Question

Find the smallest digit that should be replaced at $*$ place in the number $1723*4$ so that the number is divisible by $11$.

Answer 1

Step 1

Divisibility by 11 : If the alternate numbers from right to left are added and when you subtract the first list of alternate numbers from the second list, the difference should be 0 or a multiple of 11.

Sum of the first list $=1+2+x=3+x$ $\left[Let*=x\right]$

Sum of the second list $=7+3+4=14$

Step 2

Now subtraction $=3+x-14=0$ [As we have to find the smallest number]
$$\begin{gathered} 3+x=14 \\ x=14-3 \\ x=11 \end{gathered}$$
Because the number is equal by $11$ we will subtract$11$ from the number.
$11-11=0$
Therefore, The smallest number is $0$.