Question

If \[\overline{{3x2}}\] is a multiple of 11, where x is a digit, what is the value of x?

Answer 1

\[\text{ Sum of the digits at odd places }= 3 + 2 = 5\]
Sum of the digit at even place = x
\[ \therefore\text{ Sum of the digit at even place - Sum of the digits at odd places }= (x - 5)\]
\[ \because (x - 5) \text{ must be multiple by }11 . \]
\[ \therefore\text{ Possible values of }(x - 5)\text{ are }0, 11, 22, 33 . . . \]
\[\text{ But }x\text{ is a digit; therefore }x\text{ must be }0, 1 , 2, 3 . . . 9 . \]
\[ \therefore x - 5 = 0 \]
\[ \Rightarrow x = 5\]