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Question 16

The three digit number $$XYZ$$ when divided by $$8$$, gives as quotient the two digit number $$ZX$$ and remainder $$Y$$. The number $$XYZ$$ is


Correct Answer: 435

Solution

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Write the number as $$100X+10Y+Z$$ and the quotient as $$10Z+X$$. The division condition gives $$100X+10Y+Z=8(10Z+X)+Y$$, hence $$92X+9Y=79Z$$. The only digit solution is $$X=4$$, $$Y=3$$, $$Z=5$$, so the number is $$435$$.

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