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

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

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14 Sep 2005, 09:12
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Is x negative ?
(1) n^3(1-x^2)<0
(2) x^2-1<0
VP
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14 Sep 2005, 09:20
I will think its E.

i) n^3 (1- x^2) < 0
not sufficient unless we know n.

ii) x^2 < 1 or mod(x) < 1
-1<x<+1

not sufficient

together:
n^3 (1- x^2) < 0

if:
n < 0 and x < 0 (but > -1)
n < 0 and x > 0 (but < 1)

PS: is it n^3 or x^3?
Senior Manager
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14 Sep 2005, 09:24
I'm getting E

1) Insuff
n^3(1-x^2)<0
n^3<0 or 1-x^2<0
n^3<0 or x^2>1
or n is negative and x could be -ve or +ve integer or fraction>1

2) Insuff
x^2-1<0
or x^2<1
x could be a -ve or +ve fraction.

1 & 2) just proves 1-x^2>0 or x is a fraction either +ve or -ve. insuff
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-Vikram

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14 Sep 2005, 11:54
i am getting E too

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15 Sep 2005, 18:56
My take is C.

stem 1: n^3(1-x^2)<0
i.e. either n^3<0 or (1-x^2)<0. Not sufficient.

stem 2: x^2-1<0 = x^2<1. Not sufficient.

Now lets combine both the statements:-
According to stem 2: x^2 is less than 1 which means 1-x^2 is +ve. Therefore n^3 should be -ve [according to stem 1]. Thus both the statements taken together are sufficient to ans the question.

Lemme know if i am missing somehting in my approach.
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15 Sep 2005, 19:38
tingle wrote:
My take is C.

stem 1: n^3(1-x^2)<0
i.e. either n^3<0 or (1-x^2)<0. Not sufficient.

stem 2: x^2-1<0 = x^2<1. Not sufficient.

Now lets combine both the statements:-
According to stem 2: x^2 is less than 1 which means 1-x^2 is +ve. Therefore n^3 should be -ve [according to stem 1]. Thus both the statements taken together are sufficient to ans the question.

Lemme know if i am missing somehting in my approach.

The question is wether X is negative or not. I think you thought the question was concerning N.

X can be -ive or +ive, even in your example

x^2 is less than 1 so -1<x<1
Senior Manager
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15 Sep 2005, 22:15

From statement 1, x could be both +ve or -ve
Similarly from statement 2 could be both + ve or -ve,

And combing both statements will also not be sufficient.
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15 Sep 2005, 22:27
Antmavel wrote:
tingle wrote:
My take is C.

stem 1: n^3(1-x^2)<0
i.e. either n^3<0 or (1-x^2)<0. Not sufficient.

stem 2: x^2-1<0 = x^2<1. Not sufficient.

Now lets combine both the statements:-
According to stem 2: x^2 is less than 1 which means 1-x^2 is +ve. Therefore n^3 should be -ve [according to stem 1]. Thus both the statements taken together are sufficient to ans the question.

Lemme know if i am missing somehting in my approach.

The question is wether X is negative or not. I think you thought the question was concerning N.

X can be -ive or +ive, even in your example

x^2 is less than 1 so -1<x<1

Ooops.. I misunderstood the question! thanks antmavel for the clarification.
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16 Sep 2005, 10:36
I get E as well. Combining the statements gets you + and - possibilities.
16 Sep 2005, 10:36
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