Is x negative? 1) x^3(1-x^2)<0 2) x^2-1<0 : Quant Question Archive [LOCKED]
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# Is x negative? 1) x^3(1-x^2)<0 2) x^2-1<0

Author Message
SVP
Joined: 05 Jul 2006
Posts: 1743
Followers: 6

Kudos [?]: 316 [0], given: 49

Is x negative? 1) x^3(1-x^2)<0 2) x^2-1<0 [#permalink]

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10 Oct 2006, 12:31
This topic is locked. If you want to discuss this question please re-post it in the respective forum.

Is x negative?

1) x^3(1-x^2)<0

2) x^2-1<0
SVP
Joined: 01 May 2006
Posts: 1797
Followers: 9

Kudos [?]: 149 [0], given: 0

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10 Oct 2006, 13:07
For me (C)

Stat 1

x^3(1-x^2)<0
<=> x^3*(x^2 -1) > 0
<=> [ x > 0 and (x^2 -1)>0 ] or [ x < 0 and (x^2 -1)<0 ]
<=> x > 1 or -1 < x < 0

INSUFF

Stat 2
x^2-1<0
<=> -1 < x < 1

INSUFF

Combining (1) with (2)

[ x > 1 or -1 < x < 0 ] and -1 < x < 1
<=> -1 < x < 0

SUFF
Senior Manager
Joined: 13 Sep 2006
Posts: 281
Location: New York
Followers: 1

Kudos [?]: 17 [0], given: 0

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10 Oct 2006, 13:12
I got D by picking numbers for X. I dunno how to solve this algebraically.
Director
Joined: 06 Sep 2006
Posts: 743
Followers: 1

Kudos [?]: 36 [0], given: 0

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10 Oct 2006, 13:55
Is x negative?

1) x^3(1-x^2)<0

2) x^2-1<0

1) Insufficient.
2) Insufficient
-x^2 + 1 > 0 (multiplying both sides with -1)
(1 - x^2) > 0 -------------- (A)

1) & 2) Insufficient.

Combining
since (1 - x^2) > 0 (From (A))
so, for x^3(1-x^2) < 0 to work, x^3 < 0 => x < 0

C.
10 Oct 2006, 13:55
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