Given that x^3*y 0 and that x^2*y^3

Question

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

Luckisnoexcuse · Answer

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

TimeTraveller · Answer

(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.

danlew · Answer

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

Answer D

harikrish · Answer

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.

LeoN88 · Answer

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

I Yes, we already deduced.
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

CEdward · Answer

Given that x3∗y > 0 and that x2∗y3<0 which of the following statements must be true?

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

The stem says that x and y are both negative. It follows that I and III must be true. y does not have to be sandwiched in between x and 0.

Malar95 · Answer

I. x<0
---- Makes sense as its a (-)

II. x<y<0
------ Cant be ascertained

III. y3<x2
------- y^3 is (-) and x^2 is (+)

Thus D

bumpbot · Answer

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

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