GMAT Question of the Day: Daily via email | Daily via Instagram New to GMAT Club? Watch this Video

 It is currently 17 Feb 2020, 13:00

### 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

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

# Is x <|x|?

Author Message
TAGS:

### Hide Tags

Math Expert
Joined: 02 Aug 2009
Posts: 8268

### Show Tags

21 Feb 2017, 17:21
2
8
00:00

Difficulty:

55% (hard)

Question Stats:

55% (01:11) correct 45% (01:14) wrong based on 244 sessions

### HideShow timer Statistics

Is x<|x|?
(1) x>2x
(2) x is non-positive integer

Self made ... Some more Q testing concept of absolute modulus

_________________
Math Expert
Joined: 02 Aug 2009
Posts: 8268

### Show Tags

21 Feb 2017, 18:08
Post reserved for OE
_________________
Manager
Joined: 24 Oct 2013
Posts: 126
Location: India
Concentration: General Management, Strategy
WE: Information Technology (Computer Software)

### Show Tags

22 Feb 2017, 06:05
Option A

Statement 1 : this will be true only when x is negative

Statement 2 : x could be zero or negative. not sufficient
Intern
Joined: 18 Jan 2017
Posts: 23

### Show Tags

22 Feb 2017, 07:09
Option A... if x<|x| it would mean that x is a negative integer... going into the options with this premise, option A suggests that x < 2x; this is only possible when x is negative... Sufficient

Option 2 mentions x is non-positive which can be negative OR zero... not unique hence not sufficient...

Sent from my GT-I9060I using GMAT Club Forum mobile app
GMAT Club Legend
Joined: 11 Sep 2015
Posts: 4320

### Show Tags

22 Feb 2017, 08:22
3
Top Contributor
1
chetan2u wrote:
Is x < |x|?

(1) x > 2x
(2) x is non-positive integer

Great question, chetan2u!

Target question: Is x < |x|?
This is a great candidate for rephrasing the target question.

To see what I mean, let's examine 3 possible scenarios: x is negative, x is positive and x is zero

Scenario #1: x is negative
If x is negative, then |x| is positive. So, we get x < |x|, since x is negative and |x| is positive.
For example, if x = -2, then we have -2 < |-2|

Scenario #2: x is positive
If x is positive, then x and |x| are BOTH positive. In fact, x = |x|
For example, if x = 3, then we have 3 = |3|

Scenario #3: x is zero
Since |0| = 0, then we have the case where x = |x|

So, the ONLY time that x < |x| is when x is negative.
So, asking Is x < |x|? is the SAME as asking, Is x negative?
This means we can REPHRASE the target question....

REPHRASED target question: Is x negative?

Now onto the statements.....

Statement 1: x > 2x
Subtract x from both sides to get: 0 > x
In other words, x is negative. PERFECT!
Since we can answer the REPHRASED target question with certainty, statement 1 is SUFFICIENT

Statement 2: x is non-positive integer
If x is NOT POSITIVE, then x can be negative OR x can equal 0
In other words, x may or may not be negative.
Since we cannot answer the REPHRASED target question with certainty, statement 2 is NOT SUFFICIENT

RELATED VIDEOS FROM OUR COURSE

_________________
Test confidently with gmatprepnow.com
Director
Joined: 06 Jan 2015
Posts: 719
Location: India
Concentration: Operations, Finance
GPA: 3.35
WE: Information Technology (Computer Software)

### Show Tags

22 Feb 2017, 09:23
GMATPrepNow wrote:
chetan2u wrote:
Is x < |x|?

(1) x > 2x
(2) x is non-positive integer

Great question, chetan2u!

Target question: Is x < |x|?
This is a great candidate for rephrasing the target question.

To see what I mean, let's examine 3 possible scenarios: x is negative, x is positive and x is zero

Scenario #1: x is negative
If x is negative, then |x| is positive. So, we get x < |x|, since x is negative and |x| is positive.
For example, if x = -2, then we have -2 < |-2|

Scenario #2: x is positive
If x is positive, then x and |x| are BOTH positive. In fact, x = |x|
For example, if x = 3, then we have 3 = |3|

Scenario #3: x is zero
Since |0| = 0, then we have the case where x = |x|

So, the ONLY time that x < |x| is when x is negative.
So, asking Is x < |x|? is the SAME as asking, Is x negative?
This means we can REPHRASE the target question....

REPHRASED target question: Is x negative?

Now onto the statements.....

Statement 1: x > 2x
Subtract x from both sides to get: 0 > x
In other words, x is negative. PERFECT!
Since we can answer the REPHRASED target question with certainty, statement 1 is SUFFICIENT

Statement 2: x is non-positive integer
If x is NOT POSITIVE, then x can be negative OR x can equal 0
In other words, x may or may not be negative.
Since we cannot answer the REPHRASED target question with certainty, statement 2 is NOT SUFFICIENT

RELATED VIDEOS FROM OUR COURSE

What a great Explanation Brent!!!
_________________
आत्मनॊ मोक्षार्थम् जगद्धिताय च

Resource: GMATPrep RCs With Solution
Intern
Joined: 31 Dec 2015
Posts: 40
Location: India
GMAT 1: 670 Q44 V38
GMAT 2: 680 Q44 V39

### Show Tags

14 Mar 2017, 23:14
GMATPrepNow wrote:
chetan2u wrote:
Is x < |x|?

(1) x > 2x
(2) x is non-positive integer

Great question, chetan2u!

Target question: Is x < |x|?
This is a great candidate for rephrasing the target question.

To see what I mean, let's examine 3 possible scenarios: x is negative, x is positive and x is zero

Scenario #1: x is negative
If x is negative, then |x| is positive. So, we get x < |x|, since x is negative and |x| is positive.
For example, if x = -2, then we have -2 < |-2|

Scenario #2: x is positive
If x is positive, then x and |x| are BOTH positive. In fact, x = |x|
For example, if x = 3, then we have 3 = |3|

Scenario #3: x is zero
Since |0| = 0, then we have the case where x = |x|

So, the ONLY time that x < |x| is when x is negative.
So, asking Is x < |x|? is the SAME as asking, Is x negative?
This means we can REPHRASE the target question....

REPHRASED target question: Is x negative?

Now onto the statements.....

Statement 1: x > 2x
Subtract x from both sides to get: 0 > x
In other words, x is negative. PERFECT!
Since we can answer the REPHRASED target question with certainty, statement 1 is SUFFICIENT

Statement 2: x is non-positive integer
If x is NOT POSITIVE, then x can be negative OR x can equal 0
In other words, x may or may not be negative.
Since we cannot answer the REPHRASED target question with certainty, statement 2 is NOT SUFFICIENT

RELATED VIDEOS FROM OUR COURSE

\

Thanks for the Crystal Clear explanation !!
Non-Human User
Joined: 09 Sep 2013
Posts: 14069

### Show Tags

27 Oct 2018, 11:24
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________
Re: Is x <|x|?   [#permalink] 27 Oct 2018, 11:24
Display posts from previous: Sort by