Max@Math Revolution wrote:[Math Revolution GMAT math practice question]
Is x>x/y?
1) y>1
2) xy>0
\[x\,\,\mathop > \limits^? \,\,\frac{x}{y}\]
\[\left( 1 \right)\,\,\,y > 1\,\,\,\left\{ \begin{gathered}
\,{\text{Take}}\,\,\left( {0,2} \right)\,\,\,\, \Rightarrow \,\,\,\left\langle {{\text{NO}}} \right\rangle \,\, \hfill \\
\,{\text{Take}}\,\,\left( {1,2} \right)\,\,\,\, \Rightarrow \,\,\,\left\langle {{\text{YES}}} \right\rangle \,\, \hfill \\
\end{gathered} \right.\]
\[\left( 2 \right)\,\,\,xy > 0\,\,\,\left\{ \begin{gathered}
\,{\text{Take}}\,\,\left( {1,2} \right)\,\,\,\, \Rightarrow \,\,\,\left\langle {{\text{YES}}} \right\rangle \hfill \\
\,{\text{Take}}\,\,\left( {1,1} \right)\,\,\,\, \Rightarrow \,\,\,\left\langle {{\text{NO}}} \right\rangle \,\,\,\, \hfill \\
\end{gathered} \right.\]
\[\left( {1 + 2} \right)\,\,\,\, \Rightarrow \,\,\,\,x,y\,\, > 0\,\,\,\]
\[x\,\,\mathop > \limits^? \,\,\frac{x}{y}\,\,\,\,\,\mathop \Leftrightarrow \limits^{:\,\,x\,\, > \,\,0} \,\,\,\,1\,\,\mathop > \limits^? \,\,\,\frac{1}{y}\,\,\,\,\,\mathop \Leftrightarrow \limits^{ \cdot \,\,y\,\, > \,\,0} \,\,\,\,y\,\,\mathop > \limits^? \,\,\,1\,\,\,\,\, \Rightarrow \,\,\,\,\,\,\left\langle {{\text{YES}}} \right\rangle \]
The correct answer is therefore [spoiler]__(C)______[/spoiler] .
This solution follows the notations and rationale taught in the GMATH method.
Regards,
Fabio.
