Question

If \( p<x<q \) and \( r<y<s \), is \( x>y \)?
(1) \( p<r \)
(2) \( q<r \)

• A. Statement 1 alone is sufficient but statement 2 alone is not sufficient to answer the question asked.
• B. Statement 2 alone is sufficient but statement 1 alone is not sufficient to answer the question asked.
• C. Both statements 1 and 2 together are sufficient to answer the question but neither statement is sufficient alone.
• D. Each statement alone is sufficient to answer the question.
• E. Statements 1 and 2 are not sufficient to answer the question asked and additional data is needed to answer the statements.

Hint:

When dealing with inequalities, make sure to carefully consider the direct relationships between the variables involved. Additional data may be required in many cases.

Answer 1

Answer: (E)

Step 1: Analyze statement 1.
Statement 1 tells us that \( p<r \). This information does not give any direct relationship between \( x \) and \( y \), so statement 1 alone is insufficient.
Step 2: Analyze statement 2.
Statement 2 tells us that \( q<r \). Again, this does not provide any direct information about the relationship between \( x \) and \( y \), so statement 2 alone is also insufficient.
Step 3: Combine both statements.
Combining both statements does not give us enough information to compare \( x \) and \( y \), as we don’t know the exact relationship between \( x \), \( y \), \( p \), \( q \), \( r \), and \( s \). Therefore, additional data is needed.
Step 4: Conclusion.
The correct answer is (E). Both statements are insufficient to determine whether \( x>y \).