Som_A wrote:Is x positive?
(1) (x - 3)² > 0
(2) x³ - 1 > 0
IMPORTANT CONCEPTS
Rule #1: EVEN powers are always greater than or equal to zero. So, (POSITIVE value)^(EVEN integer) > 0, and (NEGATIVE value)^(EVEN integer) > 0
Rule #2: ODD powers PRESERVE the sign. In other words, (POSITIVE value)^(ODD integer) = POSITIVE value, and (NEGATIVE value)^(ODD integer) = NEGATIVE value
Target question: Is x positive?
Statement 1: (x - 3)² > 0
The ONLY thing this tells us is that x ≠0 (see Rule #1)
So, there are many values of x that satisfy this condition. Here are two:
Case a: x = 1, in which case
x is positive
Case b: x = -1, in which case
x is NOT positive
Since we cannot answer the
target question with certainty, statement 1 is NOT SUFFICIENT
Statement 2: x³ - 1 > 0
Add 1 to both sides to get: x³ > 1
In other words, x³ is POSITIVE
Since x is raised to an ODD power, we can apply rule #2 to conclude that
x must be positive
Since we can answer the
target question with certainty, statement 2 is SUFFICIENT
Answer =
B
Cheers,
Brent
