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Is x negative?

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Is x negative? [#permalink] New post 21 Dec 2009, 12:01
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A
B
C
D
E

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Question Stats:

84% (02:06) correct 15% (00:18) wrong based on 13 sessions
Is x negative?

(1) x^3(1-x^2) < 0
(2) x^2-1 < 0
[Reveal] Spoiler: OA
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Re: Need Help with OG 11 ed DS 154 [#permalink] New post 21 Dec 2009, 14:12
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gi wrote:
Hi All,

I'm new to this forum. I'm working through some OG DS questions and I find that some of the explanations to ans are not clear or take too long to solve in 2 mins.

Q:DS154
Is x negative?
1) x^3(1-x^2) < 0
2) x^2-1 < 0

Thanks


(1) x^3(1-x^2)<0, two cases (one of the multiples negative, another positive):

A. x^3>0 and 1-x^2<0;

x^3>0 --> x>0
----------------0----------------

1-x^2<0 --> x<-1 or x>1
-----(-1)------0------(1)-------

Hence the range for A is x>1.

B. x^3<0 and 1-x^2>0

x^3<0 --> x<0
---------------0------------

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

Hence the range for B is -1<x<0.

Two ranges: x>1 OR -1<x<0. Not sufficient.


(2) x^2-1 < 0 --> -1<x<1. Not sufficient.


(1)+(2) Inersection of the ranges from (1) and (2) is -1<x<0, hence x<0 is true. Sufficient.

Answer: C.
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Re: Need Help with OG 11 ed DS 154 [#permalink] New post 21 Dec 2009, 14:21
IMO C:

A) X^2(1-X^2) <0 so X^3<0 or X^2>1
x could be positive or negative

B) X^2-1<0
(X-1)(X+1)<0 so X<1 or X<-1
x could be positive or negative

Combined X is negative for both statements to hold true.

OA?
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Re: Need Help with OG 11 ed DS 154 [#permalink] New post 21 Dec 2009, 14:33
C; like Bunuel's details.
Inequalities without coffee can not be so much fun!!!

Bunuel,

What subject that you dont like in GMAT Maths?
Be warned, I may too know the answer...!
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Re: Need Help with OG 11 ed DS 154 [#permalink] New post 21 Dec 2009, 14:52
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DestinyChild wrote:
C; like Bunuel's details.
Inequalities without coffee can not be so much fun!!!

Bunuel,

What subject that you dont like in GMAT Maths?
Be warned, I may too know the answer...!


Some word problems make me nervous, as I'm not a native English speaker.
_________________

NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

COLLECTION OF QUESTIONS:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS ; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
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Re: Need Help with OG 11 ed DS 154 [#permalink] New post 22 Dec 2009, 06:26
adamsmith2010 wrote:
IMO C:

A) X^2(1-X^2) <0 so X^3<0 or X^2>1
x could be positive or negative

B) X^2-1<0
(X-1)(X+1)<0 so X<1 or X<-1
x could be positive or negative

Combined X is negative for both statements to hold true.

OA?


Yes the ans is C. Thanks
Re: Need Help with OG 11 ed DS 154   [#permalink] 22 Dec 2009, 06:26
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