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

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Math Expert
Joined: 02 Sep 2009
Posts: 50613
Given that x^3*y > 0 and that x^2*y^3 < 0 which of the following state  [#permalink]

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23 Jun 2017, 23:07
00:00

Difficulty:

55% (hard)

Question Stats:

55% (01:24) correct 45% (01:33) wrong based on 165 sessions

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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

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Posts: 625
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]

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24 Jun 2017, 00:22
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
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Joined: 28 Jun 2015
Posts: 293
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]

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24 Jun 2017, 01:02
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.
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Location: Australia
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Given that x^3*y > 0 and that x^2*y^3 < 0 which of the following state  [#permalink]

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24 Jun 2017, 01:27
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
Joined: 05 Nov 2014
Posts: 107
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]

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24 Jun 2017, 01:41
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.
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Re: Given that x^3*y > 0 and that x^2*y^3 < 0 which of the following state  [#permalink]

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11 Jul 2018, 04:56
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Re: Given that x^3*y > 0 and that x^2*y^3 < 0 which of the following state &nbs [#permalink] 11 Jul 2018, 04:56
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