The keys to unlocking the ability to do GMAT math efficiently
"Now, that's one from The Book!" – Paul Erdös (1913 – 1996)
The eccentric Hungarian mathematician Erdös would say this when he saw a mathematical proof that he really admired. In his private fantasy world, he imagined God had a Book of the best math proofs, and he would praise a proof by suggesting it was in "The Book." What quality would elicit his praise? Elegance. Nor is Erdös unique in this respect: elegance and economy of effort are universally esteemed in mathematics.
Elegance and Efficiency
It's not hard to understand why elegance is so valued. Even doing GMAT math, of all possible solutions, we certainly would prefer to choose a method of solution that uses the fewest steps. After all, that would be the most efficient solution.
How do you do this? Well, unfortunately, efficiency is one of the hardest things to teach. It seems to come quite naturally to all the great mathematicians in history, but it doesn't necessarily come naturally to anyone else. Here are some concrete suggestions on how you can boost your efficiency.
Suggestion #1: Two Types of Thinking
All mathematical problem solving involve two layers of thinking. The first, the more important and more obvious, is simply: what's mathematically legal? According to the laws of math, what can I do and what can't I do. For example, given the equation 2x – 5 = 13, it would be absolutely illegal to add 5 to the left and not add 5 to the right. Probably most of you, at this point in your studies, seldom have trouble determining what's mathematically legal and what's not.
There's a whole other layer that, regrettably, gets far less attention. This is the layer of strategy. Of the many mathematically legal steps I could take, which is the most strategic? That is, which one will move me from where I am closer to the answer most effectively? For example, to demonstrate the difference between the two types of thinking, in the equation 2x – 5 = 13, it would be perfectly legal to multiply both sides by 73 – but from a strategic point of view, that would be a completely bone-headed thing to do.
With a simple equation like 2x – 5 = 13, probably the process of solving it is so automatic that you can barely distinguish the two types of thinking. In harder problems, though, problems that are not automatic, the distinction becomes crucial. Step #1 of becoming more efficient is to get into the habit of approaching every GMAT Math problem with both levels of thinking, both when you are doing the problem and, even more importantly, when you are checking your answer & reviewing your solution.
Suggestion #2: Multiple Methods of Solution
Virtually every math problem on the GMAT can be solved in more than one way, and it’s important for you to start exploring and comparing these multiple solutions. If you spend more time than you should on a particular GMAT math problem fighting your way to the answer, don't just asking: is my answer right or wrong? Also ask: what approach did I take, and what approach did the official solutions take?
If no official solutions are available for a particular problem, ask a friend how she solved it to get a different perspective. Or go the forums, like GMAT Club: it's always a legitimate post to say: here's a problem I solved using this long method; can someone show me a more efficient way to solve this?
Suggestion #3: Articulate Strategies
An advanced stage is to write down, explicitly, the major points of strategy for solving, say, a quadratic or a problem with square-roots. You will have to compare solutions on several problems before you are ready to take this on. The key is: when you see any succinct formulations of points of strategy, do whatever you can to emblazon them in your mind so you can seamlessly recall them when that kind of problem arises.
Once you have integrated the points of strategies for most of the major question types on the GMAT, you will be operating near your peak efficiency for GMAT Math. And that's exactly where you want to be on test day!
Here’s a challenging GMAT Math question you can try yourself, and when you submit the answer, you will see a full video solution. Compare your strategy to the one in the video: what points of strategy can you learn here?