question_answer

If \[51x\text{ }3\]is a multiple of 9, where x is a digit, then that is the value of x?

Answer:

We have, the sum of the digits of 51x 3=5+l+x+3=9+x

Since, 51x 3 is divisible by 9.

\[\therefore \] (9+x) must be divisible by 9.

\[\therefore \](9 + x) must be equal to 0 or 9 or 18 or 27 or...

But x is a digit, then

\[9+x=9\Rightarrow x=0\]

\[9+x=18\Rightarrow x=9\]

\[x=27\Rightarrow x=18,\]which is not possible.

\[\therefore \] The required value of x = 0 or 9.