Question

Fill in the blank with smallest digit to make $92.....389$ 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 $92.....389$ divisible by $11.$

In $92x389$ , sum of all digits at odd place$=9+x+8=17+x$

sum of all digits at even place $=2+3+9=14$

difference of sum of all digits at odd place and even place $17+x-14=3+x$

If $x=8$ then $3+8=11$ which is divisible by $11.$

Hence, the smallest digit to be placed is blank space $=8$ then digit $8$ to make $928389$ divisible by $11.$