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# OG 154 Is x negative?

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Senior Manager
Joined: 01 Feb 2005
Posts: 271
OG 154 Is x negative? [#permalink]

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12 Jan 2007, 11:43
Data Sufficiency Question -
Is x negative?

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

I read the explanation in the OG but found it very confusing. Any easier way to solve it?

Thanks
SVP
Joined: 01 May 2006
Posts: 1796

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12 Jan 2007, 11:48
The statment 2 is impossible in the scope of GMAT with real numbers.

Are u sure about it x^2 < 0 ?
Senior Manager
Joined: 01 Feb 2005
Posts: 271

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12 Jan 2007, 11:50
Sorry my bad... 2nd statement is

Data Sufficiency Question -
Is x negative?

1) x^3(1-x^2) < 0
2) x^2 - 1 < 0
SVP
Joined: 01 May 2006
Posts: 1796

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12 Jan 2007, 11:58
(C) for me

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

implies that:
x^3 > 0 and 1-x^2 < 0 <=> x > 0 and x^2 > 1 <=> x > 1
or
x^3 < 0 and 1-x^2 > 0 <=> x < 0 and x^2 < 1 <=> -1 < x < 0

INSUFF.

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

INSUFF.

Both (1) and (2)
-1 < x < 1
and
(x > 1 or -1 < x < 0)

We finally have : -1 < x < 0

SUFF.
SVP
Joined: 05 Jul 2006
Posts: 1747

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12 Jan 2007, 13:12
Data Sufficiency Question -
Is x negative?

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

from one

either x^3 is -ve or 1-x^2 is

if x^3 is -ve then x is -ve

and if 1-x^2 is -ve then x^2 >1 and x is -ve or +ve ....insuff

from two

x^2<1 x could be either +ve or -ve...insuff

both together

x^2 <1 thus 1-x^2 is sure +ve

and from one thus x^3 has to be -ve and so is x

my answer is C, I BACK UP MY FRIEND FIG ALL THE WAY

CHEERS MATE
Senior Manager
Joined: 01 Feb 2005
Posts: 271

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12 Jan 2007, 13:23
Thanks guys... The OG explanation put me to sleep... Your explanations made more sense to me!
SVP
Joined: 01 May 2006
Posts: 1796

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12 Jan 2007, 15:39
axl_oz wrote:
Thanks guys... The OG explanation put me to sleep... Your explanations made more sense to me!

Well .... Sometimes a rest is good as well :D

By the way, u are welcome
SVP
Joined: 01 May 2006
Posts: 1796

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12 Jan 2007, 15:44
Welcome back Yezz

I hope u to achieve your goal .... to crack this GMAT
Senior Manager
Joined: 29 Jan 2011
Posts: 358

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10 Jul 2011, 02:09
Is this correct way to solve for statement 1??

St1 x^3(1-x^2)<0

therefore, x^3 < 0 or 1-x^2 < 0

therefore, x < 0 or 1 < x^2

which yields => x<0 OR x> 1 OR x < 1??
Current Student
Joined: 26 May 2005
Posts: 563

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10 Jul 2011, 02:22
siddhans wrote:
Is this correct way to solve for statement 1??

St1 x^3(1-x^2)<0

therefore, x^3 < 0 or 1-x^2 < 0

therefore, x < 0 or 1 < x^2

which yields => x<0 OR x> 1 OR x < 1??

X^3*(1-x^2)<0
it mean either X^3<0 or 1-x^2<0
so u have 2 scenarios;

first : X^3>0 = X>0
1-x^2 <0 = X^2>1= x> +/-1... combining this two we get X>1

second X^3 <0 = X<0
1-X^2 >0 = -X^2>-1; X^2<1 X<+/-1.. combining this two we get x<-1
Senior Manager
Joined: 29 Jan 2011
Posts: 358

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10 Jul 2011, 02:29
sudhir18n wrote:
siddhans wrote:
Is this correct way to solve for statement 1??

St1 x^3(1-x^2)<0

therefore, x^3 < 0 or 1-x^2 < 0

therefore, x < 0 or 1 < x^2

which yields => x<0 OR x> 1 OR x < 1??

X^3*(1-x^2)<0
it mean either X^3<0 or 1-x^2<0
so u have 2 scenarios;

first : X^3>0 = X>0
1-x^2 <0 = X^2>1= x> +/-1... combining this two we get X>1

second X^3 <0 = X<0
1-X^2 >0 = -X^2>-1; X^2<1 X<+/-1.. combining this two we get x<-1

can this problem be solved in a easy manner?
Senior Manager
Joined: 29 Jan 2011
Posts: 358

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10 Jul 2011, 02:33
Fig wrote:
(C) for me

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

implies that:
x^3 > 0 and 1-x^2 < 0 <=> x > 0 and x^2 > 1 <=> x > 1
or
x^3 < 0 and 1-x^2 > 0 <=> x < 0 and x^2 < 1 <=> -1 < x < 0

INSUFF.

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

INSUFF.

Both (1) and (2)
-1 < x < 1
and
(x > 1 or -1 < x < 0)

We finally have : -1 < x < 0

SUFF.

From this statement : x^3 < 0 and 1-x^2 > 0 <=> x < 0 and x^2 < 1 <=> -1 < x < 0

How do we have the lower bound -1 < x??? I dont understand ... All it says is x < 0 and x < 1 So lower bound could be even less than -1 ???
Re:   [#permalink] 10 Jul 2011, 02:33
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