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If xy ≠ 0, what is the value of x?

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Source: — Data Sufficiency |
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by fskilnik@GMATH » Thu Sep 20, 2018 6:03 pm
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.
Fabio Skilnik :: GMATH method creator ( Math for the GMAT)
English-speakers :: https://www.gmath.net
Portuguese-speakers :: https://www.gmath.com.br
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by Jay@ManhattanReview » Fri Sep 21, 2018 11:26 pm
BTGmoderatorDC wrote:If xy ≠ 0, what is the value of x?

(1) yx^2 + 4xy + 4y = 0
(2) y = 6

OA A

Source: Veritas Prep
Given that xy ≠ 0, we have neither x nor y is equal to 0.

Let's take each statement one by one.

(1) yx^2 + 4xy + 4y = 0

=> y(x^2 + 4x + 4) = 0
x^2 + 4x + 4) = 0/y
x^2 + 4x + 4 = 0; we know that y ≠ 0
=> (x + 2)^2 = 0

x = -2. Sufficient.

(2) y = 6

Certainly insufficient.

The correct answer: A

Hope this helps!

-Jay
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