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

It is currently 16 Oct 2019, 19:54

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

Is |x^2|<|x^4|?

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

Hide Tags

Find Similar Topics 
Math Revolution GMAT Instructor
User avatar
V
Joined: 16 Aug 2015
Posts: 8011
GMAT 1: 760 Q51 V42
GPA: 3.82
Is |x^2|<|x^4|?  [#permalink]

Show Tags

New post 21 Sep 2017, 00:56
00:00
A
B
C
D
E

Difficulty:

  55% (hard)

Question Stats:

63% (01:49) correct 37% (01:44) wrong based on 173 sessions

HideShow timer Statistics

Is \(|x^2|<|x^4|\)?

1) \(x<-1\)
2) \(|x|<|x^3|\)

_________________
MathRevolution: Finish GMAT Quant Section with 10 minutes to spare
The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy.
"Only $79 for 1 month Online Course"
"Free Resources-30 day online access & Diagnostic Test"
"Unlimited Access to over 120 free video lessons - try it yourself"
Current Student
User avatar
P
Joined: 02 Jul 2017
Posts: 290
Concentration: Entrepreneurship, Technology
GMAT 1: 730 Q50 V38
GMAT ToolKit User
Re: Is |x^2|<|x^4|?  [#permalink]

Show Tags

New post 21 Sep 2017, 10:46
2
2
Is \(|x^2|<|x^4|\) ?

As \(x^2\) and \(x^4\) will always be positive , so we have to find if \(x^2 < x^4\)

Also above case will always be true except when -1<x<1
1. as for fractions we know \((\frac{1}{2})^4 < (\frac{1}{2})^3 <(\frac{1}{2})^2<(\frac{1}{2})\)
that is, for x between -1 and 1 and x => \(x^4 <x^2 <x\)
2. and for x=1 => \(x =x^2 =x^4\)

So here we have to find if -1<x<1 or not.

1) x<−1
Directly tells us equation that we are looking for : that is value of x is not in between -1 and 1. So this makes above statement true.
Sufficient

2) |x|<|x^3|

Here we get magnitude of x is less than magnitude of \(x^3\). Here magnitude of x cannot be in between 0 and 1
as for x between 0 and 1 \(x^3 < x\) => \((1/2)^3 < x\)
And as we are given magnitude comparison we can say x doesn't lie between -1 and 1.
So this makes given question true
Sufficient

Answer: D
Retired Moderator
avatar
D
Joined: 25 Feb 2013
Posts: 1178
Location: India
GPA: 3.82
GMAT ToolKit User Reviews Badge
Re: Is |x^2|<|x^4|?  [#permalink]

Show Tags

New post 21 Sep 2017, 11:36
MathRevolution wrote:
Is \(|x^2|<|x^4|\)?

1) \(x<-1\)
2) \(|x|<|x^3|\)


Hi Bunuel

I have a doubt here,

Statement 1 specifically mentions that \(x<-1\) but as per statement 2 either \(x<-1\) or \(x>1\). IN either case we will get a definite Yes for the question stem hence answer will be D

But ideally both statements should provide same information.

What am I missing here?
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 58381
Re: Is |x^2|<|x^4|?  [#permalink]

Show Tags

New post 21 Sep 2017, 11:53
niks18 wrote:
MathRevolution wrote:
Is \(|x^2|<|x^4|\)?

1) \(x<-1\)
2) \(|x|<|x^3|\)


Hi Bunuel

I have a doubt here,

Statement 1 specifically mentions that \(x<-1\) but as per statement 2 either \(x<-1\) or \(x>1\). IN either case we will get a definite Yes for the question stem hence answer will be D

But ideally both statements should provide same information.

What am I missing here?


What contradiction do you see between these two?
_________________
Retired Moderator
avatar
D
Joined: 25 Feb 2013
Posts: 1178
Location: India
GPA: 3.82
GMAT ToolKit User Reviews Badge
Re: Is |x^2|<|x^4|?  [#permalink]

Show Tags

New post 21 Sep 2017, 11:57
1
Bunuel wrote:
niks18 wrote:
MathRevolution wrote:
Is \(|x^2|<|x^4|\)?

1) \(x<-1\)
2) \(|x|<|x^3|\)


Hi Bunuel

I have a doubt here,

Statement 1 specifically mentions that \(x<-1\) but as per statement 2 either \(x<-1\) or \(x>1\). IN either case we will get a definite Yes for the question stem hence answer will be D

But ideally both statements should provide same information.

What am I missing here?


What contradiction do you see between these two?


Hi,

My point is that statement 1 says that x<-1 i.e x is negative

But from statement 2 x>1 is also possible and will satisfy the inequality.

Need clarity whether such scenario is possible in a DS question
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 58381
Re: Is |x^2|<|x^4|?  [#permalink]

Show Tags

New post 21 Sep 2017, 12:02
niks18 wrote:
Bunuel wrote:
niks18 wrote:

Hi Bunuel

I have a doubt here,

Statement 1 specifically mentions that \(x<-1\) but as per statement 2 either \(x<-1\) or \(x>1\). IN either case we will get a definite Yes for the question stem hence answer will be D

But ideally both statements should provide same information.

What am I missing here?


What contradiction do you see between these two?


Hi,

My point is that statement 1 says that x<-1 i.e x is negative

But from statement 2 x>1 is also possible and will satisfy the inequality.

Need clarity whether such scenario is possible in a DS question


On the GMAT, two data sufficiency statements always provide TRUE information and these statements NEVER contradict each other or the stem.

Here statement do not contradict.

(1) says x < -1.
(2) gives x < -1 or x > 1.

Statements do NOT contradict: together they give x < -1.
_________________
Retired Moderator
avatar
D
Joined: 25 Feb 2013
Posts: 1178
Location: India
GPA: 3.82
GMAT ToolKit User Reviews Badge
Re: Is |x^2|<|x^4|?  [#permalink]

Show Tags

New post 21 Sep 2017, 12:37
1
Thanks Bunuel for the clarification :-)

To end the confusion I guess we can directly solve the question as -

Given \(|x^2|<|x^4|\) or \(\frac{|x^4|}{|x^2|}>1\)

Hence the question stem becomes Is \(|x^2|>1\)

Statement 1: \(x<-1\), squaring both sides we get \(x^2>1\) (sign of inequality will reverse because \(|x|>|-1|\)) or

\(|x^2|>1\). So we get a Yes for our question stem. Hence Sufficient

Statement 2: \(|x|<|x^3|\) or \(\frac{|x^3|}{|x|}>1\)

Hence \(|x^2|>1\). Sufficient

Option D
Math Revolution GMAT Instructor
User avatar
V
Joined: 16 Aug 2015
Posts: 8011
GMAT 1: 760 Q51 V42
GPA: 3.82
Re: Is |x^2|<|x^4|?  [#permalink]

Show Tags

New post 24 Sep 2017, 19:21
=>

|x^2|<|x^4| ⇔ |x^4| - |x^2| > 0 ⇔ |x^2| ( |x^2| - 1 ) >0
⇔ |x^2| < 0 or |x^2| > 1
⇔ |x| > 1
⇔ x < -1 or x > 1

Condition 1)
x<-1 is sufficient clearly.

Condition 2)
|x|<|x^3| ⇔ |x^3| - |x| > 0 ⇔ |x|( |x^2| - 1 ) > 0
⇔ |x|( |x| + 1 ) ( |x| - 1 ) > 0
⇔ -1 < |x| < 0 or |x| > 1
⇔ |x| > 1
⇔ x < -1 or x > 1
This is sufficient too.

Ans: D
_________________
MathRevolution: Finish GMAT Quant Section with 10 minutes to spare
The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy.
"Only $79 for 1 month Online Course"
"Free Resources-30 day online access & Diagnostic Test"
"Unlimited Access to over 120 free video lessons - try it yourself"
ISB School Moderator
User avatar
G
Joined: 08 Dec 2013
Posts: 594
Location: India
Concentration: Nonprofit, Sustainability
Schools: ISB '21
GMAT 1: 630 Q47 V30
WE: Operations (Non-Profit and Government)
Reviews Badge CAT Tests
Is |x^2|<|x^4|?  [#permalink]

Show Tags

New post 01 Jun 2019, 00:11
MathRevolution wrote:
Is \(|x^2|<|x^4|\)?

1) \(x<-1\)
2) \(|x|<|x^3|\)


1. Put any value of x<-1 it'll always be |x^2|<|x^4|. Satisfied.
Exception range [-1,1] avoided.

2. So, x can't be zero. Any +ve or -ve value will satisfy |x|<|x^3|

Exception range [-1,1] avoided.
So, |x^2|<|x^4| True. Put any +ve or -ve value to check. It'll satisfy.

D. Independently sufficient.

Lots of good GMAT sums exploit the anomaly of [-1,1] range.
_________________
Kindly drop a '+1 Kudos' if you find this post helpful.

GMAT Math Book


-I never wanted what I gave up
I never gave up what I wanted-
Manager
Manager
avatar
S
Joined: 25 Mar 2018
Posts: 72
Location: India
Concentration: Leadership, Strategy
Schools: ISB '21, IIMA , IIMB
GMAT 1: 650 Q50 V28
GPA: 4
WE: Analyst (Manufacturing)
GMAT ToolKit User Premium Member Reviews Badge CAT Tests
Re: Is |x^2|<|x^4|?  [#permalink]

Show Tags

New post 01 Jun 2019, 00:51
MathRevolution wrote:
Is \(|x^2|<|x^4|\)?

1) \(x<-1\)
2) \(|x|<|x^3|\)



The question asks whether x^4 > x^2

If at all it happens in -infinity to -1 and 1 to infinity.
We need to check if any of 2 gives any clue on x range.

A. Says x < -1. Perfect the equation is valid in this range.

B.says Mod(x) < mod (x3)
This equation is also valid when x< -1 and x > 1 which matches with our required range. Hence answer D is correct

Posted from my mobile device
_________________
Please give me +1 kudos if my post helps you a little. It will help me unlock tests. Thanks
GMAT Club Bot
Re: Is |x^2|<|x^4|?   [#permalink] 01 Jun 2019, 00:51
Display posts from previous: Sort by

Is |x^2|<|x^4|?

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





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