#### Question

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

#### Solution

\[\text{ Sum of the digits at odd places }= 3 + 2 = 5\]

Sum of the digit at even place = x

\[ \therefore\text{ Sum of the digit at even place - Sum of the digits at odd places }= (x - 5)\]

\[ \because (x - 5) \text{ must be multiple by }11 . \]

\[ \therefore\text{ Possible values of }(x - 5)\text{ are }0, 11, 22, 33 . . . \]

\[\text{ But }x\text{ is a digit; therefore }x\text{ must be }0, 1 , 2, 3 . . . 9 . \]

\[ \therefore x - 5 = 0 \]

\[ \Rightarrow x = 5\]

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Solution If 3 X 2 is a Multiple of 11, Where X is a Digit, What is the Value of X? Concept: Games with Numbers.