Last visit was: 07 Oct 2024, 03:03 It is currently 07 Oct 2024, 03:03

Close

GRE Prep 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
Your Progress

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

Practice
Pays

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

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Close

Request Expert Reply

Confirm Cancel
Tags :

Show Tags
Hide Tags

Verbal Expert
Joined: 18 Apr 2015
Posts: 29639
Own Kudos [?]: 35554 [8]
Given Kudos: 25784
Send PM
Senior Manager
Senior Manager
Joined: 23 Jan 2021
Posts: 294
Own Kudos [?]: 164 [0]
Given Kudos: 81
Concentration: , International Business
Send PM
Retired Moderator
Joined: 02 Dec 2020
Posts: 1833
Own Kudos [?]: 2140 [0]
Given Kudos: 140
GRE 1: Q168 V157

GRE 2: Q167 V161
Send PM
Senior Manager
Senior Manager
Joined: 23 Jan 2021
Posts: 294
Own Kudos [?]: 164 [0]
Given Kudos: 81
Concentration: , International Business
Send PM
Re: GRE Math Essentials - INEQUALITIES / Absolute Value / Modulus [#permalink]
rx10 wrote:
Hey, COolguy101

Take \(x = -2\), so \(x^2>x\)

COolguy101 wrote:
24. If x^2>x, then either x > 1 or x is negative (x < 0), how x to be negative is possible. I am getting x>0.

But sir, I take x to the left and solve then I got x>1 and x>0, where do I make mistake. I can not even figure it out.
Retired Moderator
Joined: 02 Dec 2020
Posts: 1833
Own Kudos [?]: 2140 [0]
Given Kudos: 140
GRE 1: Q168 V157

GRE 2: Q167 V161
Send PM
Re: GRE Math Essentials - INEQUALITIES / Absolute Value / Modulus [#permalink]
\(x^2 > x\)

\(x^2 - x > 0\)

\(x(x-1) > 0\)

What you did was just divided with \(x\) but without knowing the sign we can't do that. inequality may change by doing so.


COolguy101 wrote:
But sir, I take x to the left and solve then I got x>1 and x>0, where do I make mistake. I can not even figure it out.
Verbal Expert
Joined: 18 Apr 2015
Posts: 29639
Own Kudos [?]: 35554 [0]
Given Kudos: 25784
Send PM
Re: GRE Math Essentials - INEQUALITIES / Absolute Value / Modulus [#permalink]
Expert Reply
According to also GreenlightTestPrep statement, 26 is absolutely correct

Quote:
If \(x^2>x\), then either \(x > 1\) or x is negative \((x < 0)\)

Rearrange to get: \(x^2 - x > 0\)

Factor: \(x(x - 1) > 0\)

So, either \(x < 0\) or \(x > 1\)
Senior Manager
Senior Manager
Joined: 23 Jan 2021
Posts: 294
Own Kudos [?]: 164 [0]
Given Kudos: 81
Concentration: , International Business
Send PM
Re: GRE Math Essentials - INEQUALITIES / Absolute Value / Modulus [#permalink]
Carcass wrote:
According to also GreenlightTestPrep statement, 26 is absolutely correct

Quote:
If \(x^2>x\), then either \(x > 1\) or x is negative \((x < 0)\)

Rearrange to get: \(x^2 - x > 0\)

Factor: \(x(x - 1) > 0\)

So, either \(x < 0\) or \(x > 1\)

Got it sir!
Retired Moderator
Joined: 10 Apr 2015
Posts: 6218
Own Kudos [?]: 12115 [0]
Given Kudos: 136
Send PM
Re: GRE Math Essentials - INEQUALITIES / Absolute Value / Modulus [#permalink]
Here's a video on Inequalities:

Moderator
Moderator
Joined: 02 Jan 2020
Status:GRE Quant Tutor
Posts: 1108
Own Kudos [?]: 943 [0]
Given Kudos: 9
Location: India
Concentration: General Management
Schools: XLRI Jamshedpur, India - Class of 2014
GMAT 1: 700 Q51 V31
GPA: 2.8
WE:Engineering (Computer Software)
Send PM
Re: GRE Math Essentials - INEQUALITIES / Absolute Value / Modulus [#permalink]
Watch the following video to learn the Basics of Inequalities



Watch the following video to learn How to Solve Inequality Problems

Intern
Intern
Joined: 23 Jun 2024
Posts: 6
Own Kudos [?]: 0 [0]
Given Kudos: 2
Send PM
Re: GRE Math Essentials - INEQUALITIES / Absolute Value / Modulus [#permalink]
Carcass wrote:
According to also statement, 26 is absolutely correct

Quote:
If \(x^2>x\), then either \(x > 1\) or x is negative \((x < 0)\)

Rearrange to get: \(x^2 - x > 0\)

Factor: \(x(x - 1) > 0\)

So, either \(x < 0\) or \(x > 1\)


Hello Sir, could you please help explain why it's x<0 and not x>0

when I got to x(x - 1) > 0
I break it down to
x>0 and x-1> 0 resulting in x>0 and x>1 as an answer
Verbal Expert
Joined: 18 Apr 2015
Posts: 29639
Own Kudos [?]: 35554 [0]
Given Kudos: 25784
Send PM
Re: GRE Math Essentials - INEQUALITIES / Absolute Value / Modulus [#permalink]
Expert Reply
Which number of the above you refer to ? 24-25-26..........................which one ?
Intern
Intern
Joined: 23 Jun 2024
Posts: 6
Own Kudos [?]: 0 [0]
Given Kudos: 2
Send PM
Re: GRE Math Essentials - INEQUALITIES / Absolute Value / Modulus [#permalink]
Carcass

number 24. I got the same answer as coolguy. X>0, X>1
I mean it makes sense that If x^2>x then x>1 or x<0 but I just can't algebraically solve it

thank you,sir
Verbal Expert
Joined: 18 Apr 2015
Posts: 29639
Own Kudos [?]: 35554 [0]
Given Kudos: 25784
Send PM
GRE Math Essentials - INEQUALITIES / Absolute Value / Modulus [#permalink]
Expert Reply
\(x^2 > x \)

It looks as though we might be able to divide both sides by x to give x >1

But, in fact, we cannot do this. The two inequalities \(x^2 > x\) and x > 1 are not the same.

This is because in the inequality x > 1, x is clearly greater than 1. But in the inequality \(x^2 > x\) we have to take into account the possibility that x is negative, since if x is negative, \(x^2\) (which must be positive or zero) is always greater than x.

In fact the complete solution of this inequality is x >1 or x<0. The second part of the solution must be true since if x is negative, \(x^2\) is always greater than x.

According to the explanation above, in fact x must be

>1 for example 2 and 4>2 this is true

<0 for example -1 and 1>-1 this is true

x=0 and 0> 0 impossible this is not true

x is >0 AND <1 for example 1/2 . 1/4>1/2 impossible. This is NOT true

resource https://www.mathcentre.ac.uk/
Prep Club for GRE Bot
GRE Math Essentials - INEQUALITIES / Absolute Value / Modulus [#permalink]
Moderators:
GRE Instructor
76 posts
GRE Forum Moderator
37 posts
Moderator
1108 posts
GRE Instructor
222 posts

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