tradinggenius wrote:
If \(z^n = 1\), what is the value of z?
(1) n is a non zero integer
(2) z > 0
Target question: What is the value of z? Given: \(z^n = 1\) There are 3 possible cases in which the above equation holds true. When a given piece of information yields a small handful of possible cases, I often find it useful to
list the possible cases before dealing with the statements (which I've already scanned)
case i:
z is any integer, and n = 0 (e.g., \(5^0 = 1\))
case ii:
z = 1, and n is any number (e.g., \(1^3 = 1\))
case iii:
z = -1, and n is any EVEN INTEGER (e.g., \((-1)^4 = 1\))
Statement 1: n is a non zero integer This means we're dealing with
EITHER case ii OR case iii. Since cases ii and iii yield different answers to the
target question, statement 1 is NOT SUFFICIENT
Statement 2: z > 0This means we're dealing with
EITHER case i OR case ii. Since cases i and ii yield different answers to the
target question, statement 2 is NOT SUFFICIENT
Statements 1 and 2 combined Statement 1 tells us we're dealing with
case ii or case iiiStatement 2 tells us we're dealing with
case i or case iiSince only
case ii satisfies both statements, it must be the case that
z = 1, and n is any number
Since we can be certain that
z = 1, the combined statements are SUFFICIENT
Answer: C
Cheers,
Brent
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