If the 7-digit number 689K348 is divisible by 9, then find the value of K.

For divisibility by 9, the sum of digits must be divisible by 9.

Digits of $689K348$ are:

$6+8+9+K+3+4+8$

$=38+K$

Now, $38+K$ should be divisible by 9.

Nearest multiple of 9 after 38 is $45$

So,

$38+K=45$

$K=45-38=7$

$\therefore$ Correct Answer: 7