BTGmoderatorDC wrote:If 7 < m < 11 and −2 < n < 5, then which of the following expresses the possible values of mn ?
A. −14 < mn < 35
B. −14 < mn < 55
C. −22 < mn < 35
D. −22 < mn < 55
E."‰5 < mn < 16
Source: Princeton Review
\[?\,\,:\,\,mn\,\,{\text{possibilities}}\]
\[\left\{ {n: - 2 < n < 5} \right\} = \left\{ {n: - 2 < n < 0} \right\} \cup \left\{ {n:0 \leqslant n < 5} \right\}\]
\[\left\{ \begin{gathered}
7 < m < 11 \hfill \\
0 \leqslant n < 5 \hfill \\
\end{gathered} \right.\,\,\,\,\,\,\, \Rightarrow \,\,0 \leqslant mn < 55\,\,\,\,\,\,\left( {\text{I}} \right)\]
\[\left\{ \begin{gathered}
7 < m < 11 \hfill \\
- 2 < n < 0 \hfill \\
\end{gathered} \right.\,\,\,\,\,\, \sim \,\,\,\,\,\,\,\left\{ \begin{gathered}
7 < m < 11 \hfill \\
0 < - n < 2 \hfill \\
\end{gathered} \right.\,\,\,\,\,\,\, \Rightarrow \,\,\,\,0 < - mn < 22\,\,\,\, \Rightarrow \,\,\,\, - 22 < mn < 0\,\,\,\,\,\,\left( {{\text{II}}} \right)\]
\[? = \left( {\text{I}} \right) \cup \left( {{\text{II}}} \right)\,\,\, \Rightarrow \,\,\, - 22 < mn < 55\]
This solution follows the notations and rationale taught in the GMATH method.
Regards,
Fabio.
