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# help

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There exist digits A and B such that 30AB5 = 225*n.  Find all possible values of n.

Dec 5, 2019

#1
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There exist digits $$A$$ and $$B$$ such that $$30AB5 = 225*n$$

Find all possible values of $$n$$.

$$\mathbf{n_{\text{min}}}$$

$$\begin{array}{|rcll|} \hline \mathbf{n_{\text{min}}} &=& \dfrac{30005}{225} \\ &=& 133.3\bar{5} \\ &=& \mathbf{134} \\ \hline \end{array}$$

$$\mathbf{n_{\text{max}}}$$

$$\begin{array}{|rcll|} \hline \mathbf{n_{\text{max}}} &=& \dfrac{30995}{225} \\ &=& 137.7\bar{5} \\ &=& \mathbf{137} \\ \hline \end{array}$$

$$\begin{array}{|r|r|} \hline n & n\times225 \\ \hline 134 & 30150 \\ \color{red}135 & {\color{red}30}27{\color{red}5} \\ 136 & 30600 \\ \color{red}137 & {\color{red}30}82{\color{red}5} \\ \hline \end{array}$$

The possible values of $$n$$ are $$\mathbf{135}$$ and $$\mathbf{137}$$

Dec 5, 2019