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# If xy = -6 , what is the value of xy(x+y ) ? (1) x y = 5 (2)

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Manager
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If xy = -6 , what is the value of xy(x+y ) ? (1) x y = 5 (2) [#permalink]  18 Apr 2007, 10:00
If xy = -6 , what is the value of xy(x+y ) ?
(1) x â€“ y = 5
(2) xy^2 = 18

Thanks
Senior Manager
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st2 is sufficient:
xy^2=18 = xy*y = (-6)*y hence y must be -3 from which you can go forward and get the value of xy(x+y)

st1: is insufficient
x-y=5 (together with xy=-6) has two solutions: x=2 y=-3 and x=3 y=-2 which lead to diferent answers - hence insufficient
VP
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I can see that hobbit gave a full and detailed explanation so I will not explain again (same logic) - well done hobbit
Manager
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I agree with hobbit B.
Senior Manager
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B indeed!

xy^2=18
18=2*3^2

thus x=2 y=-3

Suff~
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St1:
x = y+5
So
y(y+5) = -6
y^2 +5y + 6 = 0
y = -2 or y = -3

If y = -2, x = 3 --> xy(x+y) = -6
If y = -3, x = 2 --> xy(x+y) = -30

Insufficient.

St2:
xy^2 = 18
x = 18/y^2

So
(18/y^2)(y) = 6
18/y = 6
y = 3.

So x = 2. One (x,y) pair will give only one result for xy(x+y).

sufficient.

Ans B
Manager
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jainvik7 wrote:
If xy = -6 , what is the value of xy(x+y ) ?
(1) x â€“ y = 5
(2) xy^2 = 18

Thanks

B.

x-y=5 gives 2 sets of solutions
while xy^2=18 gives only 1
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