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# Is x^3*y^2*z<0?

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Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 8255
GMAT 1: 760 Q51 V42
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10 Jul 2017, 01:00
00:00

Difficulty:

35% (medium)

Question Stats:

73% (01:10) correct 27% (01:11) wrong based on 74 sessions

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Is $$x^3y^2z<0?$$

1) $$x^2y<0$$
2) $$yz<0$$

_________________
MathRevolution: Finish GMAT Quant Section with 10 minutes to spare
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"Only $79 for 1 month Online Course" "Free Resources-30 day online access & Diagnostic Test" "Unlimited Access to over 120 free video lessons - try it yourself" Senior Manager Joined: 06 Jul 2016 Posts: 356 Location: Singapore Concentration: Strategy, Finance Re: Is x^3*y^2*z<0? [#permalink] ### Show Tags 10 Jul 2017, 01:06 1 Y will always be positive so can safely be ignored for now. All we need to do is prove that x and z are opposite signs. 1) (x^2)y < 0 X will always be positive this inequality => y < 0 but that doesn’t help. Insufficient. 2) yz < 0 Both are opposite signs. Nothing about x. Insufficient. 1+2) We know y < 0 and z >0 but nothing about x. Insufficient. E. Posted from my mobile device _________________ Put in the work, and that dream score is yours! Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 8255 GMAT 1: 760 Q51 V42 GPA: 3.82 Re: Is x^3*y^2*z<0? [#permalink] ### Show Tags 12 Jul 2017, 01:08 ==> If you modify the original condition and the question, when xyz≠0, you get xz<0?. There are 3 variables (x,y,z), and in order to match the number of variables to the number of equations, there must be 2 equations. Since there is 1 for con 1) and 1 for con 2), E is most likely to be the answer. By solving con 1) and con 2), you get x^2y<0, y<0 and yz<0, z>0. Since x is unknown, it is not sufficient. Therefore, the answer is E. Answer: E _________________ MathRevolution: Finish GMAT Quant Section with 10 minutes to spare The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy. "Only$79 for 1 month Online Course"
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31 Aug 2017, 11:00
MathRevolution wrote:
Is $$x^3y^2z<0?$$

1) $$x^2y<0$$
2) $$yz<0$$

Statement 1 states that y<0. We don't know anything about x. --> insufficient
Statement 2 states that either of y or z is <0. --> insufficient

Statement 1 & 2: y<0 and z>0; but still no idea about the sign of x. --> insufficient

Re: Is x^3*y^2*z<0?   [#permalink] 31 Aug 2017, 11:00
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