Max@Math Revolution wrote:[GMAT math practice question]
xy=?
1) (x-2)^2 = -|y-3|
2) |x-2| +√( y-3) =0
$$? = xy$$
$$\left( 1 \right)\,\,\,{\left( {x - 2} \right)^2} = - \left| {y - 3} \right|\,\,\,\,\,\left( * \right)$$
$$\left. \matrix{
{\left( {x - 2} \right)^2} \ge 0 \hfill \cr
- \left| {y - 3} \right| \le 0\,\, \hfill \cr} \right\}\,\,\,\,\,\mathop \Rightarrow \limits^{\left( * \right)} \,\,\,\,\,\left\{ \matrix{
\,x - 2 = 0 \hfill \cr
\,y - 3 = 0 \hfill \cr} \right.\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\left( {x,y} \right) = \left( {2,3} \right)\,\,\,\,\,\, \Rightarrow \,\,\,\,\,{\rm{SUFF}}{\rm{.}}$$
$$\left( 2 \right)\,\,\,\left| {x - 2} \right| + \sqrt {y - 3} \,\, = 0\,\,\,\,\,\,\left( {**} \right)$$
$$\left. \matrix{
\left| {x - 2} \right| \ge 0 \hfill \cr
\sqrt {y - 3} \ge 0\,\, \hfill \cr} \right\}\,\,\,\,\,\mathop \Rightarrow \limits^{\left( {**} \right)} \,\,\,\,\,\left\{ \matrix{
\,x - 2 = 0 \hfill \cr
\,y - 3 = 0 \hfill \cr} \right.\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\left( {x,y} \right) = \left( {2,3} \right)\,\,\,\,\,\, \Rightarrow \,\,\,\,\,{\rm{SUFF}}{\rm{.}}$$
The correct answer is (D).
We follow the notations and rationale taught in the GMATH method.
Regards,
Fabio.
