How algebra is like a chainsaw: or using common sense on the GMAT

algebra GMAT
By Nick S.

A question I often like to ask my students is, “If you didn’t know how to use a chainsaw, would you play around with it?” Usually the student jokes with me and says of course, but then admits that no, they probably wouldn’t. At least not until they’ve received some training. The reason is obvious: using a tool that you don’t know how to handle is dangerous. In the case of a chainsaw, you could easily lose a finger or two (and that’s if you’re lucky).

Once we’ve established that it’s not a good idea to use power tools that you’re not trained in, I like to point out that algebra is an even more powerful tool than a chainsaw. Algebra helped get us to the moon, which is more than can be said for the chainsaw. And if you misuse algebra, you could lose something more important than just a few fingers. You could lose time on the GMAT. 

To get a top score on the test, it’s best to have certain algebraic topics mastered. That can’t be denied, and the point of this post is not to tell you that you can get a great score without using algebra. However, the problem with algebra is that it takes a lot of practice to really master, but only a little bit of practice to think you’ve mastered it. As a result, you are likely to encounter the following scenario:

You get to a question that feels familiar. Maybe it seems like a quadratic you’ve seen before. Maybe it feels like a word problem you know how to set up. So, you start doing the algebra, and you might even be pretty confident about the first few steps. But then, fairly quickly, you run into a wall and you’re not sure what to do next. Perhaps you should factor out something? What if you square both sides? Maybe you might even need to go back and isolate for that other variable there… 

The problem is that you’ve learned a bit of algebra and now have all these nifty algebraic tools at your disposal. But, you don’t know exactly WHICH algebraic tool to use. And remember what happens when you try to use tools you’re not trained in? Before you know it, you’ve spent a ton of time on this question and you’re no closer to the answer. 

So, what should you do? There are two options:

1.  Keep doing what you’re doing.

2.  Do something else.

Option 1 will lead to a low score. Algebra got you into that mess, and it will not get you out. At least, not until you get better at algebra. 

Option 2 is the correct option. Instead of doing algebra, you should do something else. In general, there are three other things you can do: pick some numbers, test the answer choices, or estimate. In a future post, I will go over these in detail, but what they all have in common is that they are more of a “common sense” approach to the question than is algebra. In essence, what you’re doing is simplifying the question by replacing the unknowns with knowns, and hopefully this will uncover the path to the answer. 

To conclude, be very wary of using math you haven’t mastered. If you find yourself stuck on a question and you’re not sure about your mathematical approach, try using a common sense approach instead. 

Nick graduated from Columbia University with degrees in English and Economics. He next earned a teaching certificate and moved to Barcelona to teach English. Since 2003, he’s been teaching all over the world, usually spending winters in Berlin and summers in Barcelona.

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