It is currently 16 Dec 2017, 18:36

Close

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
Your Progress

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

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

Close

Request Expert Reply

Confirm Cancel

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

If |x| < x^2, which of the following must be true ?

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

Hide Tags

5 KUDOS received
Verbal Forum Moderator
User avatar
V
Status: Greatness begins beyond your comfort zone
Joined: 08 Dec 2013
Posts: 1850

Kudos [?]: 1072 [5], given: 90

Location: India
Concentration: General Management, Strategy
GPA: 3.2
WE: Information Technology (Consulting)
GMAT ToolKit User Reviews Badge CAT Tests
If |x| < x^2, which of the following must be true ? [#permalink]

Show Tags

New post 19 Jun 2016, 10:13
5
This post received
KUDOS
26
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  55% (hard)

Question Stats:

59% (00:48) correct 41% (00:53) wrong based on 637 sessions

HideShow timer Statistics

If |x| < x^2, which of the following must be true ?

A. x > 0
B. x < 0
C. x > 1
D. -1 < x < 1
E. x^2 > 1
[Reveal] Spoiler: OA

_________________

When everything seems to be going against you, remember that the airplane takes off against the wind, not with it. - Henry Ford
The Moment You Think About Giving Up, Think Of The Reason Why You Held On So Long
+1 Kudos if you find this post helpful


Last edited by Bunuel on 19 Jun 2016, 10:20, edited 2 times in total.
Renamed the topic and edited the question.

Kudos [?]: 1072 [5], given: 90

Expert Post
3 KUDOS received
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 42631

Kudos [?]: 135874 [3], given: 12715

Re: If |x| < x^2, which of the following must be true ? [#permalink]

Show Tags

New post 19 Jun 2016, 10:20
3
This post received
KUDOS
Expert's post
11
This post was
BOOKMARKED
Skywalker18 wrote:
If |x| < x^2, which of the following must be true ?

A. x > 0
B. x < 0
C. x > 1
D. -1 < x < 1
E. x^2 > 1


Given: \(|x|<x^2\) --> reduce by \(|x|\) (side note: we can safely do this as absolute value is non-negative and in this case we know it's not zero too, as if x would be zero inequality wouldn't hold true, so \(|x|>0\)) --> \(1<|x|\) --> \(x<-1\) or \(x>1\).

So we have that \(x<-1\) or \(x>1\).


A. x > 0. Not always true.
B. x < 0. Not always true.
C. x > 1. Not always true.
D. -1 < x < 1. Not true.
E. x^2 > 1. Always true.

Answer: E.
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

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?
Extra-hard Quant Tests with Brilliant Analytics

Kudos [?]: 135874 [3], given: 12715

Expert Post
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 42631

Kudos [?]: 135874 [0], given: 12715

Re: If |x| < x^2, which of the following must be true ? [#permalink]

Show Tags

New post 19 Jun 2016, 10:22
Bunuel wrote:
Skywalker18 wrote:
If |x| < x^2, which of the following must be true ?

A. x > 0
B. x < 0
C. x > 1
D. -1 < x < 1
E. x^2 > 1


Given: \(|x|<x^2\) --> reduce by \(|x|\) (side note: we can safely do this as absolute value is non-negative and in this case we know it's not zero too, as if x would be zero inequality wouldn't hold true, so \(|x|>0\)) --> \(1<|x|\) --> \(x<-1\) or \(x>1\).

So we have that \(x<-1\) or \(x>1\).


A. x > 0. Not always true.
B. x < 0. Not always true.
C. x > 1. Not always true.
D. -1 < x < 1. Not true.
E. x^2 > 1. Always true.

Answer: E.


Similar question to practice: if-x-x-2-which-of-the-following-must-be-true-99506.html
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

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?
Extra-hard Quant Tests with Brilliant Analytics

Kudos [?]: 135874 [0], given: 12715

Manager
Manager
User avatar
B
Joined: 12 Oct 2012
Posts: 123

Kudos [?]: 78 [0], given: 198

WE: General Management (Other)
GMAT ToolKit User
Re: If |x| < x^2, which of the following must be true ? [#permalink]

Show Tags

New post 21 Jun 2016, 19:39
I used it by plugging in ZONEF.

A. x > 0 : If x is an integer, the inequality holds true. It would be opposite for a fraction
B. x < 0 : Same as A
C. x > 1 : Same as A
D. -1 < x < 1 : Again, we can use Zero to plug in.
E. x^2 > 1 : This must be true.

IMO E.

Kudos [?]: 78 [0], given: 198

11 KUDOS received
Senior Manager
Senior Manager
User avatar
Joined: 18 Jan 2010
Posts: 257

Kudos [?]: 176 [11], given: 9

Re: If |x| < x^2, which of the following must be true ? [#permalink]

Show Tags

New post 21 Jun 2016, 21:12
11
This post received
KUDOS
8
This post was
BOOKMARKED
Skywalker18 wrote:
If |x| < x^2, which of the following must be true ?

A. x > 0
B. x < 0
C. x > 1
D. -1 < x < 1
E. x^2 > 1


|x| < x^2

Both left hand side and Right Hand side are positive, so we can square the inequalities.

\(x^2 < x^4\)

\(x^4 > x^2\)

\(x^4 - x^2 > 0\)
\(x^2(x^2 - 1)> 0\)

x^2 is always positive.

So the condition is

\(x^2 - 1> 0\)

\(x^2 > 1\)

E is the answer.

Kudos [?]: 176 [11], given: 9

Senior Manager
Senior Manager
avatar
Joined: 02 Mar 2012
Posts: 356

Kudos [?]: 91 [0], given: 4

Schools: Schulich '16
Re: If |x| < x^2, which of the following must be true ? [#permalink]

Show Tags

New post 22 Jun 2016, 07:19
aditi2013 wrote:
I used it by plugging in ZONEF.

A. x > 0 : If x is an integer, the inequality holds true. It would be opposite for a fraction
B. x < 0 : Same as A
C. x > 1 : Same as A
D. -1 < x < 1 : Again, we can use Zero to plug in.
E. x^2 > 1 : This must be true.

IMO E.


your explanation for C is wrong.if u take fraction of x>1 then it satisfies.
But this choice is just sub part of solutions of |x|<x^2 .the other solution is x<-1 which choice C doesn't say about

Kudos [?]: 91 [0], given: 4

Manager
Manager
User avatar
B
Joined: 12 Oct 2012
Posts: 123

Kudos [?]: 78 [0], given: 198

WE: General Management (Other)
GMAT ToolKit User
Re: If |x| < x^2, which of the following must be true ? [#permalink]

Show Tags

New post 26 Jun 2016, 00:31
hsbinfy wrote:
aditi2013 wrote:
I used it by plugging in ZONEF.

A. x > 0 : If x is an integer, the inequality holds true. It would be opposite for a fraction
B. x < 0 : Same as A
C. x > 1 : Same as A
D. -1 < x < 1 : Again, we can use Zero to plug in.
E. x^2 > 1 : This must be true.

IMO E.


your explanation for C is wrong.if u take fraction of x>1 then it satisfies.
But this choice is just sub part of solutions of |x|<x^2 .the other solution is x<-1 which choice C doesn't say about


Aah, thank you for catching this error. The improper fraction will satisfy, right?

Kudos [?]: 78 [0], given: 198

Intern
Intern
avatar
Joined: 01 May 2015
Posts: 45

Kudos [?]: 24 [0], given: 1

Re: If |x| < x^2, which of the following must be true ? [#permalink]

Show Tags

New post 29 Jun 2016, 22:40
aditi2013 wrote:
I used it by plugging in ZONEF.

What is ZONEF? Can you explain this.

Kudos [?]: 24 [0], given: 1

1 KUDOS received
Intern
Intern
avatar
Joined: 01 May 2015
Posts: 45

Kudos [?]: 24 [1], given: 1

Re: If |x| < x^2, which of the following must be true ? [#permalink]

Show Tags

New post 29 Jun 2016, 22:43
1
This post received
KUDOS
I looked for four range of values:

i) x<-1
Is |x| < x^2 in this range? Yes.

ii) -1 < x < 0 N
Is |x| < x^2 in this range? No.

iii) 0 < x < 1 N
Is |x| < x^2 in this range? No.

iv) x > 1 Y
Is |x| < x^2 in this range? Yes.

So, clearly |x| < x^2 only for:

i) x < -1 or
ii) x > 1

In either case, x^2 > 1. So, E.

Kudos [?]: 24 [1], given: 1

Manager
Manager
User avatar
B
Joined: 12 Oct 2012
Posts: 123

Kudos [?]: 78 [0], given: 198

WE: General Management (Other)
GMAT ToolKit User
Re: If |x| < x^2, which of the following must be true ? [#permalink]

Show Tags

New post 30 Jun 2016, 03:01
sauravpaul wrote:
aditi2013 wrote:
I used it by plugging in ZONEF.

What is ZONEF? Can you explain this.


Hi Saurav,

ZONEF is just an abbreviation to ensure no value remains untested to check the sufficiency. So, I always check ZONEF in majority of such data sufficiency questions.

Zero
One
Negative
Extremes (Lower Limit, High)
Fraction

Kudos [?]: 78 [0], given: 198

Intern
Intern
avatar
Joined: 08 Sep 2012
Posts: 14

Kudos [?]: 8 [0], given: 10

GMAT 1: 770 Q50 V45
WE: General Management (Non-Profit and Government)
Re: If |x| < x^2, which of the following must be true ? [#permalink]

Show Tags

New post 22 Jul 2016, 21:09
'C' x>1 is a subset of 'E' x^2>1
The question is which of the following must be true so if 'E' must be true then 'C' also must be true?

Kudos [?]: 8 [0], given: 10

Expert Post
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 42631

Kudos [?]: 135874 [0], given: 12715

Re: If |x| < x^2, which of the following must be true ? [#permalink]

Show Tags

New post 22 Jul 2016, 23:17

Kudos [?]: 135874 [0], given: 12715

Current Student
User avatar
S
Joined: 28 Nov 2014
Posts: 918

Kudos [?]: 220 [0], given: 79

Concentration: Strategy
Schools: Fisher '19 (M)
GPA: 3.71
Reviews Badge
If |x|<x^2 , which of the following must be true? [#permalink]

Show Tags

New post 08 Oct 2016, 23:39
If |x|< x² , which of the following must be true?

A x > 0
B x < 0
C x > 1
D -1 < x < 1
E x² > 1

Another form of the same question: if-x-x-2-which-of-the-following-must-be-true-99506.html#p767246

Kudos [?]: 220 [0], given: 79

Expert Post
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 42631

Kudos [?]: 135874 [0], given: 12715

Re: If |x| < x^2, which of the following must be true ? [#permalink]

Show Tags

New post 08 Oct 2016, 23:42
Keats wrote:
If |x|< x² , which of the following must be true?

A x > 0
B x < 0
C x > 1
D -1 < x < 1
E x² > 1

Another form of the same question: if-x-x-2-which-of-the-following-must-be-true-99506.html#p767246


Merging topics. Please refer to the discussion above.
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

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?
Extra-hard Quant Tests with Brilliant Analytics

Kudos [?]: 135874 [0], given: 12715

Manager
Manager
avatar
B
Joined: 02 Jul 2016
Posts: 83

Kudos [?]: 3 [0], given: 7

If |x| < x^2, which of the following must be true ? [#permalink]

Show Tags

New post 05 Nov 2016, 22:24
Cant we do this question by opening the Modulus>>??

My approach is as follows
Given that
|x|<x^2

Now opening the modulus accordingly
CASE 1:x<0
=> -x<x^2
=> x+x^2>0
=> x(x+1)>0

By the Line wave Method:
The range of x is x<-1 U x>0
CASE 2: x>0
=> x<x^2
=> x(x-1)>0

Now the range of x is x<0 U x>1

Combining both operations x <-1 U x>1
So C option directly suits or comes in this range..
As per option E.. if I put a value from the above range say x=-0.25..x^2=0.0625 which is less than 1

So according me C should be the correct answer.....

CAN ANYBODY TELL ME WHERE I AM WRONG???

Kudos [?]: 3 [0], given: 7

Senior Manager
Senior Manager
User avatar
G
Joined: 19 Oct 2012
Posts: 335

Kudos [?]: 60 [0], given: 103

Location: India
Concentration: General Management, Operations
GMAT 1: 660 Q47 V35
GMAT 2: 710 Q50 V38
GPA: 3.81
WE: Information Technology (Computer Software)
If |x| < x^2, which of the following must be true ? [#permalink]

Show Tags

New post 17 Oct 2017, 00:09
Skywalker18 wrote:
If |x| < x^2, which of the following must be true ?

A. x > 0
B. x < 0
C. x > 1
D. -1 < x < 1
E. x^2 > 1


Let's square both the sides, we get,

\(x^4 > x^2\)
->\(x^4 - x^2 > 0\)
-> \(x^2 (x^2 -1) > 0\)
This implies, both the terms have to have same signs.
\(x^2 > 0\) and \(x^2 - 1 > 0\).

Additionally, we can't test \(x^2< 0\) since the square of a real number is never negative.

This gives us \(x^2 > 1\) (Option E.)
_________________

Citius, Altius, Fortius

Kudos [?]: 60 [0], given: 103

Expert Post
Target Test Prep Representative
User avatar
S
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 1945

Kudos [?]: 1022 [0], given: 3

Location: United States (CA)
Re: If |x| < x^2, which of the following must be true ? [#permalink]

Show Tags

New post 19 Oct 2017, 09:20
Skywalker18 wrote:
If |x| < x^2, which of the following must be true ?

A. x > 0
B. x < 0
C. x > 1
D. -1 < x < 1
E. x^2 > 1


If x = 0, then |0| will not be less than 0^2 since they both are equal to 0. Thus, we know x can’t be 0.

Since |x| = x when x is positive and -x when x is negative, let’s rewrite the inequality without the absolute value sign. That is, if x > 0, then we have x < x^2, and if x < 0, then we have -x < x^2.

Case 1: If x > 0,

x < x^2

Dividing both sides by x, we have:

1 < x

Case 2: If x < 0,

-x < x^2

Dividing both sides by x (switching the inequality sign since x is negative), we have:

-1 > x

Thus, we have x > 1 or x < -1; in that case, x^2 must be greater than 1.

Answer: E
_________________

Scott Woodbury-Stewart
Founder and CEO

GMAT Quant Self-Study Course
500+ lessons 3000+ practice problems 800+ HD solutions

Kudos [?]: 1022 [0], given: 3

Re: If |x| < x^2, which of the following must be true ?   [#permalink] 19 Oct 2017, 09:20
Display posts from previous: Sort by

If |x| < x^2, which of the following must be true ?

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


GMAT Club MBA Forum Home| About| Terms and Conditions| GMAT Club Rules| Contact| Sitemap

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®.