Easy shortcut or invalid? Plugging 0 into a DS problem.

[paraclete]

Dear instructors,

I have a question about a problem I saw in the advanced quant book:

Try it #4-10

Is a < 0?

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

The book takes us through a long explanation and (helpful) method of testing numbers. However, when testing 0, the book says it is invalid for both statements. When testing 0, statement 1 yields:

0^3 < 0^2 + 2(0)

which is false because 0 < 0 is false, and statement 2 yields

0^2 > 0^3

which is also false for the same reason.

If I were approaching this problem, I would assume the answer is E because if a = 0, the statements are equal, and there must be other values for which each statement holds true. Is this not a valid approach? I thought it was until I saw in the advanced quant book that testing 0 is listed as "invalid," which doesn't make sense to me. Is 0 also an invalid plug-in for other inequality problems? Can someone please explain this to me?

Thanks a lot for your help :)

[RonPurewal]

Unfortunately, it seems you're going to have to go back to the very basics of data sufficiency. If you think that a = 0 is relevant to this problem, you'll need to start again from square one, because, in that case, those basics are not there.

At any point during the data sufficiency process, you are doing exactly one of the following three things:

1/
Considering only those values that satisfy statement 1, and ignoring statement 2.

2/
Considering only those values that satisfy statement 2, and ignoring statement 1.

3/ (if necessary)
Considering only those values that satisfy both statements.

a = 0 doesn't satisfy either of the statements, so it is irrelevant to the problem.

[paraclete]

You're right. Thanks for pointing that out. Looks like I still need to hammer home some basics.

[RonPurewal]

Yeah. Don't run until you can walk.

As ridiculous as this might sound, the biggest issue that people have with DS after months of studying is ... they still don't really understand how DS works.
Don't let it happen to you.