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  Options:
A) II only
B) I only
C) None
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=-1/2, b=-1/3, and c=-1/4.   (III) a^2 &lt; b^2 &lt; c^2. Not necessarily true: try a=-1, b=0, and c=1.   None of the options must be true.   Answer: None.
<result>C</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