GMAT Advanced Quant - Tryit #4-9

[TamaraM471]

Hi, I have a question about GMAT Advanced Quant - Tryit #4-9. [in chapter 4]

If A is not equal to 0, is 1/a > a/b^4+3?

(1) a = b^2
(2) a^2 = b^4

When I manipulate (2) I get |a| = b^2 from which follow two equations either a>0, then a=b^2 or a<0, then -a=b^2. To me -a=b^2 can never be true so I concluded that only the first condition a>0 and a=b^2 can be true which would make (2) sufficient.

But (2) is insufficient to I must be going wrong in how I manipulate |a| = b^2.

Thanks for your help!
Tamara

[Sage Pearce-Higgins]

The idea of the flowchart is to avoid the algebra that got you into trouble on this one. It's often easier to consider the two scenarios separately, rather than trying to express them as a single equation such as |a| = b^2 . Also, introducing your own absolute value equations is usually more complicated than you need to be. However, let me try to unpick this.

Statement (2) tells us that a^2 = b^4. If you square root both sides, then you'll get a positive root, a = b^2, and a negative root, a = -b^2. Your equation "-a=b^2" is totally acceptable if a is a negative number. Take an example and I think you'll see this.