GMAT Question of the Day: Daily via email | Daily via Instagram New to GMAT Club? Watch this Video

 It is currently 25 May 2020, 03:58

### 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

# If x^3y<0, and y/z>0, then which of the following must be less than 1?

Author Message
TAGS:

### Hide Tags

Senior Manager
Joined: 10 Jan 2013
Posts: 307
Location: India
Concentration: General Management, Strategy
GPA: 3.95
If x^3y<0, and y/z>0, then which of the following must be less than 1?  [#permalink]

### Show Tags

11 Aug 2019, 09:20
6
00:00

Difficulty:

55% (hard)

Question Stats:

60% (02:31) correct 40% (02:15) wrong based on 84 sessions

### HideShow timer Statistics

If $$x^3y<0$$, and $$y/z>0$$, then which of the following must be less than 1?

A. $$\sqrt[3]{x}$$

B. $$y/(x)^2$$

C. $$x^3z^4$$

D. $$x^2yz$$

E. $$xy^2z^3$$
Manager
Joined: 26 Apr 2019
Posts: 147
Location: India
GMAT 1: 690 Q49 V34
GMAT 2: 700 Q49 V36
GMAT 3: 720 Q50 V37
GPA: 3.99
Re: If x^3y<0, and y/z>0, then which of the following must be less than 1?  [#permalink]

### Show Tags

11 Aug 2019, 09:32
2
as z and y will have same sign , x and y with opposite sign so only e option will have negative soln in all condition and is less than 1 in all cases.
Senior Manager
Joined: 10 Jan 2013
Posts: 307
Location: India
Concentration: General Management, Strategy
GPA: 3.95
Re: If x^3y<0, and y/z>0, then which of the following must be less than 1?  [#permalink]

### Show Tags

12 Aug 2019, 10:02
saurabh9gupta wrote:
If $$x^3y<0$$, and $$y/z>0$$, then which of the following must be less than 1?

A. $$\sqrt[3]{x}$$

B. $$y/(x)^2$$

C. $$x^3z^4$$

D. $$x^2yz$$

E. $$xy^2z^3$$

Rice (Jones) School Moderator
Joined: 18 Jun 2018
Posts: 351
Concentration: Finance, Healthcare
Re: If x^3y<0, and y/z>0, then which of the following must be less than 1?  [#permalink]

### Show Tags

12 Aug 2019, 11:52
Alternate approach:

Given: $$x^{3}$$y < 0 and $$\frac{y}{z}$$>0

Let x = -1, y = 1, and z = 2 ==> test these numbers in the answer choices and you can quickly eliminate B (1) and D (2). A (-1), C (-16) & E (-8) are < 1 so keep them and pick new set of numbers.

Let x =1, y = -1, and z = -2 ==> test these numbers in the remaining answer choices and you will get A(1), C (16), and E (-8 which is < 1), so E is the answer.
Director
Joined: 16 Jan 2019
Posts: 597
Location: India
Concentration: General Management
WE: Sales (Other)
Re: If x^3y<0, and y/z>0, then which of the following must be less than 1?  [#permalink]

### Show Tags

12 Aug 2019, 13:02
1
$$x^3y<0$$

$$x^3$$ and $$x$$ have the same sign so $$xy<0$$, which means $$x$$ and $$y$$ have opposite signs

$$\frac{y}{z}>0$$, which means $$y$$ and $$z$$ have the same sign

Therefore $$x$$ and $$z$$ have opposite signs and so $$xz<0$$ and $$\frac{x}{z}<0$$

Note that at this point we do not know the exact sign of $$x$$, $$y$$ or $$z$$ but we do know how the sign of one affects the other

A. $$\sqrt[3]{x}$$

$$\sqrt[3]{x}$$ and $$x$$ have the same sign but we don't know what that sign is

B. $$\frac{y}{x^2}$$

It is possible that $$x$$ is negative and $$y$$ is positive in which case $$\frac{y}{x^2}$$ is positive

C. $$x^3z^4$$

It is possible that $$x$$ is positive and $$z$$ is negative in which case $$x^3z^4$$ is positive

D. $$x^2yz$$

Since $$y$$ and $$z$$ have same sign $$yz>0$$ and $$x^2>0$$, so $$x^2yz>0$$

E. $$xy^2z^3$$

$$xy^2z^3$$ = $$(xz)(yz)^2$$

$$(yz)^2$$ is always positive and as we established above $$xz$$ is negative

This means $$(xz)(yz)^2$$ = $$xy^2z^3$$ is negative and therefore less than 1

Hit Kudos if this helped!
Manager
Joined: 01 Nov 2018
Posts: 79
GMAT 1: 690 Q48 V35
GPA: 3.88
Re: If x^3y<0, and y/z>0, then which of the following must be less than 1?  [#permalink]

### Show Tags

15 Aug 2019, 16:25
1
Picking numbers here is a bit tedious. Just list out the 2 possible cases.
Case 1: X=pos Y=neg Z=neg
Case 2: X=neg Y=pos Z=pos

Just putting the signs in choice E shows that if X is positive, Z will be negative and hence the answer will be negative (<1)
Likewise, if X is negative, the entire expression will be negative and hence <1.
Re: If x^3y<0, and y/z>0, then which of the following must be less than 1?   [#permalink] 15 Aug 2019, 16:25