harshal123 wrote:
is xy+xy <xy?
(1) x^2/y<0
(2) x^9(y^3)^3 < (x^2)^4 y^8
Dear
harshal123,
I'm happy to respond.
I will say that this Jamboree question looks remarkably like
this MGMAT question. At least these are how the sources have been cited on GMAT Club. If these two companies really are the authors of these respective questions, I would say that something is suspicious here. I will let
MGMAT and Jamboree sort that out.
Here are a couple blog articles you may find relevant:
Exponent Properties on the GMATExponent Powers on the GMATFirst, let's decipher the prompt:
xy + xy < xy
subtract xy
xy < 0
That's what the question is really asking: is the product of those two variables negative?
Statement #1: \(\frac{x^2}{y} < 0\)
We know that neither variable can equal zero. Anything non-zero squared is positive, so x^2 is positive. Divide both sides by this.
\(\frac{1}{y} < 0\)
We know that y is negative. We know nothing about x. Thus, this statement, alone and by itself, is
insufficient.
Statement #2: \(x^9(y^3)^3 < (x^2)^4 y^8\)
This can be simplified to
\((xy)^9 < (xy)^8\)
Again, we know that neither variable can be zero. Thus, xy is a non-zero product, and any non-zero number raised to an even power is positive. We know \((xy)^8\) is a positive number, so we can divide both sides of the inequality by this.
xy < 1
We know that the product is less than 1. It could be less than zero, but it doesn't have to be. Thus, this statement, alone and by itself, is
insufficient.
Combined:
From S#1, we know y < 0
From S#2, we know xy < 1
Example #1: \(x = +2\), \(y = -3\). This satisfies both statements and gives a "yes" answer to the prompt.
Example #2: \(x = -2\), \(y = -\frac{1}{3}\). This satisfies both statements and gives a "no" answer to the prompt.
Two different answers, nothing is sufficient. Combined, the statements are
not sufficient.
OA =
(E) Does all this make sense?
Mike
_________________
Mike McGarry
Magoosh Test PrepEducation is not the filling of a pail, but the lighting of a fire. — William Butler Yeats (1865 – 1939)