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If xy = -6 , what is the value of xy(x+y ) ?

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If xy = -6 , what is the value of xy(x+y ) ? [#permalink] New post 07 Oct 2010, 05:46
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If xy = -6 , what is the value of xy(x+y ) ?

(1) x – y = 5
(2) x*y^2 = 18

OPEN DISCUSSION OF THIS QUESTION IS HERE: if-xy-6-what-is-the-value-of-xy-x-y-167646.html
[Reveal] Spoiler: OA
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Re: If xy = -6 , what is the value of xy(x+y ) ? [#permalink] New post 07 Oct 2010, 05:56
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agnok wrote:
If xy = -6 , what is the value of xy(x+y ) ?
(1) x – y = 5
(2) x*y square = 18


We're given \(xy = -6\), so \(xy(x+y) = -6(x+y)\).

(1) x - y = 5 -> x = 5+y, so we have:

\((5+y)(y) = -6\)
\(5y + y^2 = -6\)
\(y^2 + 5y + 6 = 0\)
\(y = -2\) or \(y = -3\).

Two solutions for y - insufficient.

(2) \(x(y^2) = 18\). We know that \(y = \frac{-6}{x}\), so we have \(x(\frac{-6}{x^2}) = 18\). So:

\(x(\frac{36}{x^2}) = 18\)
\(\frac{36}{x} = 18\)
\(x = 2\)

Then y = -3, and \(xy(x+y) = -6(2-3) = 6\). Sufficient.

B

Last edited by TehJay on 07 Oct 2010, 06:02, edited 1 time in total.
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Re: If xy = -6 , what is the value of xy(x+y ) ? [#permalink] New post 07 Oct 2010, 06:01
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agnok wrote:
If xy = -6 , what is the value of xy(x+y ) ?
(1) x – y = 5
(2) x*y square = 18


If xy = -6 , what is the value of xy(x+y ) ?

Given: \(xy=-6\).
Question: \(xy(x+y)=-6(x+y)=?\)

(1) \(x-y=5\) --> \(x=y+5\) --> \(xy=(y+5)y=-6\) --> \(y^2+5y+6=0\) --> either \(y=-3\) and \(x=y+5=2\) so \(xy(x+y)=-6(x+y)=6\) OR \(y=-2\) and \(x=y+5=3\) so \(xy(x+y)=-6(x+y)=-6\). Two different answers, hence not sufficient.

(2) \(x*y^2=18\) --> \(xy*y=-6*y=18\) --> \(y=-3\) --> \(x=2\) --> \(xy(x+y)=-6(x+y)=6\). Sufficient.

Answer: B.
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Re: If xy = -6 , what is the value of xy(x+y ) ? [#permalink] New post 08 Oct 2010, 10:14
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ans is B :-)...well in GMAT maths ques are not tough bt tricky..mainly in DS
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Re: If xy = -6 , what is the value of xy(x+y ) ? [#permalink] New post 09 Jun 2015, 07:31
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Re: If xy = -6 , what is the value of xy(x+y ) ? [#permalink] New post 09 Jun 2015, 07:44
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Re: If xy = -6 , what is the value of xy(x+y ) ?   [#permalink] 09 Jun 2015, 07:44
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