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If xy = – 6, what is the value of xy(x + y)? (1) x – y = 5

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If xy = – 6, what is the value of xy(x + y)? (1) x – y = 5 [#permalink] New post 27 Apr 2012, 09:39
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If xy = – 6, what is the value of xy(x + y)?

(1) x – y = 5
(2) xy^2= 18
[Reveal] Spoiler: OA

Last edited by Bunuel on 27 Apr 2012, 09:43, edited 1 time in total.
Edited the question and added the OA
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Re: If xy = – 6, what is the value of xy(x + y)? (1) x – y = 5 [#permalink] New post 27 Apr 2012, 09:48
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If xy = – 6, what is the value of xy(x + y)?

(1) \(x-y=5\) --> \(x=y+5\) --> \(xy=(y+5)y=-6\) --> \(y^2+5y+6=0\) --> \(y=-3\) or \(y=-2\). If \(y=-3\) then \(x=y+5=2\) so \(xy(x+y)=-6(x+y)=6\). But if \(y=-2\) then \(x=y+5=3\) 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)? (1) x – y = 5 [#permalink] New post 27 Apr 2012, 09:52
Bunuel wrote:
If xy = – 6, what is the value of xy(x + y)?

(1) \(x-y=5\) --> \(x=y+5\) --> \(xy=(y+5)y=-6\) --> \(y^2+5y+6=0\) --> \(y=-3\) or \(y=-2\). If \(y=-3\) then \(x=y+5=2\) so \(xy(x+y)=-6(x+y)=6\). But if \(y=-2\) then \(x=y+5=3\) 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.


B is OA, thank you!!!
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Re: If xy = -6 , what is the value of xy(x+y ) [#permalink] New post 14 Feb 2013, 08:39
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roopika2990 wrote:
If xy = -6 , what is the value of xy(x+y ) ?
(1) x – y = 5
(2)xy^2 = 48


xy=-6 ----> x=-6/y

S1) x-y=5 ---------------> x=y+5 -------------> -6/y=y+5 --------> y^2 + 5y + 6 = 0 -------> y = -3 or -2 two values for y so not sufficiesnt

S2) xy^2 = 48 -------> We know x=-6/y -------> therefore (-6/y)(y^2)=48 -------> -6y = 48 -------> y = -8 and x = 6/8 so now we can calculate the value of xy(x+y) hence statement is sufficient

Regards,

Abhijit
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Re: If xy = -6 , what is the value of xy(x+y ) [#permalink] New post 14 Feb 2013, 10:36
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\((x+y)^2 = (x-y)^2+4xy\)

= 5^2+4(-6) = 25-24 = 1

From F.S 1, we know that (x+y)^2 will have two values 1 and -1. Hence, insufficient.

But, from F.S 2, we know that y will have only one value. Thus sufficient. No need to solve for either of the options.

B.
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Re: If xy = – 6, what is the value of xy(x + y)? (1) x – y = 5 [#permalink] New post 30 Sep 2014, 22:27
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Re: If xy = – 6, what is the value of xy(x + y)? (1) x – y = 5   [#permalink] 30 Sep 2014, 22:27
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