Absolute Value Question

GRE Quant Problem Solving
1

If |z| < 1, which of the following statements must be true? Indicate
Indicate all such statements.

A) z^2 ≤ 1
B) z^2 ≤ z
C) z^3 ≤ z

I am confused why the answer is not A,B and C (correct answer is just A). If we plug 0 in the question we have 0<1 which is verified and if we plug zero on each scenario it’s always verified. Am I missing something? Should we not consider 0 elevated to a number because is undefined?

2

You have to pick an answer that is true for all -1 < z < 1. Checking only z = 0 is not sufficient, since it’s just one value from the infinitely many within that interval.