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Is x <|x|?

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Is x <|x|?  [#permalink]

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New post 21 Feb 2017, 18:21
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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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Re: Is x <|x|?  [#permalink]

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New post 21 Feb 2017, 19:08
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Re: Is x <|x|?  [#permalink]

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New post 22 Feb 2017, 07:05
Option A

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

Statement 2 : x could be zero or negative. not sufficient
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Re: Is x <|x|?  [#permalink]

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New post 22 Feb 2017, 08:09
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...

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Re: Is x <|x|?  [#permalink]

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New post 22 Feb 2017, 09:22
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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

Answer: A

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Re: Is x <|x|?  [#permalink]

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New post 22 Feb 2017, 10:23
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

Answer: A

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What a great Explanation Brent!!! :clap: :-D
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Re: Is x <|x|?  [#permalink]

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New post 15 Mar 2017, 00:14
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

Answer: A

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Thanks for the Crystal Clear explanation !!
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Re: Is x <|x|?  [#permalink]

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Re: Is x <|x|?   [#permalink] 27 Oct 2018, 12:24
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