Carcass 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