Help with this problem

[emptysunday]

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 !!

[emptysunday]

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.

[professorofgmat]

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.

[jnelson0612]

Thanks everyone!

[rachelhong2012]

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"

[jnelson0612]

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