If x^3 y^2 and y 0, which of the following must be true ?

Question

If  x^3>y^2  and  y>0 , which of the following must be true?

I.  x>y 
II.  x>0 
III.  \frac{x}{y}<0

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

BrentGMATPrepNow · Accepted Answer

If y ≠ 0, then we can be certain that y² > 0
Since we're told x³ > y²
So, we can write: x³ > y² > 0
If x³ > 0, then we can be certain that x is positive. 
So,  statement II is true .

Next, if x³ > y², then it COULD be the case that x = 2 and y = 2
If x = 2 and y = 2, then x = y, which means  statement I is not necessarily true . 
Similarly, if x = 2 and y = 2, then x/y = 2/2 = 1, which means  statement III is not necessarily true.

Answer: B

Chasingthesun · Answer

since y>0, y is positive
for x^3>y^2 , x should also be positive
statement II must be true

statement I : x>y - can be but not necessary
x=y, and still x^3>y^2 holds true

statement III : for x/y < 0 one of them is negative,
since y>0 is already given, then x<0. But this does not justify the given x^3>y^2

Option B

Kinshook · Answer

Asked: If  x^3>y^2  and  y>0 , which of the following must be true?

Since y>0
x^3 > y^2 > 0
x > 0

But there is no way to ascertain whether x> y
Since both x>0 and y>0;  \frac{x}{y} >0

I.  x>y 
II.  x>0 
III.  \frac{x}{y}<0

IMO B

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If x^3 > y^2 and y > 0, which of the following must be true ?

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