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## QuestionMathsClass 8

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 $$x$$.
(A) $$4$$

We know that the given number$$\overline { 64x 19 }$$is divisible by $$11$$.

A number is divisible by $$11$$ if and only if the difference between the sum of odd and even place digits is a multiple of $$11$$.

i.e., Sum of even placed digits Sum of odd placed digits $$= 0, 11, 22$$

$$(6 + x + 9) (7+1) = 0, 11, 22$$

$$x + 7$$ is a multiple of $$11$$

$$x + 7 = 11$$

Therefore, $$x = 4$$

Hence, the possible value of $$x$$ is $$4$$.