If a < b < c , which of the following must be true?

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

Quiz

Answer/Solution

None

Steps/Work

(I) a < b^2. Not necessarily true fractions: try a=1/3 and b=1/2.
(II) b − a < c. Not necessarily true: try a=-1, b=0, and c=1.
(III) a^2 < b^2 < c^2. Not necessarily true: try a=1, b=2, and c=3.
None of the options must be true.
Answer: A.