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x is +ve ???

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Source: — Data Sufficiency |
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by Bill@VeritasPrep » Thu Mar 13, 2014 8:38 am
|x + 6|> 6 means either:

x + 6 > 6

x > 0

or:

x + 6 < -6

x < -12

X could be positive, but it doesn't have to be.

|x - 6| > 6 means either:

x - 6 > 6

x > 12

or

x - 6 < -6

x < 0

Again, x could be positive, but it doesn't have to be.


Combined, x could be a negative less than 12 (-14 satisfies both statements) or it could be a positive greater than 12 (14 satisfies both statements). We still can't guarantee that x is positive.
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by Patrick_GMATFix » Thu Mar 13, 2014 11:43 am
Often the easiest way to solve absolute value Qs is to think of abs. val. as a measure of distance. |a - b| is the distance between a and b on the number line.

|10-5| = |5-10| = distance between 5 and 10.
|10+5| = |10 - (-5)| = distance between 10 and -5.

Ok let's solve.
Is x positive ?
(1) |x+6| > 6
(2) |x- 6| > 6
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by [email protected] » Thu Mar 13, 2014 4:52 pm
Hi candygal79,

This question is perfect for TESTing Values.

In an absolute value question, it's important to consider multiple possibilities (positive vs. negative, for example) to make sure that you're being thorough.

Here, we're asked "is X positive?" This is a YES/NO question.

Fact 1: |X+6| > 6

If X = 1, then |7| > 6 and the answer to the question is YES
If X = -100, then |-94| = 94 > 6 and the answer to the question is NO
Fact 1 is INSUFFICIENT

Fact 2: |X-6| > 6

If X = 13, then |7| > 6 and the answer to the question is YES
If X = -1, then |-7| = 7 > 6 and the answer to the question is NO
Fact 2 is INSUFFICIENT

Combined, we know that
|X+6| > 6 and
|X-6| > 6

If X = 100, then |106| > 6 and |94| > 6 and the answer to the question is YES
If X = -100, then |-94| > 6 and |-106| > 6 and the answer to the question is NO
Combined, INSUFFICIENT

Final Answer: E

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