Is a<0? (1) a^3 < a^2 +2a

[THANHD377]

Is a<0?

(1) a^3 < a^2 +2a
(2) a^2 > a^3

Source: GMAT Advanced Quant. Try-It #4-10

Hi. I know that the correct answer is (E), as a can be <-1 OR 0<a<1.

However, I wonder why it doesn't work if I do it this way...

(1) a^3 < a^2 + 2a
(2) a^3 < a^2 (switch order)

(1) - (2) <=> a^3 - a^3 < a^2 - a^2 +2a <=> 0 < 2a <=> a>0

Thanks,

[Sage Pearce-Higgins]

You have to be careful when subtracting inequalities (basically, don't do it). Take the following example:

5 > 4
3 > 1

However, if I subtract them, then I get 2 > 3, which clearly isn't true. The reason for this is that an inequality doesn't tell you how much greater it is. Adding inequalities, on the other hand, is fine.