Question

If \( \frac{x + y}{z}>0 \), is \( x<0 \)?
(1) \( x = y + 2 \)
(2) \( z<0 \)

• 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 working with inequalities, consider the signs of the terms involved and apply them carefully to solve for unknowns.

Answer 1

The Correct Option is B

Step 1: Analyze statement (1).
Statement (1) tells us that \( x = y + 2 \). This does not give us sufficient information to determine whether \( x<0 \), so statement (1) alone is not sufficient.
Step 2: Analyze statement (2).
Statement (2) tells us that \( z<0 \). From the inequality \( \frac{x + y}{z}>0 \), since \( z \) is negative, \( x + y \) must also be negative. Thus, \( x<-y \). This implies that \( x \) is less than 0.
Thus, statement (2) alone is sufficient.
\[ \boxed{B} \]