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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...

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

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

RELATED VIDEOS FROM OUR COURSE

What a great Explanation Brent!!!
_________________

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

RELATED VIDEOS FROM OUR COURSE

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Thanks for the Crystal Clear explanation !!

gmatclubot

Re: Is x <|x|? &nbs
[#permalink]
15 Mar 2017, 00:14