This post is really about quadratics, but we are going to begin with a discussion of times tables. Off the top of your head, think of the result of . If you know your times tables, and you should, you likely immediately said 20. You did not sit down and actually figure this out, calculating the number you would have if you had four 5′s. And why would you? shows up often enough that it is worth memorizing the result even if you could figure it out mathematically every time.
Now let’s shift over to quadratics as promised. Even if you know how to factor quadratics, which is a skill you should master, some quadratics show up so often that it worth it memorizing their factorization. Just as is the case with times tables, you will be able to solve more quickly on a regular basis by learning common quadratics, regardless of your ability to work out the factorization.
Specifically, you should memorize three common quadratics. These are , which equals ; , which equals ; and , which equals . Whenever one of these appears, you can immediately break it down into its component factors without needing to actually work it out. This will allow you to save a significant amount of time, which, in turn, will give you more time for other problems and ultimately lead to a higher score on test day.
Keeping these quadratics in mind, try the data sufficiency question below and see how you do.
What is the value of ?
This is a value question. We need to be able to arrive at a single value for the expression in the stem. Analyzing the stem, you should be able to recognize the common quadratic:
If you didn’t see this, you would have to reverse FOIL it.
Now let’s take a look at each statement in turn:
Statement 1: b could be anything, so this statement is insufficient.
Statement 2: if , then . There is a single answer, and, thus, the statement is sufficient.
The answer is (B).