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Question

If $${3x2}$$ is a multiple of $$11$$, where $$x$$ is a digit, what is the value of $$x$$?


Solution

The alternating sum of the of digits of a number divisible by $$11$$ are in multiples of 11 
i.e, sum of the even places subtracted from sum of odd places will be in multiples of 11
For $$3x2,$$ sum of the even places $$=x,$$
Sum of the odd places $$= 3+2=5$$ 
So, $$5-x = 11n,$$ 
At $$n = 0 \Rightarrow 5-x = 0,$$ 
$$\therefore x = 5$$

Mathematics

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