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# If x^3y^4z^5<0, is xyz>0?

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Math Revolution GMAT Instructor
Joined: 16 Aug 2015
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GMAT 1: 760 Q51 V42
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25 Aug 2017, 01:12
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Difficulty:

65% (hard)

Question Stats:

56% (01:26) correct 44% (01:21) wrong based on 105 sessions

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If $$x^3y^4z^5<0$$, is $$xyz>0$$?

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

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MathRevolution: Finish GMAT Quant Section with 10 minutes to spare
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"Only $149 for 3 month Online Course" "Free Resources-30 day online access & Diagnostic Test" "Unlimited Access to over 120 free video lessons - try it yourself" Math Expert Joined: 02 Aug 2009 Posts: 7575 If x^3y^4z^5<0, is xyz>0? [#permalink] ### Show Tags 25 Aug 2017, 01:32 3 MathRevolution wrote: If $$x^3y^4z^5<0$$, is $$xyz>0$$? 1) $$y<0$$ 2) $$x<0$$ Hi.. In $$x^3y^4z^5<0$$, y^4 will always be POSITIVE so y can be NEGATIVE or POSITIVE Also one of x and z is + and other -, xz<0.. our answer will depend on y. lets see the statements 1) y<0.. sufficient as shown above.. xz<0 and y<0 so xyz>0 sufficient 2) x<0 we just know that z>0 nothing about y.. insuff A _________________ Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 7236 GMAT 1: 760 Q51 V42 GPA: 3.82 Re: If x^3y^4z^5<0, is xyz>0? [#permalink] ### Show Tags 27 Aug 2017, 19:09 =>The original condition $$x^3y^4z^5<0$$ is equivalent to xy < 0 after dividing both sides of the inequality by $$x^2y^4z^4$$. Then the question is equivalent to y>0, since xy < 0 from the equivalent condition. Thus the condition 1) is sufficient, since the question is if y > 0. Ans: A _________________ 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$149 for 3 month Online Course"
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Re: If x^3y^4z^5<0, is xyz>0?  [#permalink]

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11 Sep 2017, 00:40
Given $$x^3$$$$y^4$$$$z^5$$<0
is xyz>0 ?

$$x^3$$$$y^4$$$$z^5$$<0 by this as total product is -ve and power of y is even => either x is -ve or z is -ve but not both. And here we don't know if y is +ve or -ve
Also as product is greater than 0, none of it is equal to 0.

so for xyz>0 the value will be dependent on y. as xz is always -ve (as 1 of it is +ve and other is -ve)
=> if y= -ve => xyz >0
=> if y= +ve => xyz <0

1) y<0
This directly tells us that y is -ve . => xyz >0 true. Sufficient

2) x<0
This just tell x=-ve and we can imply z=+ve. But we don't know anything about y.
So not sufficient.

Re: If x^3y^4z^5<0, is xyz>0?   [#permalink] 11 Sep 2017, 00:40
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