Question Bank, Inequalities, # 10

If r is not equal to 0, is r^2/|r|<1?


(1) r > -1

(2) r < 1

(1) AND (2) SUFFICIENT: Together, the statements tell us that r is between -1 and 1. The square of a proper fraction (positive or negative) will always be smaller than the absolute value of that proper fraction.

The correct answer is C.
why in this question is not possible the following when c is the answer if r=1/2 then r^2=1/2^2=1/4 then lrl = to -1/2 (since from an absolute value we have positive and negative ) then result = 1/4>-1/2 . I understand when r=-1/2 then r^2=-1/2^2 = 1/4 and lrl=1/2 then this gives us 1/4<1/2

A variable inside an absolute value does mean that the variable could be positive or negative, but you start your question by saying "if r = 1/2" - so you've just set that variable to be positive 1/2, not negative 1/2. You have to keep using that value for r throughout the problem once you set it.