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Is x negative?
(1) x^3(1-x^2) < 0
(2) x^2-1 < 0
OA C
Source: Official Guide
(1) x^3(1-x^2) < 0
(2) x^2-1 < 0
OA C
Source: Official Guide
Let's take each statement one by one.BTGmoderatorDC wrote:Is x negative?
(1) x^3(1 - x^2) < 0
(2) x^2 - 1 < 0
OA C
Source: Official Guide
(1) x^3(1 - x^2) < 0
Since x^3(1 - x^2) is less than 0, x cannot be 0.
From x^3(1 - x^2) < 0, we have x^3 - x^5 < 0. Divinding the inequality throught by x^2, we get x < x^2.
From x < x^2, we get
Case 1: Say x = 2, then x^2 = 4; thus, we do not have x as negative. The answer is no.
Case 2: Say x = -1/2, then x^2 = 1/4; thus, we have x as negative. The answer is yes.
No unique answer. Insufficient.
(2) x^2 - 1 < 0
x^2 < 1
Case 1: Say x = -1/2, then x^2 = 1/4; thus, we have x as negative. The answer is yes.
Case 2: Say x = 1/2, then x^2 = 1/4; thus, we do not have x as negative. The answer is no.
No unique answer. Insufficient.
(1) and (2)
From both, we have x < x^2 < 1; thus, Case 1 of Statement 1 and Case 2 of Statement 2 are not applicable. Thus, x is negative. Sufficient.
The correct answer: C
Hope this helps!
-Jay
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