If xy ≠0, what is the value of x?
(1) yx^2 + 4xy + 4y = 0
(2) y = 6
OA A
Source: Veritas Prep
If xy ≠0, what is the value of x?
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\[? = x\]BTGmoderatorDC wrote:If xy ≠0, what is the value of x?
(1) yx^2 + 4xy + 4y = 0
(2) y = 6
Source: Veritas Prep
\[xy \ne 0\,\,\,\,\, \Rightarrow \,\,\,\,x \ne 0\,\,\,{\text{AND}}\,\,\,y \ne 0\,\,\,\left( * \right)\]
\[\left( 1 \right)\,\,\,0 = y\left( {{x^2} + 4x + 4} \right) = y{\left( {x + 2} \right)^2}\,\,\,\,\,\,\mathop \Rightarrow \limits^{\left( * \right)} \,\,\,\,{\left( {x + 2} \right)^2} = 0\,\,\,\,\, \Rightarrow \,\,\,x = - 2\,\,\,\,\, \Rightarrow \,\,\,{\text{SUFF}}.\]
\[\left( 2 \right)\,\,y = 6\,\,\,\left\{ \begin{gathered}
{\text{Take}}\,\,x = 1 \hfill \\
{\text{Take}}\,\,x = 2 \hfill \\
\end{gathered} \right.\,\,\,\,\,\, \Rightarrow \,\,\,\,\,{\text{INSUFF}}.\]
This solution follows the notations and rationale taught in the GMATH method.
Regards,
Fabio.
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Given that xy ≠0, we have neither x nor y is equal to 0.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
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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