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# If X Denotes the Digit at Hundreds Place of the Number 67 X 19 Such that the Number is Divisible by 11. Find All Possible Values of X. - Mathematics

Sum

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.

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#### Solution

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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#### APPEARS IN

RD Sharma Class 8 Maths
Chapter 5 Playing with Numbers
Exercise 5.2 | Q 7 | Page 20
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