More X & Y variables

[smclean23]

If xy = -6 , what is the value of xy(x+y ) ?
(1) x – y = 5
(2) xy^2=18


Answer is B.

[sudhir3127]

Ru sure the second statement is right....i feel it shd be (x+y)^2.. please us know

[Stuart@KaplanGMAT]

If xy = -6 , what is the value of xy(x+y ) ?
(1) x – y = 5
(2) xy^2=18


Answer is B.

(1) 2 equations and 2 unknowns, but xy = -6 isn't linear, so we'll get more than 1 value: insuffcient.

(2) 2 equations and 2 unknowns, but x(y^2) = 18 isn't linear. HOWEVER, we can actually divide the equation in (2) by the original to get:

x(y^2)/xy = 18/-6
y = -3

Once we know that y = -3, we know that x = 2 (from either equation). Once we have values for both x and y, we can certainly solve: statement (2) is sufficient alone, choose (B).

[sudhir3127]

hey sorrie abt misunderstanding the question!!!..I thought its(Xy)^2.. actually its x(y)^2.. a bracket there would have eliminated the confusion,...Anyways... if that the case I go with B as well.. exactly the way stuart did it.. U need to find Y and we can do it from taking the original eqn and statement 2.

thanks stuart!!

[4meonly]

I think B:

(1) obviously insuff.
(2) xy^2=18. Prime factorization of 18 is 2*3^2, but from the main statement we know that x or y is negative (because their product is negative). Thus, we have xyy=18=2*(-3)*(-3)
x+y=2+(-3)=-1. xy(x+y)=(-6)(-1)=6
Answer is B

[Stuart@KaplanGMAT]

I think B:

(1) obviously insuff.
(2) xy^2=18. Prime factorization of 18 is 2*3^2, but from the main statement we know that x or y is negative (because their product is negative). Thus, we have xyy=18=2*(-3)*(-3)
x+y=2+(-3)=-1. xy(x+y)=(-6)(-1)=6
Answer is B

One thing you always need to be careful about is making assumptions in DS.

If the ONLY thing we knew from the original was that x or y is negative, 2 wouldn't have been sufficient - because one thing we're never told is that x and y have to be integers. Even if they had to be integers, prime factorization wouldn't be enough without knowing the actual value of xy.

For example, why couldn't x = -18 and y = 1?

It's only because we know that xy = -6 (i.e. we know the actual value, not just the sign) that we can solve.

[anksbhandari]

I think D,

A is sufficient if we plug the value;

ab = -6

here ab can be = 1, -6 $ 2,-3

x - y = 5

only 2 - (-3) = 5

therefore, a = 2, and b = -3

sufficient to answer the problem

In the same way B is also sufficient

Therefore answer is D

Let me know if i am wrong