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Math Expert V
Joined: 02 Aug 2009
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Difficulty:   55% (hard)

Question Stats: 57% (01:11) correct 43% (01:14) wrong based on 227 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

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Math Expert V
Joined: 02 Aug 2009
Posts: 7764

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Post reserved for OE
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Manager  S
Joined: 24 Oct 2013
Posts: 130
Location: India
Concentration: General Management, Strategy
WE: Information Technology (Computer Software)

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Option A

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

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

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CEO  V
Joined: 12 Sep 2015
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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

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Concentration: Operations, Finance
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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!!!  _________________
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Resource: GMATPrep RCs With Solution
Current Student S
Joined: 31 Dec 2015
Posts: 49
Location: India
GMAT 1: 670 Q44 V38 GMAT 2: 680 Q44 V39 ### Show Tags

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 !!
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