GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 17 Jan 2019, 19:40

### 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

## Events & Promotions

###### Events & Promotions in January
PrevNext
SuMoTuWeThFrSa
303112345
6789101112
13141516171819
20212223242526
272829303112
Open Detailed Calendar
• ### The winning strategy for a high GRE score

January 17, 2019

January 17, 2019

08:00 AM PST

09:00 AM PST

Learn the winning strategy for a high GRE score — what do people who reach a high score do differently? We're going to share insights, tips and strategies from data we've collected from over 50,000 students who used examPAL.
• ### Free GMAT Strategy Webinar

January 19, 2019

January 19, 2019

07:00 AM PST

09:00 AM PST

Aiming to score 760+? Attend this FREE session to learn how to Define your GMAT Strategy, Create your Study Plan and Master the Core Skills to excel on the GMAT.

# Is x^2 * y^5 * z>0 ?

Author Message
TAGS:

### Hide Tags

Manager
Joined: 14 Apr 2010
Posts: 179
Is x^2 * y^5 * z>0 ?  [#permalink]

### Show Tags

31 Jul 2010, 20:41
6
00:00

Difficulty:

45% (medium)

Question Stats:

62% (01:48) correct 38% (02:00) wrong based on 210 sessions

### HideShow timer Statistics

Is x^2 * y^5 * z>0 ?

(1) xz/y>0
(2) y/z<0
Math Expert
Joined: 02 Sep 2009
Posts: 52231

### Show Tags

09 Sep 2010, 20:58
4
3
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.
_________________
##### General Discussion
Manager
Joined: 31 May 2010
Posts: 70

### Show Tags

31 Jul 2010, 20:47
Hi,

To have expression > 0 , there are two cases -
1) both y and z is positive or
2) both y and z is negative ( because x2 is alwasy positive, irrespecitve of sign of x )

Option 1 is not sufficient .

Option 2 is sufficient as it tells that y and z is of opposite sign. So expression is less than zero.
_________________

Kudos if any of my post helps you !!!

Manager
Joined: 02 Apr 2010
Posts: 66

### Show Tags

01 Aug 2010, 06:08
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: 143
Location: United States (MI)
Concentration: Marketing, General Management

### Show Tags

01 Aug 2010, 07:51
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: 179

### Show Tags

02 Aug 2010, 23:06
what if X=0? Why are we not considering that?
Manager
Joined: 16 Jun 2010
Posts: 103

### Show Tags

03 Aug 2010, 04:56
1
@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 )
_________________

R E S P E C T

Finally KISSedGMAT 700 times 450 to 700 An exprience

Intern
Joined: 15 Aug 2010
Posts: 13

### Show Tags

03 Sep 2010, 05:03
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: 52231
Re: Is x^2 * y^5 * z>0 ?  [#permalink]

### Show Tags

04 Sep 2013, 02:46
Bumping for review and further discussion.
_________________
Non-Human User
Joined: 09 Sep 2013
Posts: 9419
Re: Is x^2 * y^5 * z>0 ?  [#permalink]

### Show Tags

12 Apr 2017, 15:23
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 ? &nbs [#permalink] 12 Apr 2017, 15:23
Display posts from previous: Sort by