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Is x negative? (1) x^3(1-x^2) < 0 (2) x^2 - 1 < 0 [#permalink ]
23 Aug 2007, 18:12

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Is x negative?
(1) x^3(1-x^2) < 0
(2) x^2 - 1 < 0

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Re: Is x negative? - DS [#permalink ]
23 Aug 2007, 18:47

above720 wrote:

Is x negative? (1) x^3 (1 - x^2) < 0 (2) x^2 - 1 < 0

from i, x^3 (1 - x)(1 + x) < 0

from ii, x^2 - 1 < 0

(x - 1) (x + 1) < 0

from i and ii: 1 + x < 0.

x < - 1

so its C.

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I come up with A ..
(1) x^3 (1 - x^2) < 0
X(cube) - X ( power of 5) < 0
checking for values..
when X is positive - the equation is satisified
when X is negative
the equation is not satisfied....
(2)
X(square) -1 < 0
X(square) < 1
X could be a negative fraction or positive fraction
Is the answer A?

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Got B:
I: Ins: plug in x = -1/2 and x = 2
II: Suff: (x-1)(x+1)<0
x < 1 and x <1> Common solution: x < -1. To check - again plug in.
UPD: Sorry, I made a mistake in II: x = -1/2 and x = 1/2 also satisfy the exuation. I change my answer to E.

Last edited by

Whatever on 23 Aug 2007, 22:54, edited 1 time in total.

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i come up with E.
All the guys above-did u try positive and negative fraction values for X.
With 1/2 and -1/2 both the eqn are satisfied so can't say for sure if it is positive or -ve.

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I got C. Nic to see all the options in play though

VP

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Is x negative ?

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

x^3-x^5 < 0

x^3 < x^5

can be false for x=1/2 or true for x=2

can be true for x=-1/2 or false for x=-2

insufficient

Statement 2
x^2 - 1 < 0

x^2 < 1

can be true for x=1/2 or false for x=2

can be true for x=-1/2 or false for x=-2

insufficient

Statements 1&2
x has to be negative - the only way for both formulas to work !

the answer is (C)

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I will go with C.
From St1:
x^3 < 0 hence x < 0 or 1-x^2 < 0 i.e. -x^2 <1> 1 i.e. x>1 or x < -1
Therefore A & D are ruled out.
From St1:
x^2 - 1 < 0 hence x^2 < 1
-1 < x < 1
if St1 and St 2 are combined, then -1 < x < 0
Hence C

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Subhen

Last edited by

subhen on 25 Aug 2007, 03:21, edited 1 time in total.

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subhen wrote:

x^2 - 1 < 0 hence x^2 < 1 -1 < x < 1 Even if St1 and St 2 are combined, we do not know if x is +ve or -ve. Hence E.

If X^2 < 1

combining 1 and 2.

1-x^2 > 0

so x^3 <0

=> x <0

C is SUFF

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Re: Is x negative? - DS [#permalink ]
25 Aug 2007, 03:59

above720 wrote:

Is x negative? (1) x^3(1-x^2) < 0 (2) x^2 - 1 < 0

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

The above statement is false if x < -1, true if -1< x < 0 , false if 0<x<1> 1.

Thus (1) tells is that x is either a negative number greater than - 1 or a postive number greater than 1.

NOT SUFF

(2) -1 < x < 1

NOT SUFF

(T) x is either a negative number greater than - 1

SUFF

C

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Re: Is x negative? - DS [#permalink ]
25 Aug 2007, 10:42

above720 wrote:

Is x negative? (1) x^3(1-x^2) < 0 (2) x^2 - 1 < 0

we need to solve inequalities system of 1 and 2 combined then it gives us the range of negative x.s so it is C

Re: Is x negative? - DS
[#permalink ]
25 Aug 2007, 10:42