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.
, 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 valueCase 2:
z = -1; n is an even integerCase 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.