All the Quant (7th edition), page 142, is b<0?

[sshin]

Hi,

I am struggling to solve this problem by using algebra:

Is b<0?
(1) b^3 < b
(2) b^2 > b

If you simplify statement (1) b^3 < b, that should result in b^2<1, therefore, -1<b<1.
Same simplification of statement (2) b^2>b, however, should result in b>1. Shouldn't then be B is sufficient?

Thank you

[Sage Pearce-Higgins]

Well, here's a reason to avoid algebra on GMAT! Most GMAT takers (including me) would mess up the algebra for this one, so I'd strongly advise you to master the strategy of testing cases, i.e. picking examples for b.

The problem with your algebra is that, when dealing with inequalities, we need to switch the sign if we divide by a negative number. For example, we know that 3 < 5, but what's the sign between -3 and -5? Since we don't know whether b is negative, your following step is incorrect:

b^3 < b, that should result in b^2<1

Really, I advise you to look at these statements and think "what numbers work for b?".

[sshin]

That makes sense, thank you!

[Sage Pearce-Higgins]

You're welcome.