Summer is Coming! Join the Game of Timers Competition to Win Epic Prizes. Registration is Open. Game starts Mon July 1st.

 It is currently 16 Jul 2019, 13:41 ### 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.  # Given that x^3*y > 0 and that x^2*y^3 < 0 which of the following state

Author Message
TAGS:

### Hide Tags

Math Expert V
Joined: 02 Sep 2009
Posts: 56244
Given that x^3*y > 0 and that x^2*y^3 < 0 which of the following state  [#permalink]

### Show Tags 00:00

Difficulty:   45% (medium)

Question Stats: 56% (01:23) correct 44% (01:32) wrong based on 186 sessions

### HideShow timer Statistics Given that $$x^3*y > 0$$ and that $$x^2*y^3 < 0$$ which of the following statements must be true?

I. $$x < 0$$
II. $$x < y < 0$$
III. $$y^3 < x^2$$

A. I only
B. II only
C. I and II only
D. I and III only
E. I, II, and III

_________________
Current Student P
Joined: 18 Aug 2016
Posts: 617
Concentration: Strategy, Technology
GMAT 1: 630 Q47 V29 GMAT 2: 740 Q51 V38 Re: Given that x^3*y > 0 and that x^2*y^3 < 0 which of the following state  [#permalink]

### Show Tags

1
Bunuel wrote:
Given that $$x^3*y > 0$$ and that $$x^2*y^3 < 0$$ which of the following statements must be true?

I. $$x < 0$$
II. $$x < y < 0$$
III. $$y^3 < x^2$$

A. I only
B. II only
C. I and II only
D. I and III only
E. I, II, and III

From the stem we can deduce that y<0 and x<0
(x^3)*y >0 means either both are -ve or both are +ve
(x^2)*(y^3)<0 means y is -ve

Hence y<0 and x<0
I holds true
II does not always (e.g. y = -4 and x = -2)
III will always hold as (y = -ve number)^3 < Positive number (x = -ve number)^2

Hence D
_________________
We must try to achieve the best within us

Thanks
Luckisnoexcuse
Senior Manager  B
Joined: 28 Jun 2015
Posts: 286
Concentration: Finance
GPA: 3.5
Re: Given that x^3*y > 0 and that x^2*y^3 < 0 which of the following state  [#permalink]

### Show Tags

Bunuel wrote:
Given that $$x^3*y > 0$$ and that $$x^2*y^3 < 0$$ which of the following statements must be true?

I. $$x < 0$$
II. $$x < y < 0$$
III. $$y^3 < x^2$$

A. I only
B. II only
C. I and II only
D. I and III only
E. I, II, and III

(i) $$x^3*y > 0$$
Either both $$x$$ and $$y$$ must be negative or both must be positive for the above result to be true.

(ii) $$x^2*y^3 < 0$$
Since square of any number must be positive, $$y$$ must be negative for the above result to be true.

From (i) and (ii), it can be concluded that both $$x$$ and $$y$$ are negative.

I) This is true from the above.
II) This need not necessarily be true. For e.g., let $$x = y = -2$$, then $$(-2)^{2} * (-2)^{3} = 4 * -8 = -32$$, but here $$x$$ is not less than $$y$$.
III) This must be true as both $$x$$ and $$y$$ are negative numbers.

So, only I and III are true. Ans - D.
_________________
I used to think the brain was the most important organ. Then I thought, look what’s telling me that.
Manager  B
Joined: 03 Feb 2017
Posts: 74
Location: Australia
GMAT 1: 720 Q48 V40 Given that x^3*y > 0 and that x^2*y^3 < 0 which of the following state  [#permalink]

### Show Tags

Given conditions are $$x^3$$∗y>0 and $$x^2$$∗$$y^3$$<0
Assume x=1 and y=1, both conditions cannot be satisfied
Assume x=1 and y=-1, first conditions cannot be satisfied
Assume x=-1 and y=-1, both conditions can be satisfied

Manager  S
Joined: 05 Nov 2014
Posts: 104
Location: India
Concentration: Strategy, Operations
GMAT 1: 580 Q49 V21 GPA: 3.75
Re: Given that x^3*y > 0 and that x^2*y^3 < 0 which of the following state  [#permalink]

### Show Tags

Bunuel wrote:
Given that $$x^3*y > 0$$ and that $$x^2*y^3 < 0$$ which of the following statements must be true?

I. $$x < 0$$
II. $$x < y < 0$$
III. $$y^3 < x^2$$

A. I only
B. II only
C. I and II only
D. I and III only
E. I, II, and III

Solution:

The second question stem says that y is negative. So for the first equation to be true, x has to be negative too.
But the value of x can be greater or lesser than y. We can't answer this with the available information.

Therefore, I and III are true.
Option D.
ISB School Moderator G
Joined: 08 Dec 2013
Posts: 524
Location: India
Concentration: Nonprofit, Sustainability
GMAT 1: 630 Q47 V30 WE: Operations (Non-Profit and Government)
Re: Given that x^3*y > 0 and that x^2*y^3 < 0 which of the following state  [#permalink]

### Show Tags

Bunuel wrote:
Given that $$x^3*y > 0$$ and that $$x^2*y^3 < 0$$ which of the following statements must be true?

I. $$x < 0$$
II. $$x < y < 0$$
III. $$y^3 < x^2$$

A. I only
B. II only
C. I and II only
D. I and III only
E. I, II, and III

From two given statements we can deduce the following-
xy>0
y<0
So, x<0

II Can't say, we don't know which one is greater. We just know that both are -ve numbers.
III y^3 < x^2; definitely. y^3 gives -ve and x^2 gives +ve number.

D. I & III
_________________
Kindly drop a '+1 Kudos' if you find this post helpful.

GMAT Math Book

-I never wanted what I gave up
I never gave up what I wanted- Re: Given that x^3*y > 0 and that x^2*y^3 < 0 which of the following state   [#permalink] 23 May 2019, 20:04
Display posts from previous: Sort by

# Given that x^3*y > 0 and that x^2*y^3 < 0 which of the following state  