Question

Fill in the blank with smallest digit to make $701.....9308$ divisible by $11.$

Answer 1

Since as we know that 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 $701.....9308$ divisible by $11.$

In $701x9308$ , sum of all digits at odd place$=7+1+9+0=17$

Sum of all digits at even place $=0+x+3+8=11+x$

Difference of sum of all digits at odd place and even place $=17-11-x=6-x$

If $x=6$ then $6-6=0$ which is divisible by $11.$

Hence, the smallest digit to be placed is blank space $=6$ then digit $6$ to make $701.....9308$ divisible by $11.$