Question

Is the range of the integers 6, 3, \( y \), 4, 5, and \( x \) greater than 9?
(1) \( y>3x \)
(2) \( y>x>3 \)

• A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
• B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
• C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
• D. EACH statement ALONE is sufficient.
• E. Statements (1) and (2) TOGETHER are not sufficient

Hint:

When solving range problems, check if the given information allows you to determine both the maximum and minimum values of the set.

Answer 1

Answer: (E)

Step 1: Analyze statement (1).
Statement (1) tells us that \( y>3x \), but we do not know the actual values of \( x \) or \( y \), so this does not give us enough information to determine the range of the set.
Step 2: Analyze statement (2).
Statement (2) tells us that \( y>x>3 \), but again, we do not know the values of \( x \) or \( y \), so we cannot determine the range of the set from statement (2) alone.
Step 3: Combine statements (1) and (2).
Combining both statements still does not provide enough information about the values of \( x \) and \( y \) to determine the range of the set. For example, if \( x = 4 \) and \( y = 10 \), the range is 6, but if \( x = 5 \) and \( y = 8 \), the range is 4.
Thus, the combined statements are not sufficient. \[ \boxed{E} \]