Is xy + xy

Question

Is  xy + xy < xy  ?

(1)  \frac{x^2}{y} < 0

(2)  x^9*(y^3)^3 < (x^2)^4*y^8

Bunuel · Answer

Is xy+xy cancel xy in both sides: is xy<0 ? So, the question basically asks whether x and y have the opposite signs. (1) x^2/y<0. This statement implies that y is negative and x can be anything but zero. Not sufficient. (2) x^9*(y^3)^3 < (x^2)^4*y^8 --> (xy)^9<(xy)^8 . Since (xy)^8>0 (from the inequality we can deduce that neither of the unknowns is zero, thus even power of xy will ensure that it's positive), then we can safely reduce by it: xy<1 ( xy eq{0} ). So, we cannot say whether xy<0 . Not sufficient. (1)+(2) y<0 and xy<1 . If x=-\frac{1}{2} and y=-1 , then the answer is NO but if x=1 and y=-1 , then the answer is YES. Not sufficient. Answer: E. Hope it's clear. P.S. Please read carefully and follow: rules-for-posting-please-read-this-before-posting-133935.html pay attention to rules, 2, 3, 5 and 7. Thank you.

harshal123 · Answer

Is xy + xy < xy?

(1) x^2/y<0

(2) x^9(y^3)^3 < (x^2)^4*y^8

mikemcgarry · Answer

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 GMAT Exponent Powers on the GMAT First, 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 :-)

Bunuel · Answer

____________________________________
Merging topics.

bumpbot · Answer

Automated notice from GMAT Club BumpBot: 

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

 This post was generated automatically.

Is xy + xy < xy ? (1) x^2/y < 0 (2) x^9(y^3)^3 < (x^2)^4y^8

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

Is xy + xy < xy ? (1) x^2/y < 0 (2) x^9*(y^3)^3 < (x^2)^4*y^8