Bunuel wrote:
The Official Guide For GMAT® Quantitative Review, 2ND EditionIf xy = - 6, what is the value of xy(x + y)?
(1) \(x - y = 5\)
(2) \(xy^2 = 18\)
Data Sufficiency
Question: 100
Category: Algebra First- and second-degree equations
Page: 160
Difficulty: 650
Hi
NandishSSI totally advocate the use of smart numbers for solving such problems.
The generalization of any method (ALgebraic or number plugging) is difficult as it works based on your first instinct.
P.S. When I solved this problem for teh first time, then I used numbers instead of algebraic approachHowever, a good suggestion will be to simplify the expressions algebraically if it seems possible. When stcuk in solving/inferring it further then start using numbers
My flow of thought is as follows:Given: If xy = - 6 Some possible values of (x,y) are (2, -3) (-2, 3) (3, -2) (-3, 2) but the values ,may be Non-integers too
Question: xy(x + y) = ? so we need only (x+y) as we know the value of x*yStatement 1: \(x - y = 5\)(2, -3) and (3, -2) satisfy but the value of x+y may be +1 or -1 hence
NOT SUFFICIENT
Statement 2: \(xy^2 = 18\)i.e. Y must be negative and x must be positive
Also, \(18 = 2*3^2\) therefore (x, y) = (2, -3)
i.e. x+y = -1
SUFFICIENT
Answer: Option B
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