Official Solution:
If \(x\), \(y\), and \(z\) are positive numbers such that \(3x < 2y < 4z\), which of the following statements could be true?
I. \(y = z\)
II. \(y > z\)
III. \(x > z\)
A. I only
B. I and II only
C. I and III only
D. II and III only
E. I, II and III
Notice that the question asks: "
which of the following statements COULD be true?" NOT "
which of the following statements MUST be true?"
I. \(y = z\). From the stem we know that \(2y < 4z\). So, \(y < 2z\). It's certainly possible that \(y = z\), for example, \(y = z=1\).
II. \(y > z\) From the stem we know that \(2y < 4z\). So, \(y < 2z\). It's certainly possible that \(y > z\), for example, \(y = 3\) and \(y=2\).
III. \(x > z\). From the stem we know that \(3x < 4z\). And again, it's possible that \(x > z\), for example, \(x=10\) and \(z=9\).
Answer: E