Saturday, December 25, 2010

CP #22

GMATClub m#02 test:

Is $x \gt y^2$ ?
1. $x \gt y + 5$
2. $x^2 - y^2 = 0$
(C) 2008 GMAT Club - [t]m02#19[/t]
• Statement (1) ALONE is sufficient, but Statement (2) ALONE is not sufficient
• Statement (2) ALONE is sufficient, but Statement (1) ALONE is not sufficient
• BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient
• EACH statement ALONE is sufficient
• Statements (1) and (2) TOGETHER are NOT sufficient
Statement (1) by itself is insufficient. Consider $(x,y)=(5, -1)$ or $(5, -3)$ .
Statement (2) by itself is insufficient. Consider $(x,y)=(\frac{1}{2}, \frac{1}{2})$ or $(2, 2)$ .
Statements (1) and (2) combined are sufficient. The absolute values of $x$ and $y$ are equal and $x \gt y$ , implying that $x$ is positive and $y$ is negative. Therefore, $x \gt y^2$ is false.
The correct answer is C.