If a < b < c , which of the following must be true?
(I) a < b^2
(II) b − a < c
(III) a^2 > b^2 > c^2
Choose one.
A) None B) I only C) II only D) III only E) II and III
(I) a &lt; b^2. Not necessarily true fractions: try a=1/3 and b=1/2.   (II) b − a &lt; c. Not necessarily true: try a=-1, b=0, and c=1.   (III) a^2 &lt; b^2 &lt; c^2. Not necessarily true: try a=1, b=2, and c=3.   None of the options must be true.   Nonenswer: None.
<result>A</result>
If a < b < c , which of the following must be true?
(I) a < b^2
(II) b − a < c
(III) a^2 > b^2 > c^2