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

 Dec 5, 2019
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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 \(\mathbf{137}\)

 

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 Dec 5, 2019

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