Stiv
If z^n = 1, what is the value of z?
(1) n is a nonzero integer.
(2) z > 0
Zero raised to any power is zero and any number raised to the power of 0 equals one?
Is that the rule of it is reversed?
This is not a difficult question by itself, but
clarity of approach matters a lot in getting it right. The low accuracy for this question suggests that most students could not think through this question clearly.
At
eGMAT, we strongly advocate that
in DS Questions, the student should first analyze the question statement thoroughly and only then move on to analyzing the two statements. You'll see how elegantly this question will simplify with this approach.
We are given that z^n = 1. So, what cases are possible for the value of z and n?
Case 1: z = 1; n has any integral value
Case 2: z = -1; n is an even integer
Case 3: z has any non-zero value; n = 0
Please note that only after this analysis are we going to the first Statement.
As per the first statement,n is a non-zero integer
This rules out Case 3.
However, this still leaves out Case 1 and 2. So, z can either be equal to 1 or z can be equal to -1. So, Statement 1 alone is not sufficient.
As per the second statement,
z > 0
This rules out Case 2. However, Case 1 and 3 still remain. Again, we have not been able to determine a unique value of z. So, Statement 2 alone is not sufficient either.
Combining both the Statements, From Statement 1, z could either be 1 or -1
From Statement 2, z > 0
Therefore, only possible value of z is 1.
Thus, by combining both the statements together, we have been able to determine a unique value of z. So, the correct answer is Choice C.
Takeaway: The correct answer is only a byproduct of a clear approach. Hope this helps.
Japinder