Question

Fill in the blank with smallest digit to make $8.....9484$ 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 $8...9484$ divisible by $11.$

In $8x9484$ , sum of all digits at odd place$=8+9+8=25$

sum of all digits at even place $=x+4+4=8+x$

difference of sum of all digits at odd place and even place $=25-(8+x)=25-8-x=17-x$

If $x=6$ then $17-6=11$ which is divisible by $11.$

Hence, the smallest digit to be placed is a blank space $=6$ then the digit $6$ to make $869484$ divisible by $11.$