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# Is x negative?

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Director
Joined: 14 Dec 2012
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03 May 2013, 01:11
abhi758 wrote:
Is x negative?

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

Hi all,

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

let x=10....==>therefore 10^3(1-100)=-99*10^3<0
satisfying for positive X
now let x= -0.1===> therefore (-0.1)^3(1-0.01)= -0.99*0.1^3<0
satisfying when X is negative...
so X can be positive and negative both so not definite answer.

(2) x^2-1 < 0
this holds for -1<x<1

again not sufficient

now combining
from statement 2 we got 2 things:
==> x^2-1<0....therefore 1-x^2>0-----(1)
==>range of x...-1<x<1-----(2)

now coming to statement 1...
we know 1-x^2>0.....from (1)
therefore for
x^3(1-x^2) < 0....to hold true...x^3 <0....since we know 1-x^2 is positive from (1)
now we have x^3<0....therfeore x<0----(3)

now using (2) and (3)
x belongs to-1<x<0
menas x is negative.hence sufficient

therefore (C)

hope it helps.

SKM
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Re: Is p a negative number?  [#permalink]

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21 May 2013, 09:07
Statement 1:
p³(1-p²) < 0
Both p³ and 1-p² must be of opposite signs.

If p<0
implies p³<0
implies 1-p²>0
implies 1>p²
implies -1<p<0

If p>0
implies p³>0
implies 1-p²<0
implies 1<p²
implies p>1

So, from statement 1, p can either lie between -1 or 0 or it can be greater than 1.
So, it is not sufficient to answer.

Statement 2:
p²-1<0
implies p²<1
implies -1<p<1 (excluding 0)
So, this statement alone is also not sufficient to answer.

Combining the two statements.
we get -1<p<0
So, p is -ve.

Hope it is clear.
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Re: Is p a negative number?  [#permalink]

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Updated on: 21 May 2013, 09:16
1
fozzzy wrote:
Is p a negative number?

(1) p^3(1 – p^2) < 0

(2) p^2 – 1 < 0

Is p a negative number?

(1) p^3(1 – p^2) < 0

Hence p^3 and 1 - p^2 have opposite sign .

If p^3 is positive and 1-p^2 is negative : Then p is positive
If p^3 is negative and 1-p^2 is positive: Then p is negative

2) p^2 – 1 < 0

Hence p^2 < 1 and thus: -1<p<1 so p could be positive or negative : INSUFFICIENT

(1) p^3(1 – p^2) < 0 AND 2) p^2 – 1 < 0

So we are in the second case for the first statement : i.e : p^3 is negative and 1-p^2 is positive , Thus p is negative

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Originally posted by Rock750 on 21 May 2013, 09:10.
Last edited by Rock750 on 21 May 2013, 09:16, edited 1 time in total.
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Re: Is p a negative number?  [#permalink]

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21 May 2013, 09:14
fozzzy wrote:
Is p a negative number?

(1) p^3(1 – p^2) < 0

(2) p^2 – 1 < 0

1) $$p^5 > p^3$$

p>1 or -1<p<0

Insufficient.

2) $$p^2 < 1$$

-1 < p < 1

Insufficient.

1 & 2 together... -1 < p < 0. Sufficient

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Re: Is p a negative number?  [#permalink]

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22 May 2013, 02:56
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23 May 2013, 20:06
1
Is x negative?

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

Hi Bunuel, please verify whether my approach is valid or not?

Statement 1: Insufficient becasue valid for positive 2 and -1/3
statement 2 : Insufficient becasue -1<x<1

Combining 1 and 2: take negitive "-" common from statement 1

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

As from statement 2 we know x^2-1 is negative, In statement 1 (-x^3) must be negative so that -x^3(x^2-1) be negative.
Thus we can conclude that x is negative.

sorry for the poor writing.....

Regards
Atal Pandit
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24 May 2013, 00:50
1
atalpanditgmat wrote:
Is x negative?

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

Hi Bunuel, please verify whether my approach is valid or not?

Statement 1: Insufficient becasue valid for positive 2 and -1/3
statement 2 : Insufficient becasue -1<x<1

Combining 1 and 2: take negitive "-" common from statement 1

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

As from statement 2 we know x^2-1 is negative, In statement 1 (-x^3) must be negative so that -x^3(x^2-1) be negative.
Thus we can conclude that x is negative.

sorry for the poor writing.....

Regards
Atal Pandit

Your approach correct, though the red part is not.

We have that -x^3 (x^2-1)<0 --> -x^3*negative<0 --> -x^3>0 --> x^3<0 --> x<0.

Hope it's clear.
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24 May 2013, 03:03
Bunuel wrote:
atalpanditgmat wrote:
Is x negative?

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

Hi Bunuel, please verify whether my approach is valid or not?

Statement 1: Insufficient becasue valid for positive 2 and -1/3
statement 2 : Insufficient becasue -1<x<1

Combining 1 and 2: take negitive "-" common from statement 1

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

As from statement 2 we know x^2-1 is negative, In statement 1 (-x^3) must be negative so that -x^3(x^2-1) be negative.
Thus we can conclude that x is negative.

sorry for the poor writing.....

Regards
Atal Pandit

Your approach correct, though the red part is not.

We have that -x^3 (x^2-1)<0 --> -x^3*negative<0 --> -x^3>0 --> x^3<0 --> x<0.

Hope it's clear.

oh my bad, though i mean to say similar thing.....Thank you for your response...
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03 Nov 2018, 03:45
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Re: Is x negative?   [#permalink] 03 Nov 2018, 03:45

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