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

RELATED VIDEOS FROM OUR COURSE