6-digit number 649389 so that it is completely divisible by 11 is:

Correct option is C

Given:

Number: 649389

Divisor: 11

Formula Used:

A number is divisible by 11 if the difference between the sum of digits at odd places and the sum of digits at even places is 0 or a multiple of 11. 

Solution: 

Sum of odd digit = 9 + 3 + 4 = 16

Sum of even place digit = 8 + 9 + 6 = 23

difference = 23 - 16 = 7 not multiple of 11 or 0 

Observing the digits we can see that if we add 7 in unit digit . 

Number became 649396

Sum of odd digit = 6 + 3 + 4 = 13

Sum of even place digit = 9 + 9 + 6 = 24

Difference = 24 - 13 = 11 which makes the number divisible by 11 .

Thus, 7 is the smallest 1-digit number that makes the number divisible by 11.

Option (c) is right.