Data Sufficiency

BTGmoderatorDC wrote:If xy ≠ 0, what is the value of x?

(1) yx^2 + 4xy + 4y = 0
(2) y = 6
Source: Veritas Prep

\[? = x\]
\[xy \ne 0\,\,\,\,\, \Rightarrow \,\,\,\,x \ne 0\,\,\,{\text{AND}}\,\,\,y \ne 0\,\,\,\left( * \right)\]
\[\left( 1 \right)\,\,\,0 = y\left( {{x^2} + 4x + 4} \right) = y{\left( {x + 2} \right)^2}\,\,\,\,\,\,\mathop \Rightarrow \limits^{\left( * \right)} \,\,\,\,{\left( {x + 2} \right)^2} = 0\,\,\,\,\, \Rightarrow \,\,\,x = - 2\,\,\,\,\, \Rightarrow \,\,\,{\text{SUFF}}.\]
\[\left( 2 \right)\,\,y = 6\,\,\,\left\{ \begin{gathered}
{\text{Take}}\,\,x = 1 \hfill \\
{\text{Take}}\,\,x = 2 \hfill \\
\end{gathered} \right.\,\,\,\,\,\, \Rightarrow \,\,\,\,\,{\text{INSUFF}}.\]

This solution follows the notations and rationale taught in the GMATH method.

Regards,
Fabio.