GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 20 Jul 2018, 11:26

GMAT Club Daily Prep

Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

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

Author Message
TAGS:

Hide Tags

Manager
Joined: 03 Oct 2016
Posts: 83
Concentration: Technology, General Management
WE: Information Technology (Computer Software)
Is x < 0? (1) x^3 + x^2 + x + 2 = 0 (2) x^2 - x - 2 < 0  [#permalink]

Show Tags

Updated on: 07 Oct 2016, 10:34
1
1
00:00

Difficulty:

65% (hard)

Question Stats:

63% (02:05) correct 38% (01:41) wrong based on 96 sessions

HideShow timer Statistics

Is x < 0?

(1) x^3 + x^2 + x + 2 = 0

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

_________________

KINDLY KUDOS IF YOU LIKE THE POST

Originally posted by idontknowwhy94 on 07 Oct 2016, 09:56.
Last edited by idontknowwhy94 on 07 Oct 2016, 10:34, edited 1 time in total.
Manager
Joined: 03 Oct 2016
Posts: 83
Concentration: Technology, General Management
WE: Information Technology (Computer Software)
Re: Is x < 0? (1) x^3 + x^2 + x + 2 = 0 (2) x^2 - x - 2 < 0  [#permalink]

Show Tags

07 Oct 2016, 10:32
Guys IHO ,

the answer is as the only way for the equation to be 0 is when x is -ve

for st 2 ; we have 2 answers
_________________

KINDLY KUDOS IF YOU LIKE THE POST

Director
Joined: 05 Mar 2015
Posts: 980
Re: Is x < 0? (1) x^3 + x^2 + x + 2 = 0 (2) x^2 - x - 2 < 0  [#permalink]

Show Tags

07 Oct 2016, 10:47
idontknowwhy94 wrote:
Is x<0?

1) $$x^{3} + x^{2}$$ + x + 2 = 0
2) $$x^{2}$$-x-2 < 0

Keep the Kudos coming in and let the questions come out

1) if x>=0 then the expression will never be 0.

thus x<0.........suff

2) X^2-x-2<0
(x+1)(x-2)<0
X satisfies for range -1<x<2
as x could be >0 or <0 ..........insuff....

Ans A
Intern
Joined: 13 Dec 2015
Posts: 7
Re: Is x < 0? (1) x^3 + x^2 + x + 2 = 0 (2) x^2 - x - 2 < 0  [#permalink]

Show Tags

08 Oct 2016, 03:15
You can solve the equation algebraically as well.

1) x^3+x^2+x+2=0

on solving you get the following values of x :- -2/-3,-2.In all cases x<0. Therefore x must be <0. Statement is Sufficient.

2) on Solving statement number 2, we get 2 values of x, x<2 OR x<-1. Two different solns. i.e X can be +ve and X can be -ve. Therefore,statement is not sufficient.

Ans: A
GMAT Club Legend
Joined: 16 Oct 2010
Posts: 8132
Location: Pune, India
Re: Is x < 0? (1) x^3 + x^2 + x + 2 = 0 (2) x^2 - x - 2 < 0  [#permalink]

Show Tags

13 Oct 2016, 03:00
idontknowwhy94 wrote:
Is x<0?

1) $$x^{3} + x^{2}$$ + x + 2 = 0
2) $$x^{2}$$-x-2 < 0

Keep the Kudos coming in and let the questions come out

Responding to a pm:
Quote:
For statement 1 it is clear that x >= 0 but when I tested -ve values I didn't find any which can satisfy the equation. Though I knew that x < 0, I continuously tried to find some -ve value that satisfied the equation. But it was a waste of time to find the value. How can I crack these type of traps on GMAT or it is my lack of understanding of concepts.

In stmnt 1, note that the point is that x cannot be positive or 0. So it has to be negative (since it has to be real).
If x is positive, all terms are positive and their sum cannot be 0.
If x is 0, you get 2 = 0 which is not valid.
So x has to be negative. No need to look for the actual value. It will not be an integer.

$$x^{3} + x^{2}+ x + 2 = 0$$
If you plug in x = -1, you get 1 = 0
If you plug in x = -2, you get -4 = 0
So somewhere in between -1 to -2, x will take a value such that you will get 0 = 0
_________________

Karishma
Private Tutor for GMAT
Contact: bansal.karishma@gmail.com

Intern
Joined: 14 Nov 2012
Posts: 23
GMAT 1: 740 Q51 V38
Re: Is x < 0? (1) x^3 + x^2 + x + 2 = 0 (2) x^2 - x - 2 < 0  [#permalink]

Show Tags

19 Oct 2017, 20:02
idontknowwhy94 wrote:
Is x<0?

1) $$x^{3} + x^{2}$$ + x + 2 = 0
2) $$x^{2}$$-x-2 < 0

Keep the Kudos coming in and let the questions come out

1) $$x^{3} + x^{2}$$ + x + 2 = 0
=> x^2(x+1) + (x + 1) + 1 =0
=> (x+1)(x^2+1) + 1 = 0
=> (x+1)(x^2+1) = -1

RHS= -1 < 0 => LHS <0. As x^2+1 > 0, then x +1 <0 => x < -1 => x <0 (suff)

2)2) $$x^{2}$$-x-2 < 0
=> -1 < x < 2
=> Insuff
Re: Is x < 0? (1) x^3 + x^2 + x + 2 = 0 (2) x^2 - x - 2 < 0 &nbs [#permalink] 19 Oct 2017, 20:02
Display posts from previous: Sort by

Events & Promotions

 Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.