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# Let $m$ and $n$ denote the greatest and least positive three-digit multiples of 7, respectively. What is the value of $m + n$ ?

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Let $m$ and $n$ denote the greatest and least positive three-digit multiples of 7, respectively. What is the value of $m + n$ ?

RektTheNoob  Aug 13, 2017
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Let $$m$$ and $$n$$ denote the greatest and least positive three-digit multiples of 7, respectively.

What is the value of $$m + n$$ ?

$$\begin{array}{|rcll|} \hline m &=& 7\cdot \left \lfloor{ \frac{999}{7} }\right \rfloor{} \\ &=& 7\cdot 142 \\ &=& 994 \\\\ n &=& 7\cdot \left \lceil{ \frac{100}{7} }\right \rceil{} \\ &=& 7\cdot 15 \\ &=& 105 \\\\ m+n &=& 994 + 105 \\ &=& 1099 \\ \hline \end{array}$$

heureka  Aug 14, 2017

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