Max@Math Revolution wrote:[Math Revolution GMAT math practice question]
Is x > y?
1) x+y > 2
2) x^2 < 2y
$$x\,\,\mathop > \limits^? \,\,y$$
$$\left( 1 \right){\kern 1pt} \,\,x + y\,\, > \,\,2\,\,\,\,\,\left\{ \matrix{
\,\,{\rm{Take}}\,\,\left( {x,y} \right) = \left( {0,3} \right)\,\,\,\, \Rightarrow \,\,\,\left\langle {{\rm{NO}}} \right\rangle \,\, \hfill \cr
\,\,{\rm{Take}}\,\,\left( {x,y} \right) = \left( {3,0} \right)\,\,\,\, \Rightarrow \,\,\,\left\langle {{\rm{YES}}} \right\rangle \hfill \cr} \right.$$
$$\left( 2 \right)\,\,{x^2} < 2y\,\,\,\left\{ \matrix{
\,\,\left( {{\mathop{\rm Re}\nolimits} } \right){\rm{Take}}\,\,\left( {x,y} \right) = \left( {0,3} \right)\,\,\,\, \Rightarrow \,\,\,\left\langle {{\rm{NO}}} \right\rangle \,\, \hfill \cr
\,\,{\rm{Take}}\,\,\left( {x,y} \right) = \left( {{1 \over 2},{1 \over 4}} \right)\,\,\,\, \Rightarrow \,\,\,\left\langle {{\rm{YES}}} \right\rangle \hfill \cr} \right.\,$$
$$\left( {1 + 2} \right)\,\,\,\,\left\{ \matrix{
\,\,\left( {{\mathop{\rm Re}\nolimits} } \right){\rm{Take}}\,\,\left( {x,y} \right) = \left( {0,3} \right)\,\,\,\, \Rightarrow \,\,\,\left\langle {{\rm{NO}}} \right\rangle \,\, \hfill \cr
\,\,{\rm{Take}}\,\,\left( {x,y} \right) = \left( {{3 \over 2},{4 \over 3}} \right)\,\,\,\, \Rightarrow \,\,\,\left\langle {{\rm{YES}}} \right\rangle \hfill \cr} \right.$$
The correct answer is (E).
This solution follows the notations and rationale taught in the GMATH method.
Regards,
Fabio. 
