There are many ways to answer most algebra problems. You can use algebra—setting up and working out equations. You can plug numbers into equations to try and avoid using algebra. In some cases, you might even be able to solve a question by being a particularly intuitive genius and finding a magnificent shortcut.

We want to stress that none of these methods is necessarily better than another. Which method is best for you relies on your math ability and your target score. Trying to solve problems with algebra is more conceptually demanding, but can take less time. Plugging in numbers makes questions easier to understand but will likely take more time. In general, if you are uncomfortable with algebra, you should generally try to use plugging in. If you are comfortable with algebra, using it is probably the best way to go. Still, these suggestions are not hard and fast rules. If you are generally comfortable with algebra but come upon a question that is stumping you, try plugging in answers. If you usually prefer plugging in answers but come upon a question you can solve using algebra, then use algebra. When you study your practice tests, while looking at the algebra questions you got wrong, you should think about the method you employed. Did you plug in when you should have used algebra? Did you use algebra when you should have plugged in? As for being an intuitive math genius, it can’t just be taught—though we will show you how one might think.

Here’s an example algebra question:

If you answer this question with algebra, you realize that if heads are represented by the variable x, then tails are represented by (x – 62). Therefore,

As you can see, there’s simply less math to do for this problem when you use algebra. Using algebra will only take you longer than plugging in if you have trouble coming up with the equation x + (x – 62) = 162.

Therefore, if you can quickly come up with the necessary equation, then use algebra to solve algebra problems. If you have the sense that it will take you a while to figure out the correct equation, then plug in.

If you were to answer this problem by plugging in, you would pick (C) 108 as the first number to try, since if it does not happen to be the answer, you can still discard either the numbers smaller than it or larger than it. So, if the coin came up heads 108 times, then how many times did it land tails? It landed tails 162 – 108 = 54. Is 108 heads landings 62 more than 54 tails landings? No, 108 – 54 = 54. In order for the problem to work out you need more head landings. You can eliminate (A) and (B) as possibilities. Let’s say we choose (D) 112 as our next plug in number. 162 – 112 = 50. Does 112 – 50 = 62? Yes. (D) is the answer.

It is quite possible that you just looked at this problem and said to yourself, “Other than the 62 more heads, all the other flips were equally heads and tails. So: if you take the 62 out of the total of 162, then you know that the other 100 flips were 50 heads and 50 tails. Now I can just add 62 + 50 = 112. Man, I am an amazing genius!”

Hopefully, our example has convinced you that there isn’t any “right way” to answer a question dealing with algebra. There are faster ways and slower ways, and it always benefits you to use the faster way if you can, but the most important thing is getting the question right. Therefore, when you come to a question, don’t insist on using only one method to try to answer it. Just do what you have to in order to answer the question correctly in as little time as possible.

Now we’ll cover the topics of algebra tested by the SAT.