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प्रश्न
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.
उत्तर
A number is divisible by 11, if the difference of the sum of its digits at odd places and the sum of its digits at even places is either 0 or a multiple of 11.
\[\text{ Sum of digits at odd places - Sum of digits at even places }\]
\[ = (6 + x + 9) - (7 + 1)\]
\[ = (15 + x) - 8 = x + 7\]
\[ \therefore x + 7 = 11\]
\[ \Rightarrow x = 4\]
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