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

It is currently 18 Aug 2018, 05:21

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/|x|<x which of the following must be true about x?

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

Hide Tags

Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 47981
Re: If x/|x|<x which of the following must be true about x?  [#permalink]

Show Tags

New post 07 Jul 2014, 01:41
Kconfused wrote:
Bunuel wrote:
nmohindru wrote:
If \(\frac{x}{|x|}<x\) which of the following must be true about \(x\)?

(A) \(x>1\)

(B) \(x>-1\)

(C) \(|x|<1\)

(D) \(|x|=1\)

(E) \(|x|^2>1\)


This question was well explained by Durgesh and Ian Stewart, but since there are still some doubts, I'll try to add my 2 cents.

First of all let's solve this inequality step by step and see what is the solution for it, or in other words let's see in which ranges this inequality holds true.

Two cases for \(\frac{x}{|x|}<x\):

A. \(x<0\) --> \(|x|=-x\) --> \(\frac{x}{-x}<x\) --> \(-1<x\) --> \(-1<x<0\);

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

So given inequality holds true in the ranges: \(-1<x<0\) and \(x>1\). Which means that \(x\) can take values only from these ranges.

------{-1}xxxx{0}----{1}xxxxxx

Now, we are asked which of the following must be true about \(x\). Option A can not be ALWAYS true because \(x\) can be from the range \(-1<x<0\), eg \(-\frac{1}{2}\) and \(x=-\frac{1}{2}<1\).

Only option which is ALWAYS true is B. ANY \(x\) from the ranges \(-1<x<0\) and \(x>1\) will definitely be more the \(-1\), all "red", possible x-es are to the right of -1, which means that all possible x-es are more than -1.

Answer: B.


Bunnel, if I were to multiply the original stem with |x| (since |x| is always positive) it would result in x*(|x|-1) > 0.
This would mean x > 0 and |x| > 1
|x| > 1 would lead to x < -1 and x > 1 . This is completely different from the answer you've reached. I see that your method is accurate and the answer justified, but can you please correct my method here.
Thanks in advance!


It would give the same answer.

\(x*(|x|-1) > 0\). This implies that both multiples have the same sign.

\(x>0\) and \(|x|>1\) (since we consider positive x, then this transforms to x>1) --> \(x>1\).
\(x<0\) and \(|x|<1\) (since we consider negative x, then this transforms to -x<1 --> -1<x) --> \(-1<x<0\).

The same ranges as in my solution.

Hope it's clear.
_________________

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

Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 47981
If x/|x|<x which of the following must be true about x?  [#permalink]

Show Tags

New post 15 Aug 2014, 09:28
1
sri30kanth wrote:
Bunuel,

What if we square the inequality x/ |x| < x. Then we get (x^2 / x ) < x^2 which implies that x^2 < x^3. Is this correct? Please explain. Thanku


We can raise both parts of an inequality to an even power if we know that both parts of an inequality are non-negative (the same for taking an even root of both sides of an inequality), which is not the case here.

Also, the second step in your solution: never multiply (or reduce) an inequality by a variable (or the expression with a variable) if you don't know the sign of it, we don't know the sign of x, so we cannot multiply x^2/x < x^2 by x here.

For more check here: inequalities-tips-and-hints-175001.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

Senior Manager
Senior Manager
User avatar
S
Joined: 25 Mar 2013
Posts: 263
Location: United States
Concentration: Entrepreneurship, Marketing
GPA: 3.5
GMAT ToolKit User Reviews Badge
If x/|x|<x which of the following must be true about x?  [#permalink]

Show Tags

New post 30 Nov 2014, 08:44
As Bunnel states.
Two cases for \frac{x}{|x|}<x:

A. x<0 --> |x|=-x --> \frac{x}{-x}<x --> -1<x --> -1<x<0;

B. x>0 --> |x|=x --> \frac{x}{x}<x --> 1<x.

Concept is the absolute value of -5 equals 5, or, in mathematical
symbols, I-51 = 5.
From above A.
x<0 mean x is negative Assume x = -1
lxl = l -x l becz x is negative /positive = X is always positive
But not |x|=-x ?????
_________________

I welcome analysis on my posts and kudo +1 if helpful. It helps me to improve my craft.Thank you

Veritas Prep GMAT Instructor
User avatar
P
Joined: 16 Oct 2010
Posts: 8189
Location: Pune, India
Re: If x/|x|<x which of the following must be true about x?  [#permalink]

Show Tags

New post 30 Nov 2014, 22:08
kanusha wrote:
x<0 mean x is negative Assume x = -1
lxl = l -x l becz x is negative /positive = X is always positive
But not |x|=-x ?????



You assumed x = -1
You got |x| = 1

Is |x| = x? No. |x| is 1 but x is -1
Then what is |x| in terms of x?

|x| = -x
1 = -(-1) = 1

That is why you say that |x| = -x when x is negative because then -x becomes positive.
_________________

Karishma
Veritas Prep GMAT Instructor

Save up to $1,000 on GMAT prep through 8/20! Learn more here >

GMAT self-study has never been more personalized or more fun. Try ORION Free!

Intern
Intern
User avatar
Joined: 21 Apr 2014
Posts: 39
Re: If x/|x|<x which of the following must be true about x?  [#permalink]

Show Tags

New post 23 Feb 2015, 01:53
So, since we know that the absolute value is positive, we can multiply both sides by abs(x) without having to change the sign.

x<x * |x| This means that x has to be greater than 1 or in between -1 and 0. You can figure this out from intuition or by testing number. 0 and -1 don't work because that would make both sides equal.

We are looking for something that must be true, so if we can find a scenario for x that works outside the given parameters, we can eliminate it right away.
A) doesn't have to be true, because x could because -1/2 works for x
B) does have to be true there is no value for x that works and is below -1
C) doesn't have to be true, because -1/2 works
D) doesn't have to be true, because x=1 doesn't even work
E) doesn't have to be true because -1/2 works
_________________

Eliza
GMAT Tutor
bestgmatprepcourse.com

Director
Director
User avatar
Joined: 07 Aug 2011
Posts: 560
Concentration: International Business, Technology
GMAT 1: 630 Q49 V27
GMAT ToolKit User
Re: If x/|x|<x which of the following must be true about x?  [#permalink]

Show Tags

New post 06 Apr 2015, 18:53
nmohindru wrote:
If \(\frac{x}{|x|}<x\) which of the following must be true about \(x\)?

(A) \(x>1\)

(B) \(x>-1\)

(C) \(|x|<1\)

(D) \(|x|=1\)

(E) \(|x|^2>1\)

Attachments

gmatclub.jpg
gmatclub.jpg [ 77.27 KiB | Viewed 1657 times ]


_________________

Thanks,
Lucky

_______________________________________________________
Kindly press the Image to appreciate my post !! :-)

Intern
Intern
avatar
Joined: 01 Apr 2014
Posts: 4
Re: If x/|x|<x which of the following must be true about x?  [#permalink]

Show Tags

New post 09 Feb 2016, 00:29
CAN I SOLVE THE QUESTION IN THIS WAY..
x/|x|<x---->|x|/X>1/X----->|x|>1

Two Cases---> X>1 or X<-1

since,

|ax+b|>s--->ax+b>1 or ax+b<-1
Veritas Prep GMAT Instructor
User avatar
P
Joined: 16 Oct 2010
Posts: 8189
Location: Pune, India
Re: If x/|x|<x which of the following must be true about x?  [#permalink]

Show Tags

New post 09 Feb 2016, 03:52
akshay4gmat wrote:
CAN I SOLVE THE QUESTION IN THIS WAY..
x/|x|<x---->|x|/X>1/X----->|x|>1

Two Cases---> X>1 or X<-1

since,

|ax+b|>s--->ax+b>1 or ax+b<-1



You cannot cancel off x's from the denominator without knowing the sign of x.
_________________

Karishma
Veritas Prep GMAT Instructor

Save up to $1,000 on GMAT prep through 8/20! Learn more here >

GMAT self-study has never been more personalized or more fun. Try ORION Free!

DS Forum Moderator
User avatar
P
Joined: 27 Oct 2017
Posts: 674
Location: India
Concentration: International Business, General Management
GPA: 3.64
WE: Business Development (Energy and Utilities)
Premium Member CAT Tests
Re: If x/|x|<x which of the following must be true about x?  [#permalink]

Show Tags

New post 14 Apr 2018, 02:04
Hi

The main point in this question is to understand what the question is asking.
which of the following must be true about x?

It means the question is asking about a Set of Values, which contains all the value of x which satisfy the given inequality.
But the Big Idea is that the set may contain other values also which does not satisfy the inequality.

It simply means the set must contains all the value of x satisfying the inequality but vice versa is not required.

only after solving the inequality as explained above,
-1<x<0 , when x is negative , or
x>1 when x is positive.

So option B x>-1 is the only the set of values which contains all the above required values of x.

Hence Answer B
_________________

SC: Confusable words
All you need for Quant, GMAT PS Question Directory,GMAT DS Question Directory
Error log/Key Concepts
Combination Concept: Division into groups
Question of the Day (QOTD)
Free GMAT CATS

Manager
Manager
avatar
B
Joined: 02 Jan 2016
Posts: 98
Reviews Badge
Re: If x/|x|<x which of the following must be true about x?  [#permalink]

Show Tags

New post 26 May 2018, 05:50
Its always a good idea to simply or manipulate the Question Stem

X divided by |X| will either give a "1" or "-1", depending on "sign of X"

Incase "1" then X > 1 and Incase "-1" X > "-1",

If you think on this X >1 might be true but not always true, but X > -1 will always be true.


Even if "X" is a fraction, X>-1 is true and this also matches our answer.
Re: If x/|x|<x which of the following must be true about x? &nbs [#permalink] 26 May 2018, 05:50

Go to page   Previous    1   2   3   [ 51 posts ] 

Display posts from previous: Sort by

If x/|x|<x which of the following must be true about 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®.