Last visit was: 15 Jul 2024, 00:34 It is currently 15 Jul 2024, 00:34
Toolkit
GMAT Club Daily Prep
Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

# Is x^2*y^5*z > 0 ? (1) xz/y > 0 (2) y/z < 0

SORT BY:
Tags:
Show Tags
Hide Tags
Manager
Joined: 14 Apr 2010
Posts: 99
Own Kudos [?]: 1001 [15]
Given Kudos: 1
Math Expert
Joined: 02 Sep 2009
Posts: 94342
Own Kudos [?]: 640890 [11]
Given Kudos: 85011
General Discussion
Intern
Joined: 31 May 2010
Posts: 43
Own Kudos [?]: 200 [0]
Given Kudos: 25
Intern
Joined: 02 Apr 2010
Posts: 38
Own Kudos [?]: 64 [0]
Given Kudos: 1
Re: Is x^2*y^5*z > 0 ? (1) xz/y > 0 (2) y/z < 0 [#permalink]
bibha wrote:
Is x^2 * y^5 * z>0 ?
1.xz/y>0
2.y/z<0

s1: --> x,y, z not = 0.
---> if y = -ve, then xz must be -ve so either x or z is -ve.
if y = +ve, then xz must be +ve x and z must be same sign.

consider y = -ve and x=-ve and z = +ve , evaluate question, answer is false.
consider y= -ve and x=+ve and z = -ve, evaluation question, answer is true.

Therefore: s1 not sufficient.

s2: --> either y=-ve and z=+ve OR y=+ve and z=-ve

Ignore x=+ve or x=-ve since there is a x^2 in question
consider y=-ve and z=+ve, evaluation question, answer is false.
consider y=+ve and z=-ve, evaluation question, answer is false.

s2 alone sufficient.

How to quickly see s1 is insufficient?
Manager
Joined: 03 Jun 2010
Posts: 97
Own Kudos [?]: 528 [0]
Given Kudos: 40
Location: United States (MI)
Concentration: Marketing, General Management
Re: Is x^2*y^5*z > 0 ? (1) xz/y > 0 (2) y/z < 0 [#permalink]
1. xz/y>0
we need y & z to have similar signs.
but we can't be sure from the first statement, z>0, y<0, x<0, the statement is true
z>0, y>0, x>0, true
z<0, y>0, x>0 true.
Thus, 1) unsuff.
Manager
Joined: 14 Apr 2010
Posts: 99
Own Kudos [?]: 1001 [0]
Given Kudos: 1
Re: Is x^2*y^5*z > 0 ? (1) xz/y > 0 (2) y/z < 0 [#permalink]
what if X=0? Why are we not considering that?
Manager
Joined: 16 Jun 2010
Posts: 68
Own Kudos [?]: 105 [1]
Given Kudos: 1
Q48  V36
Re: Is x^2*y^5*z > 0 ? (1) xz/y > 0 (2) y/z < 0 [#permalink]
1
Kudos
@Bibha

We are not concidering X = 0 because 2) makes it clear that x^2 * y^5 * z <= 0

< because y & z have different signs

= When X = 0. ( also Y & Z cannot be zero as per statement 2 )
Intern
Joined: 15 Aug 2010
Posts: 11
Own Kudos [?]: 3 [0]
Given Kudos: 0
Re: Is x^2*y^5*z > 0 ? (1) xz/y > 0 (2) y/z < 0 [#permalink]
My approach to see St:1 is insufficient is
xz/y>0 mean both are of same sign.
x^2*y^5*z => x*((x*z)*y^5) here ((x*z)*y^5) is positive since y^5 does not change y sign and xz is same so both give positive, here we dont know remaining x therefore insufficient.
Math Expert
Joined: 02 Sep 2009
Posts: 94342
Own Kudos [?]: 640890 [0]
Given Kudos: 85011
Re: Is x^2*y^5*z > 0 ? (1) xz/y > 0 (2) y/z < 0 [#permalink]
Bumping for review and further discussion.
Director
Joined: 28 Sep 2018
Posts: 710
Own Kudos [?]: 571 [0]
Given Kudos: 248
GMAT 1: 660 Q48 V33 (Online)
GMAT 2: 700 Q49 V37
Re: Is x^2*y^5*z > 0 ? (1) xz/y > 0 (2) y/z < 0 [#permalink]
Bunuel wrote:
bibha wrote:
Is x^2 * y^5 * z>0 ?
(1) xz/y>0
(2) y/z<0

For $$x^2*y^5*z>0$$ to hold true:
1. $$x$$ must not be zero;
and
2. $$y$$ and $$z$$ must be either both positive or both negative.

(1) $$\frac{xz}{y}>0$$ --> first condition is satisfied: $$x\neq{0}$$, but we don't know aout the second one: $$\frac{xz}{y}>0$$ means that either all of them are positive (answer YES) or ANY two are negative and the third one is positive, so it's possible $$y$$ and $$z$$ to have opposite signs (answer NO). Not sufficient.

(2) $$\frac{y}{z}<0$$ --> $$y$$ and $$z$$ have opposite signs --> second condition is already violated, so the answer to the question is NO. Sufficient.

Side note for (2): $$\frac{y}{z}<0$$ does not mean that $$x^2*y^5*z<0$$, it means that $$x^2*y^5*z\leq{0}$$ because it's possible $$x$$ to be equal to zero and in this case $$x^2*y^5*z=0$$. But in any case $$x^2*y^5*z$$ is not MORE than zero, so we can answer NO to the question.

Hoe it's clear.

Bunuel shouldn't it be

1) x, y, and z must ≠ 0 AND (why only x ≠ 0?)
2) y and z must be both positive or both negative
Math Expert
Joined: 02 Sep 2009
Posts: 94342
Own Kudos [?]: 640890 [1]
Given Kudos: 85011
Re: Is x^2*y^5*z > 0 ? (1) xz/y > 0 (2) y/z < 0 [#permalink]
1
Kudos
Hoozan wrote:
Bunuel wrote:
bibha wrote:
Is x^2 * y^5 * z>0 ?
(1) xz/y>0
(2) y/z<0

For $$x^2*y^5*z>0$$ to hold true:
1. $$x$$ must not be zero;
and
2. $$y$$ and $$z$$ must be either both positive or both negative.

(1) $$\frac{xz}{y}>0$$ --> first condition is satisfied: $$x\neq{0}$$, but we don't know aout the second one: $$\frac{xz}{y}>0$$ means that either all of them are positive (answer YES) or ANY two are negative and the third one is positive, so it's possible $$y$$ and $$z$$ to have opposite signs (answer NO). Not sufficient.

(2) $$\frac{y}{z}<0$$ --> $$y$$ and $$z$$ have opposite signs --> second condition is already violated, so the answer to the question is NO. Sufficient.

Side note for (2): $$\frac{y}{z}<0$$ does not mean that $$x^2*y^5*z<0$$, it means that $$x^2*y^5*z\leq{0}$$ because it's possible $$x$$ to be equal to zero and in this case $$x^2*y^5*z=0$$. But in any case $$x^2*y^5*z$$ is not MORE than zero, so we can answer NO to the question.

Hoe it's clear.

Bunuel shouldn't it be

1) x, y, and z must ≠ 0 AND (why only x ≠ 0?)
2) y and z must be both positive or both negative

If either of the unknowns is 0, then x^2*y^5*z = 0, and not > 0. The fact that y and z should not be 0 included in the second point: if y and z are both positive or both negative than neither of them is 0.
Director
Joined: 28 Sep 2018
Posts: 710
Own Kudos [?]: 571 [0]
Given Kudos: 248
GMAT 1: 660 Q48 V33 (Online)
GMAT 2: 700 Q49 V37
Re: Is x^2*y^5*z > 0 ? (1) xz/y > 0 (2) y/z < 0 [#permalink]
Quote:
If either of the unknowns is 0, then x^2*y^5*z = 0, and not > 0. The fact that y and z should not be 0 included in the second point: if y and z are both positive or both negative than neither of them is 0.

Ahh missed that one. Thank you
Non-Human User
Joined: 09 Sep 2013
Posts: 33969
Own Kudos [?]: 851 [0]
Given Kudos: 0
Re: Is x^2*y^5*z > 0 ? (1) xz/y > 0 (2) y/z < 0 [#permalink]
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
Re: Is x^2*y^5*z > 0 ? (1) xz/y > 0 (2) y/z < 0 [#permalink]
Moderator:
Math Expert
94342 posts