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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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GPA: 3.82

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25 Aug 2017, 00:12
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58% (02:13) correct 42% (01:12) wrong based on 99 sessions

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

1) $$y<0$$
2) $$x<0$$
[Reveal] Spoiler: OA

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25 Aug 2017, 00:32
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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

insuff

A
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Re: If x^3y^4z^5<0, is xyz>0? [#permalink]

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27 Aug 2017, 18:09
=>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
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Joined: 02 Jul 2017
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Re: If x^3y^4z^5<0, is xyz>0? [#permalink]

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10 Sep 2017, 23:40
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] 10 Sep 2017, 23:40
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