M7MBA wrote:Is x greater than zero? $$(1)\ \ \ x^6 > x^2$$ $$(2)\ \ \ x^5 < x^2$$ The OA is the option C.
Each statement implies that x is NONZERO, with the result that any EVEN POWER of x will yield a POSITIVE value.
Thus, we can simplify the inequalities by dividing each side by x².
Statement 1: x� > x²
x�/x² > x²/x²
x� > 1.
The resulting inequality requires that x>1 or that x<-1.
Since it's possible that x is greater than 0 or that x is less than 0, INSUFFICIENT.
Statement 2: x� < x²
x�/x² < x²/x²
x³ < 1.
The resulting inequality requires that x<1.
Since it's possible that x is greater than 0 or that x is less than 0, INSUFFICIENT.
Statements combined:
The only range that satisfies both statements is x<-1.
Since x must be less than 0, the answer to the question stem is YES.
SUFFICIENT.
The correct answer is
C.
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