Question

If x is a digit of the number $\overline{66784x}$ such that it is divisible by 9, find the possible values of x.

• A. 6
• B. 5
• C. 14
• D. 2

Answer 1

The correct option is B

5

$\because$ The number 66784x, is divisible by 9
$\therefore$ The sum of its digits will also be divisible by 9
$\Rightarrow$ 6+6+7+8+4+x is divisible by 9
$\Rightarrow$ 31+x is divisible by 9

Hence 31 + $x$ = 9 , 18 , 27,36,45 ..........

If 31 + $x$ = 9 then $x$ = -22

If 31 + $x$ = 18 then $x$ = -13

If 31 + $x$ = 27 then $x$ = -4

If 31 + $x$ = 36 then $x$ = 5

If 31 + $x$ = 45 then $x$ = 14
From the above , only possible value of x = 5

$\therefore$ x = 5