BTGmoderatorDC wrote:If x and y are positive, what is the value of y ?
(1) xy is the square of an integer.
(2) 600 percent of x equals 200 percent of y.
Source: Magoosh
\[x,y\,\, > 0\,\,\]
\[? = y\]
Let´s go straight to (1+2). Our BIFURCATION will guarantee that the correct answer is (E) immediately!
$$\left( {1 + 2} \right)\,\,\,\,\left\{ \matrix{
\,xy = {M^2}\,,\,\,M\,\,{\mathop{\rm int}} \hfill \cr
\,6x = 2y\,\,\, \Rightarrow \,\,\,y = 3x \hfill \cr} \right.\,\,\,\,\,\left( * \right)\,\,\,\,\,\,\,\,\,\left[ {\, \Rightarrow \,\,\,\,\,\,3{x^2} = {M^2}\,\,,\,\,\,M\,\,{\mathop{\rm int}} \,} \right]$$
$$\left\{ \matrix{
\,{\rm{Take}}\,\,\left( {x,y} \right) = \left( {\sqrt 3 ,3\sqrt 3 } \right)\,\,\,\, \Rightarrow \,\,\,\,\,\left( * \right)\,\,\,{\rm{ok}}\,\,\,\, \Rightarrow \,\,\,\,\,y = 3\sqrt 3 \,\,\, \hfill \cr
\,{\rm{Take}}\,\,\left( {x,y} \right) = \left( {2\sqrt 3 ,6\sqrt 3 } \right)\,\,\,\, \Rightarrow \,\,\,\,\,\left( * \right)\,\,\,{\rm{ok}}\,\,\,\, \Rightarrow \,\,\,\,\,y = 6\sqrt 3 \,\, \hfill \cr} \right.$$
This solution follows the notations and rationale taught in the GMATH method.
Regards,
Fabio.
