Recognizing disguised quadratics in problems (generally)

[DCS80]

Hi Guys,

reviewing the perversities of quadratics, I was curious as to if there is a list/sample of the most commonly rephrased equations

for example,

(36/b) = b-5
or
3w^2 = 6w


maybe a small collection of equations that can be rewritten as clear quadratic equations?

[Tommy Wallach]

Hey DCS80,

I wouldn't attempt to find a long list of quadratics, because you'll just be wasting your time. Instead, try to notice the most typical signals. There are the three major identities: 1) (x+y) * (x+y) 2) (x-y) * (x-y) and the most important, 3) (x+y) * (x-y).

The third identity (sometimes called "Difference of squares") comes up constantly on tough GMAT questions, so you need to always be on the lookout for it in different forms.

As for the examples you give, those aren't situations you need to memorize. Anytime you have something in the form of ax^2 + bx + c, you're dealing with a quadratic. Your first example will clearly become that form when you multiply both sides by b (which is the logical first step to take). The second example may be slightly more confusing, because it's missing the c part of the quadratic (technically, c = 0), but it should still set off alarm bells when you have ax^2 + bx.

Does that help? Let me know if you have more questions!

-t

[DCS80]

awesome, thanks. any particular examples for the difference of squares reference?

[Tommy Wallach]

Hey DCS80,

This page has some tips and tricks: https://www.manhattangmat.com/strategy-s ... -roots.cfm As for questions, there are plenty out there, but likely only a few in the official guides. I recommend, after studying a bit, see if you can page through the official guide and pick them out by sight (then you can check in the back to see if you're right).

Good luck!

-t