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Help with this problem

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emptysunday
 Post subject: Help with this problem
 Post Posted: Mon Jan 02, 2012 11:15 pm 
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Good day, I have a question regarding the next DS question:

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

(1) x - y = 5

(2) xy^2 = 18


The OA goes "B" but I would like to know why statement (1) is not sufficient.

We know that the value of xy = -6 so basically we only need to calculate the value of x+y. A possible combination of x and y values that satisfy the condition "xy = - 6" is x = 3 and y = -2

From (1) we know that x = 5 + y, so the value of x and y must be 3 and -2 respectively. I cannot find another pair of values for x and y that satisfy these conditions. If there is something I have learned is that OA are always correct, so, could someone explain me please where am I commiting the mistake?

Gracias !!
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emptysunday
 Post subject: Re: Help with this problem
 Post Posted: Mon Jan 02, 2012 11:25 pm 
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Oh god Im so sorry. I already found another x y combination
(2,-3)

I must be very tired so as to overlook such an easy easy thing.


My bad.

Feel free to delete this thread.
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professorofgmat
 Post subject: Re: Help with this problem
 Post Posted: Wed Jan 04, 2012 4:05 pm 
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As you later rihtly realised that statement 1 throws 2 values of x and y (x=3, y=-2) and (x=2, y=-3). But the question does not stop here. We must substitute thaese values in the expression
xy(x+y) to check whether this expression actually gives 2 values.

If the question had been "find the value of (x+y-1)(x-y-5)" then statement 1 would have been sufficient.

I hope that helps.
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jnelson0612
 Post subject: Re: Help with this problem
 Post Posted: Wed Jan 11, 2012 10:48 pm 
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ManhattanGMAT Staff


Posts: 1857
Thanks everyone!

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Jamie Nelson
ManhattanGMAT Instructor
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rachelhong2012
 Post subject: Re: Help with this problem
 Post Posted: Fri Feb 10, 2012 11:59 am 
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Posts: 47
emptysunday wrote:
Good day, I have a question regarding the next DS question:

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

(1) x - y = 5

(2) xy^2 = 18


The OA goes "B" but I would like to know why statement (1) is not sufficient.

We know that the value of xy = -6 so basically we only need to calculate the value of x+y. A possible combination of x and y values that satisfy the condition "xy = - 6" is x = 3 and y = -2

From (1) we know that x = 5 + y, so the value of x and y must be 3 and -2 respectively. I cannot find another pair of values for x and y that satisfy these conditions. If there is something I have learned is that OA are always correct, so, could someone explain me please where am I commiting the mistake?

Gracias !!


going back to your comment about:
A possible combination of x and y values that satisfy the condition "xy = - 6" is x = 3 and y = -2

Be careful though, don't forget they never told us that x and y are integers, so the possibilities go beyond integer value for x and y given that xy=-6


when you combine statement one with xy=-6, you can either generate values conceptually or you can do it algebraically:


x - y = 5


so: x = 5+y, substitute this into xy=-6 for x, you get:
(5+y) (y) = -6
5y + y^2 = -6
y^2 + 5y +6 = 0
(y+2) (y+3)
y=-2 y=-3

And as professorofgmat mentioned: "But the question does not stop here. We must substitute thaese values in the expression
xy(x+y) to check whether this expression actually gives 2 values"
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jnelson0612
 Post subject: Re: Help with this problem
 Post Posted: Sun Feb 12, 2012 12:03 am 
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ManhattanGMAT Staff


Posts: 1857
rachel, I really enjoy your posts. You make great points!

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Jamie Nelson
ManhattanGMAT Instructor
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