Given that x^3 > y^2 and y > 0, which of the… | GMAT Sprint

Free Practice Question

PS · Problem Solving

655-705

Inequalities

Given that $x^3 > y^2$ and $y > 0$ , which of the following statements must hold true?
I. $x > y$
II. $x > 0$
III. $\frac{x}{y} < 0$

Answer Choices

Correct answer marked below

I only

II only

Correct

I and II only

II and III only

I, II, and III

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Explanation

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Official Explanation

Official

Since

y > 0

, we know that

y^2 > 0

. Given that

x^3 > y^2

, we can conclude that

x^3 > 0

. This implies that

x > 0

, confirming that statement II is true. However, it is possible for

x = 3

and

y = 3

, which would mean…

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What this question tests

What it tests

Your ability to solve and combine linear inequalities and reason about ranges of values.

Common trap

Failing to flip the inequality sign when multiplying or dividing by a negative, or missing an inclusive/exclusive endpoint.

Given that x3>y2x^3 > y^2x3>y2 and y>0y > 0y>0, which of the following statements must hold true? I. x>yx > yx>y II. x>0x > 0x>0 III. xy<0\frac{x}{y} < 0yx​<0