Is a>0? Need help with this inequality?

[kouranjelika]

My recommendation is "do whatever comes to mind".
If you see something that has a conceptual meaning for you, then think conceptually. If not, don't. (For instance, "|x| = y - z", from the problem you posted above, has no immediate conceptual meaning to me.)
More importantly, you should NEVER try to have one "primary" method for approaching these problems. The entire point of this test is that no method is going to work all the time; you're going to need flexibility.

Yea, it is starting to click now. Sometimes I test cases, sometimes just think conceptually, sometimes actually do algebraic manipulations. Totally with you on staying flexible.

To answer this question, I would have to search the study-hall page in exactly the same way you would. (I don't remember the contents of previous study halls, especially if they are more than a few months old.)

Gotcha. I just meant in case there was one particular session that burnt into your mind as a very good one. Obv did not mean for you to go searching (that's exactly what I did).
So far, I watched the Absolute Value session from way back. The three Inequalities Workshops from 2010 & 2012. Very helpful. Thanks Ron!

[kouranjelika]

I think you're assuming that "-x" is never positive. That's incorrect; if x is negative, then -x is positive. (For instance, if x is -14, then -x is 14.)
That seems to be the only issue here.
(Incidentally, if you spend too much time studying "advanced" math, you'll be more likely to make mistakes like this one. The GMAT tests math that's pretty close to the ground.)

Wow, that was super helpful. You just changed my world. Bravo!

And thanks for critiquing my reasoning on the problem in this thread. I was laughing out loud on some of the mistakes you caught me doing (0>x>1???? hahah) and the great catch of not accounting for 0 in statement 2. Really, thanks a lot!

[RonPurewal]

You're welcome"”but I'm honestly not doing much beyond pointing out what's tested and what isn't.

They've done a nice job of convincing students that the quant section is actually a math test. Ha! It's not.
It's a test of ...
... organization
... careful thinking
... flexible thinking (especially for multiple-choice problems)
... having a goal
... staying focused on that goal
... following directions.

And other things of that sort. Your elementary-school teachers would be ecstatic.

[kouranjelika]

I think once you're solid on the material it becomes this. It's like your analogy with music. Probably most can learn how to play a certain famous piece of music, but to play it exquisitely and with passion requires more than just the knowledge of the notes and their order.

[RonPurewal]

Yep.