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

 It is currently 18 Oct 2019, 17:28

### 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^12 – 2x^11 negative? (1) x^2 < |x| (2) x^(-1) < -1

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics
Author Message
TAGS:

### Hide Tags

Retired Moderator
Joined: 29 Apr 2015
Posts: 822
Location: Switzerland
Concentration: Economics, Finance
Schools: LBS MIF '19
WE: Asset Management (Investment Banking)
Is x^12 – 2x^11 negative? (1) x^2 < |x| (2) x^(-1) < -1  [#permalink]

### Show Tags

Updated on: 14 May 2018, 02:24
1
3
00:00

Difficulty:

75% (hard)

Question Stats:

57% (02:28) correct 43% (02:25) wrong based on 106 sessions

### HideShow timer Statistics

Is $$x^{12}- 2x^{11}$$ negative?

(1) $$x^2 < |x|$$

(2) $$x^{-1} < -1$$

_________________
Saving was yesterday, heat up the gmatclub.forum's sentiment by spending KUDOS!

PS Please send me PM if I do not respond to your question within 24 hours.

Originally posted by reto on 10 Sep 2015, 03:47.
Last edited by Bunuel on 14 May 2018, 02:24, edited 3 times in total.
Renamed the topic and edited the question.
Retired Moderator
Status: On a mountain of skulls, in the castle of pain, I sit on a throne of blood.
Joined: 30 Jul 2013
Posts: 300
Re: Is x^12 – 2x^11 negative? (1) x^2 < |x| (2) x^(-1) < -1  [#permalink]

### Show Tags

10 Sep 2015, 04:13
1
reto wrote:
Is x^12 – 2x^11 negative?

(1) x^2 < |x|
(2) x^(-1) < -1

Simplifying,

x^11(x-2)<0--->?
This can only be possible when 0<x<2

1. x^2<|x|
-1<x<1

Not Sufficient.

2. 1/x<-1
-1<x<0

Sufficient.

Manager
Joined: 10 Aug 2015
Posts: 103
Re: Is x^12 – 2x^11 negative? (1) x^2 < |x| (2) x^(-1) < -1  [#permalink]

### Show Tags

10 Sep 2015, 04:33
1
reto wrote:
Is x^12 – 2x^11 negative?

(1) x^2 < |x|
(2) x^(-1) < -1

Solution: x^12 – 2x^11 ==> x^11(x-2) It basically asks about x.
If x<=0 NO.
If 0<x<2 yes.
If x>=2 NO.

(1) Both LHS and RHS are non-negetive. x cannot be 0 and x^2 < x only when 0<x<1 or -1<x<0
Therefore, Yes or No. Insufficient.

(2)-x>1 ==> x<-1 ==> x^11<-1 and x-2<-1.
x^11(x-2) > 0 . NO. Sufficient

Option, B
CEO
Joined: 20 Mar 2014
Posts: 2597
Concentration: Finance, Strategy
Schools: Kellogg '18 (M)
GMAT 1: 750 Q49 V44
GPA: 3.7
WE: Engineering (Aerospace and Defense)
Re: Is x^12 – 2x^11 negative? (1) x^2 < |x| (2) x^(-1) < -1  [#permalink]

### Show Tags

09 Mar 2016, 10:53
1
reto wrote:
Is $$x^{12}$$– $$2x^{11}$$negative?

(1) $$x^2$$ < |x|
(2) $$x^{-1}$$ < -1

The question asks whether , $$x^{12} – 2*x^{11}<0$$ ---> $$x^{11}*(x-2)<0$$. Remember that $$x^{odd} <0$$ for $$x<0$$and $$x^{odd}>0$$ for $$x>0$$

Per statement 1, $$x^2< |x|$$ ---> carefully note this statement tells us that a squared positive quantity (x^2) < another positive quantity (|x|). This is only possible when -1<x<0 or 0<x<1. For these 2 ranges, you will get both "no" for -1<x<0 and "yes" for 0<x<1, making this statement NOT sufficient.

Per statement 2, $$x^{-1} < -1$$ ---> (DO NOT MULTIPLY BY x as you do not know the sign of x) $$x^{-1} < -1 = x^{-1}+1 < 0$$ ---> (x+1)/x < 0 ---> as the result of this fraction <0 ---> (x+1) and x are of OPPOSITE SIGNS.

2 cases :

Case 1: x+1 > 0 and x < 0 ---> x>-1 and x<0 ---> -1<x<0 and

Case 2: x+1<0 --> x<-1 and x>0 ---> not possible.

Thus, the only range possible -->-1<x<0 and for this range you get a NO for the question asked. Thus statement 2 is sufficient. B is thus the correct answer.

Hope this helps.
Non-Human User
Joined: 09 Sep 2013
Posts: 13262
Re: Is x^12 – 2x^11 negative? (1) x^2 < |x| (2) x^(-1) < -1  [#permalink]

### Show Tags

14 May 2018, 02:23
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________
Re: Is x^12 – 2x^11 negative? (1) x^2 < |x| (2) x^(-1) < -1   [#permalink] 14 May 2018, 02:23
Display posts from previous: Sort by

# Is x^12 – 2x^11 negative? (1) x^2 < |x| (2) x^(-1) < -1

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics

 Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne