Question

If x denotes the digit at hundreds place of the number $\overline{67x19}$ such that the number is divisible by 11. Find possible values of x.

• A. x = 5
• B. x = 4
• C. x = 7
• D. x = 2

Answer 1

The correct option is B

x = 4

$\because$ The number $\overline{67x19}$ is divisible by 11
$\therefore$ A number is divisible by 11, if the difference of the sum of its digits in odd places from the right side and sum of its digits in even places from the right side is divisible by 11.
$\therefore$ Difference of (9 + x + 6) and (1+7) is zero or divisible by 11
$\Rightarrow$ 15 + x- 8=0, or multiple of 11,
7 + x = 0 $\Rightarrow x=-7$, which is not possible.
$\therefore$ 7 + x = 11, 7 + x = 22 etc.
$\Rightarrow x=11-7=4,x=22-7$ $\Rightarrow$ x = 15 which is not a digit
$\therefore$ x = 4