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If $x$ denotes the digit at hundreds place of the number $\overline{67x19}$ such that the number is divisible by 11. Find all possible values of $x$.
Given:
$x$ denotes the digit at hundreds place of the number $\overline{67x19}$ such that the number is divisible by 11.
To do:
We have to find all the possible values of $x$.
Solution:
The number $\overline{67x19}$ is divisible by 11.
This implies,
The difference of the sums of its alternate digits will be 0 or divisible by 11.
Therefore,
Difference of $(9 + x + 6)$ and $(1 + 7)$ is zero or divisible by 11.
$15+x-8 = 0$ or multiple of 11.
$7 + x = 0$
$x = -7$ which is not possible.
If $7 + x = 11$, then $x = 11-7=4$.
The possible value of $x$ is $4$.
Updated on: 10-Oct-2022
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