Pugalenthi wrote:OG 11th edition DS question:
Is X negative?
(1) X^3(1-x^2)<0
(2) X^2 -1 < 0
Please explain your response.
Statement 1: x³(1-x²)<0.
x=2:
2³(1-2²) < 0.
-24 < 0.
x= -1/2:
(-1/2)³(1- (-1/2)² )<0
(-1/8)(3/4) < 0
-3/32 < 0.
Since it's possible that x=2 or that x=-1/2, we cannot determine whether x<0.
Insufficient.
Statement 2: x² < 1.
x = 1/2:
(1/2)² < 1.
1/4 < 1.
x = -1/2:
(-1/2)² < 1.
1/4 < 1.
Since it's possible that x=1/2 or that x=-1/2, we cannot determine whether x<0.
Insufficient.
Statements 1 and 2:
Since x²-1 < 0, we know that 1-x² > 0.
Thus, statement 1 becomes x³ * positive < 0, implying that x³ < 0 and that x<0.
Sufficient.
The correct answer is
C.
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