If x<0, y>0, and |x^3| > |y^2|, which of the following must be true?	Select
A) x > y
B) y^2 > x^2
C) -x^3 < y^2
D) –x < y
E) x < –y
Let’s go through each answer choice: (A) can never be true, since no negative is greater than a positive. (B) doesn’t have to be true – consider what would happen if x = -2 and y = 1. (C) can never be true, as x^3 must be negative, and y^2 must be positive. (D) can never be true, since if x &lt; 0, -x is the same thing as |x|, and |x| &gt; y. (E) can be manipulated by multiplying both sides by -1, which gives us –x &gt; y. Remember that x &lt; 0, so –x = |x|, and y is positive, so |y| = y. Thus –x^3 &gt; y^2 is the same statement as |x^3| &gt; |y^2|, and (y^2 &gt; x^2) must be true.
<result>B</result>
If x<0, y>0, and |x^3| > |y^2|, which of the following must be true?