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 11For $$3x2,$$ 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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