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

It is currently 17 Aug 2018, 20:02

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

If x is not equal to 0, is |x| less than 1? (1) x/|x|< x (2) |x| > x

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

Hide Tags

Intern
Intern
avatar
B
Joined: 11 Feb 2018
Posts: 29
Re: If x is not equal to 0, is |x| less than 1? (1) x/|x|< x (2) |x| > x  [#permalink]

Show Tags

New post 02 May 2018, 07:19
Bunuel wrote:
If x is not equal to 0, is |x| less than 1?

Is \(|x|<1\)?
Is \(-1<x<1\)? (\(x\neq{0}\))
So, the question asks whether x is in the range shown below:
Image


(1) \(\frac{x}{|x|}< x\)

Two cases:
A. \(x<0\) --> \(\frac{x}{-x}<x\) --> \(-1<x\). But remember that \(x<0\), so \(-1<x<0\)

B. \(x>0\) --> \(\frac{x}{x}<x\) --> \(1<x\).

Two ranges \(-1<x<0\) or \(x>1\). Which says that \(x\) either in the first range or in the second. Not sufficient to answer whether \(-1<x<1\). (For instance \(x\) can be \(-0.5\) or \(3\))

Second approach: look at the fraction \(\frac{x}{|x|}\) it can take only two values:
1 for \(x>0\) --> so we would have: \(1<x\);
Or -1 for \(x<0\) --> so we would have: \(-1<x\) and as we considering the range for which \(x<0\) then completer range would be: \(-1<x<0\).

The same two ranges: \(-1<x<0\) or \(x>1\):
Image


(2) \(|x| > x\). Well this basically tells that \(x\) is negative, as if x were positive or zero then \(|x|\) would be equal to \(x\). Only one range: \(x<0\), but still insufficient to say whether \(-1<x<1\). (For instance \(x\) can be \(-0.5\) or \(-10\))

Or consider two cases again:
\(x<0\)--> \(-x>x\)--> \(x<0\).
\(x>0\) --> \(x>x\): never correct.
Image


(1)+(2) Intersection of the ranges from (1) and (2) is the range \(-1<x<0\) (\(x<0\) (from 2) and \(-1<x<0\) or \(x>1\) (from 1), hence \(-1<x<0\)):
Image

Every \(x\) from this range is definitely in the range \(-1<x<1\). So, we have a definite YES answer to the question. Sufficient.


Answer: C.


Attachment:
MSP340910303aagbh2c14gf0000420i437if9d12bhg.gif

Attachment:
MSP2380151735322d2i2d790000280i6giebh17fdf3.gif

Attachment:
MSP8506173e0f30207c4a2700005eg6g59c48d51i5b.gif

Attachment:
MSP111401047g43cgaehag920000640367fgf148e668.gif


Hi Bunuel

Surely i am missing something here..my basic doubt is in scenario when we take X<0

If we assume, x<0, then shouldn't the statement x/|x|<x = -x/-x <-x (my thinking here is if we considering x<0, then x should be negative throughout )
So, the equation becomes 1<-x = -1>x, we can keep this option as we have initially assumed X<0
Then if we take any values of x less then -1, |x| will always be greater than 1

if we assume X>0, then x/|x|<x = x/x<x.....which is 1<x, we can keep this option as initially we have assumed X>0
Then we take any values of x greater than 1 then |x| will always be greater than 1.

So statement 1 in either case is sufficient..

Thanks in advance for your help..
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 47977
Re: If x is not equal to 0, is |x| less than 1? (1) x/|x|< x (2) |x| > x  [#permalink]

Show Tags

New post 02 May 2018, 09:24
cruiseav wrote:
Bunuel wrote:
If x is not equal to 0, is |x| less than 1?

Is \(|x|<1\)?
Is \(-1<x<1\)? (\(x\neq{0}\))
So, the question asks whether x is in the range shown below:
Image


(1) \(\frac{x}{|x|}< x\)

Two cases:
A. \(x<0\) --> \(\frac{x}{-x}<x\) --> \(-1<x\). But remember that \(x<0\), so \(-1<x<0\)

B. \(x>0\) --> \(\frac{x}{x}<x\) --> \(1<x\).

Two ranges \(-1<x<0\) or \(x>1\). Which says that \(x\) either in the first range or in the second. Not sufficient to answer whether \(-1<x<1\). (For instance \(x\) can be \(-0.5\) or \(3\))

Second approach: look at the fraction \(\frac{x}{|x|}\) it can take only two values:
1 for \(x>0\) --> so we would have: \(1<x\);
Or -1 for \(x<0\) --> so we would have: \(-1<x\) and as we considering the range for which \(x<0\) then completer range would be: \(-1<x<0\).

The same two ranges: \(-1<x<0\) or \(x>1\):
Image


(2) \(|x| > x\). Well this basically tells that \(x\) is negative, as if x were positive or zero then \(|x|\) would be equal to \(x\). Only one range: \(x<0\), but still insufficient to say whether \(-1<x<1\). (For instance \(x\) can be \(-0.5\) or \(-10\))

Or consider two cases again:
\(x<0\)--> \(-x>x\)--> \(x<0\).
\(x>0\) --> \(x>x\): never correct.
Image


(1)+(2) Intersection of the ranges from (1) and (2) is the range \(-1<x<0\) (\(x<0\) (from 2) and \(-1<x<0\) or \(x>1\) (from 1), hence \(-1<x<0\)):
Image

Every \(x\) from this range is definitely in the range \(-1<x<1\). So, we have a definite YES answer to the question. Sufficient.


Answer: C.


Attachment:
MSP340910303aagbh2c14gf0000420i437if9d12bhg.gif

Attachment:
MSP2380151735322d2i2d790000280i6giebh17fdf3.gif

Attachment:
MSP8506173e0f30207c4a2700005eg6g59c48d51i5b.gif

Attachment:
MSP111401047g43cgaehag920000640367fgf148e668.gif


Hi Bunuel

Surely i am missing something here..my basic doubt is in scenario when we take X<0

If we assume, x<0, then shouldn't the statement x/|x|<x = -x/-x <-x (my thinking here is if we considering x<0, then x should be negative throughout )
So, the equation becomes 1<-x = -1>x, we can keep this option as we have initially assumed X<0
Then if we take any values of x less then -1, |x| will always be greater than 1

if we assume X>0, then x/|x|<x = x/x<x.....which is 1<x, we can keep this option as initially we have assumed X>0
Then we take any values of x greater than 1 then |x| will always be greater than 1.

So statement 1 in either case is sufficient..

Thanks in advance for your help..


Negative x does not mean that you should replace x with -x. x just represents a negative number. You should replace |x| with -x, though because if x < 0, then |x| = -x.
_________________

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

Intern
Intern
avatar
B
Joined: 11 Feb 2018
Posts: 29
Re: If x is not equal to 0, is |x| less than 1? (1) x/|x|< x (2) |x| > x  [#permalink]

Show Tags

New post 03 May 2018, 08:37
Bunuel wrote:
cruiseav wrote:
Bunuel wrote:
If x is not equal to 0, is |x| less than 1?

Is \(|x|<1\)?
Is \(-1<x<1\)? (\(x\neq{0}\))
So, the question asks whether x is in the range shown below:
Image


(1) \(\frac{x}{|x|}< x\)

Two cases:
A. \(x<0\) --> \(\frac{x}{-x}<x\) --> \(-1<x\). But remember that \(x<0\), so \(-1<x<0\)

B. \(x>0\) --> \(\frac{x}{x}<x\) --> \(1<x\).

Two ranges \(-1<x<0\) or \(x>1\). Which says that \(x\) either in the first range or in the second. Not sufficient to answer whether \(-1<x<1\). (For instance \(x\) can be \(-0.5\) or \(3\))

Second approach: look at the fraction \(\frac{x}{|x|}\) it can take only two values:
1 for \(x>0\) --> so we would have: \(1<x\);
Or -1 for \(x<0\) --> so we would have: \(-1<x\) and as we considering the range for which \(x<0\) then completer range would be: \(-1<x<0\).

The same two ranges: \(-1<x<0\) or \(x>1\):
Image


(2) \(|x| > x\). Well this basically tells that \(x\) is negative, as if x were positive or zero then \(|x|\) would be equal to \(x\). Only one range: \(x<0\), but still insufficient to say whether \(-1<x<1\). (For instance \(x\) can be \(-0.5\) or \(-10\))

Or consider two cases again:
\(x<0\)--> \(-x>x\)--> \(x<0\).
\(x>0\) --> \(x>x\): never correct.
Image


(1)+(2) Intersection of the ranges from (1) and (2) is the range \(-1<x<0\) (\(x<0\) (from 2) and \(-1<x<0\) or \(x>1\) (from 1), hence \(-1<x<0\)):
Image

Every \(x\) from this range is definitely in the range \(-1<x<1\). So, we have a definite YES answer to the question. Sufficient.


Answer: C.


Attachment:
MSP340910303aagbh2c14gf0000420i437if9d12bhg.gif

Attachment:
MSP2380151735322d2i2d790000280i6giebh17fdf3.gif

Attachment:
MSP8506173e0f30207c4a2700005eg6g59c48d51i5b.gif

Attachment:
MSP111401047g43cgaehag920000640367fgf148e668.gif


Hi Bunuel

Surely i am missing something here..my basic doubt is in scenario when we take X<0

If we assume, x<0, then shouldn't the statement x/|x|<x = -x/-x <-x (my thinking here is if we considering x<0, then x should be negative throughout )
So, the equation becomes 1<-x = -1>x, we can keep this option as we have initially assumed X<0
Then if we take any values of x less then -1, |x| will always be greater than 1

if we assume X>0, then x/|x|<x = x/x<x.....which is 1<x, we can keep this option as initially we have assumed X>0
Then we take any values of x greater than 1 then |x| will always be greater than 1.

So statement 1 in either case is sufficient..

Thanks in advance for your help..


Negative x does not mean that you should replace x with -x. x just represents a negative number. You should replace |x| with -x, though because if x < 0, then |x| = -x.


Hi Bunuel

Thanks for your reply. But i am still not able to get why we shouldn't consider negative x's throughout the equation.
If we assuming |x|= -x, we are assuming x<0, which means we are assuming the variable "X" as negative . So, we consider it negative only for Mode but keep it positive in other parts of the equation it seems inconsistent

Thanks again..
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 47977
Re: If x is not equal to 0, is |x| less than 1? (1) x/|x|< x (2) |x| > x  [#permalink]

Show Tags

New post 03 May 2018, 09:53
cruiseav wrote:
Hi Bunuel

Thanks for your reply. But i am still not able to get why we shouldn't consider negative x's throughout the equation.
If we assuming |x|= -x, we are assuming x<0, which means we are assuming the variable "X" as negative . So, we consider it negative only for Mode but keep it positive in other parts of the equation it seems inconsistent

Thanks again..


Consider simple example: x = -1. So, we know that x is negative. Do you replace x there by -x and write -x = -1?
_________________

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

Re: If x is not equal to 0, is |x| less than 1? (1) x/|x|< x (2) |x| > x &nbs [#permalink] 03 May 2018, 09:53

Go to page   Previous    1   2   3   [ 44 posts ] 

Display posts from previous: Sort by

If x is not equal to 0, is |x| less than 1? (1) x/|x|< x (2) |x| > x

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

Events & Promotions

PREV
NEXT


GMAT Club MBA Forum Home| About| Terms and Conditions and Privacy Policy| 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®.