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

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Bunuel
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If x^3 > y^2 and y > 0, which of the following must be true ? [#permalink] New post   04 Nov 2021, 08:00
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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
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B
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BrentGMATPrepNow
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Re: If x^3 > y^2 and y > 0, which of the following must be true ? [#permalink] New post   04 Nov 2021, 10:12
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Bunuel wrote:
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


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
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Re: If x^3 > y^2 and y > 0, which of the following must be true ? [#permalink] New post   04 Nov 2021, 12:39
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
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Re: If x^3 > y^2 and y > 0, which of the following must be true ? [#permalink] New post   04 Nov 2021, 17:38
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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Re: If x^3 > y^2 and y > 0, which of the following must be true ? [#permalink]
04 Nov 2021, 17:38
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