I have often been asked, what do I think is the most important piece of advice I can give to students to succeed in the math section of the GMAT.
Is it something brilliant about time management, or how to do a data sufficiency question more quickly? Perhaps there is a better way to do permutations and combinations (there is). While all of these are important in achieving a higher score, I think that they pale in comparison to two pieces of advice that are intertwined with each other:
- Know what the question is asking you to find (where are you going).
- Know where you are starting (what are you being given).
These seem like very simple concepts, but most students don’t take the time to address every question with this in mind. I can’t tell you how many time I have worked with students on math questions and they have done the mathematics correctly and put in a wrong answer because they have only done part of the question, perhaps discovered what x was, yet the question asked you to find 4x. Many students have lost points because they have not rechecked what was being asked.
It has been my experience that most students rush through the beginnings of math problems and have poor attention to the detail, in the hope that they can get to the solving part. The problem with this is that you may be looking for the wrong thing. If this is the case then it doesn’t matter how good your technique is, you probably won’t get to the right answer.
When I work with students I make the following recommendations:
- Take the time with each question to determine exactly what is being looked for.
- Are you being asked to find x or 4x?
- Do you need to find a value or an algebraic expression?
- Is it a multiple choice or data sufficiency question? This is crucial, since the multiple choice has an answer that you need to find, whereas the data sufficiency question is asking you whether you have sufficient information to resolve the question (and no solution is required).
This is the ‘what am I looking for’ component – to the extent that you can be as specific as possible, the better your chances of getting a right answer.
However, this is only half of the advice. The other part is knowing what you are given. What data or equations do you have to work with? These are the ingredients that you will be working with to get to the correct answer.
With all math problems there are multiple techniques to get from beginning to end. How do you decide which one to use? The answer to that depends on what your strengths and weaknesses are. Different students will use different techniques to arrive at the same answer.
Since I teach in Boston, I will use an analogy that I often use in my classes. I pose the question, “How do you get from Harvard Square to the Prudential building?” I purposely leave it a little ambiguous to generate discussion.
One student might answer it in terms of methods of travel; another might answer it in terms of the physical directions from one location to another. In fact, the way in which I posed the question is not specific enough to generate an answer yet. So I take the next step and specify that I am looking for directions.
It turns out that there are many streets you can use, multiple ways to go, a half dozen bridges you can travel over to get from one side of the river to the other and multiple means of travel even with the same set of directions.
So what is the point of the exercise? When looking at a math problem, you have to determine, based on your skills and abilities, what is the best method to use.
Consider the following problem:
Johnny travels a total of one hour to and from school. On the way there he jogs at 5 miles per hour and on the return trip he gets picked up by the bus and returns home at 20 miles per hour. How far is it to the school?
a) 2 miles
b) 4 miles
c) 4.8 miles
d) 8 miles
e) 10 miles
Let’s use my technique.
What is the question asking?
The question is looking for a distance that Johnny travels. Good news for us. All the answer choices are in miles.
Where are you starting?
I have two rates of travel and a total time to apportion to and from the school. Let me suggest that there are many ways to attack this one. I will offer just a few to demonstrate that multiple methods lead to the same spot.
A) The Algebra Student says: I will work with the rates and I can see that one is four times the other in terms of time, because D=R*T (Distance = Rate X Time). I know they are inversely related. So 5T= 1 hour. Therefore T=.2 hours. I can take either the bus speed or the bicycle speed and plug in: 20 miles an hour multiplied by .2 hours results in 4 miles. We check the work and we are right.
B) The Plug-In Master says, let me try each of the distances and see what I get. So he starts at 4.8 miles and divides that by 4 miles per hour and recognizes that he is already over an hour time, tries 4 miles and the math works.
C) The Class Math Wiz tells us that there is an elegant way to take the reciprocal of the rates, add them together, flip that result over and voilá we get 4 miles. While our Wiz is absolutely correct, we all shake our heads and look for something that we all can use.
D) Finally, our Class Ball Parker says that all of this was unnecessary, because we only had an hour available to us for both jogging and the bus. Since this is true, we exclude answers C, D, and E. They are too big. We look at 2 miles and realize it is too small and won’t even come close to totaling one hour and without any math, arrive at the exact same answer.
I guarantee that there are even more ways to attack this one problem. Which method is the best? There really is no answer to that. As a student taking the GMAT you really have to determine for yourself which method works for you. However, the first step is to understand where you are starting and where you are going. You need to know exactly what you are looking for, and what tools and information you have available to help you get to the answer.
This is why it is crucial to work as many problems in your practice tests as possible. The more familiar you are, both with the math and the way in which the questions are presented, the better the chances for success.