My interpretation of this is X could be either smaller than 3 or greater than -3 and hence INSUFFICIENT:
X<3
or -X<3 => X>-3
Since the keyword here is OR, not AND, I thought this is insufficient. X>-3 means X could have any value smaller or greater than 3.
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If |X|<3, is X<3?
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Mike@Magoosh
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Hi, there. I'm happy to help with this. 
First of all, this is odd, because it's not a complete DS question. I assume it comes from something like:
Prompt: is x<3
one of the statements: |x|<3
Well, think about |x|<3. That means x is has a distance less than 3 from the origin. The solution to |x|<3 is the compound inequality -3 < x < 3. The value of x must be between -3 and 3. Of course, if x is anywhere in that range, it's less than 3, so this is sufficient.
The problem with pdshah's solution is: the proper word in the solution to that particular inequality is "and", not "or."
If |x|<3, then x<3 and -x<3 ==> x>-3. That gives us a narrow range on the number line that's a solution.
If the word were "or", and the solution x<3 or x>-3, that's the entire number line. Every real number is either less than 3 or greater than -3. Clearly, this inequality does not have a solution of all real numbers. That's why "or" is wrong.
Does that make sense? Please let me know if you have any further questions.
Mike
First of all, this is odd, because it's not a complete DS question. I assume it comes from something like:
Prompt: is x<3
one of the statements: |x|<3
Well, think about |x|<3. That means x is has a distance less than 3 from the origin. The solution to |x|<3 is the compound inequality -3 < x < 3. The value of x must be between -3 and 3. Of course, if x is anywhere in that range, it's less than 3, so this is sufficient.
The problem with pdshah's solution is: the proper word in the solution to that particular inequality is "and", not "or."
If |x|<3, then x<3 and -x<3 ==> x>-3. That gives us a narrow range on the number line that's a solution.
If the word were "or", and the solution x<3 or x>-3, that's the entire number line. Every real number is either less than 3 or greater than -3. Clearly, this inequality does not have a solution of all real numbers. That's why "or" is wrong.
Does that make sense? Please let me know if you have any further questions.
Mike
Magoosh GMAT Instructor
https://gmat.magoosh.com/
https://gmat.magoosh.com/
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Very important and helpful explanation given.... Thank You!!!
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