EricKryk wrote:If z^n = 1, what is the value of z?

(1) n is a nonzero integer.

(2) z > 0

Target question: What is the value of z?

Given: z^n = 1

Before we examine the two statements, let's take some time to draw some conclusions about z and n if we are told that z^n = 1.

If z^n = 1, there are 3 possible cases:
case a: z = any number, and n = 0
case b: z = 1 and n = any number
case c: z = -1 and n = any even integer

Statement 1: n is a nonzero integer.
This rules out case a, which leaves us with case b (z = 1) and case c (z = -1)
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: z > 0
This rules out case c, which leaves us with case a (z = any positive number) and case b (z = 1)
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined
Statement 1 rules out case a
Statement 2 rules out case c
This leaves ONLY case b. In other words, z must equal 1
Since we can answer the target question with certainty, the combined statements are SUFFICIENT

Answer = C

Cheers,
Brent