Question

Fill in the blank with smallest digit to make $4...6837$ divisible by$11.$

Answer 1

Since as we know the difference between the sum of all digits at even or odd place is$0$ and multiple of $11.$

Let the smallest digit $x$ to make $4...6837$ divisible by $11.$

In $4x6837$ , sum of all digits at odd place$=4+6+3=13$

sum of all digits at even place $=x+8+7=x+15$

difference of sum of all digits at odd place and even place $x+15-13=x+2$

If $x=9$ then $9+2=11$ which is divisible by $11.$

Hence, the smallest digit to be placed in blank space is $9$ then the digit $9$ to make $4...6837$ divisible by $11.$