Just because successful people share certain habits does not mean that those habits leads to success. Spend some time teaching successful adults – the pre-MBA crowd with great academic resumes and good work experience, for example – and you’ll see that they often study ineffectively. Watch them complete homework problems and you’ll find the same. What are they doing?
They’re learning the problem and not the takeaway. They’re memorizing the skill and not conceptualizing the strategy. They’re treating the back-of-the-book solution as a step-by-step guide and not a reference point.
Simply put, they’re learning 1,000 ways to solve 1,000 problems, when all the while the questions that truly matter to them on test day – those 600+ level questions – are questions #1,001, 1,0002, etc.
Consider this example from the Official Guide for GMAT Review, one of our favorite to showcase the thought processes required on the GMAT:
When positive integer x is divided by positive integer y, the remainder is 9. If x/y = 96.12, what is the value of y?
And here’s the official solution (again appearing courtesy the Official Guide for GMAT Review):
The remainder is 9 when x is divided by y, so x = yq + 9 for some positive integer q. Dividing both sides by y gives x/y = q + 9/y. But, x/y = 96.12 = 96.012. Equating the two expressions for x/y gives q + 9/y = 96 + 0.12. Thus, q = 96 and 9/y = 0.12.
9 = 0.12y
y = 9/0.12
y = 75
Now…you can try to memorize that solution, or memorize “Dividend = divisor(quotient) + remainder,” but in doing so you’re likely missing the point of this question. Similarly, if this comes up in a class, you can, like many, copy down all the mathematical steps to review later. But again you’re likely missing the point – you won’t see *this* exact setup on the GMAT, but you will see this concept of “Reverse Engineering” in which they provide you with several (but not all) “outputs” of a mathematical operation (here the result of the division and the remainder) and ask you to find your way back to some of the “inputs” (here the divisor, y). What you *really* need to take away from this problem is that overall concept – the GMAT likes to test mathematical operations out-of-order through Reverse Engineering – and a strategy to attack future problems. We’d suggest:
STRATEGY: Try a simple problem with the same operation and small, easy-to-use numbers to remind yourself how the operation works. If you have, say, 11 divided by 4, you know how that works:
2, remainder 3
2 and 3/4
Now you take that small problem and relate it to the bigger one – in the bigger one they gave you the integer-plus-decimal result (96.12 looks like 2.75) and the remainder (9, which performs the role of the remainder of 3 in our smaller problem). How do those two relate? In our smaller problem we divided 3 by the divisor of 4 to get to the decimals of .75. In the larger, then, do the same thing – take the remainder of 9 and divide by the divisor y, and that will equal the decimals .12. So:
9/y = .12
9 = .12y
900 = 12y (and then since you don’t have a calculator you can do the math in small chunks)
450 = 6y
225 = 3y
75 = y
So what’s the difference in the approaches/takeaways? The written solution isn’t written specifically to “teach” but rather to explain, to justify the validity of the right answer. And many students study in class the same way – they copy the steps and hope to remember them as a step-by-step “how to” manual. But in doing so you just learn how to solve this particular problem, you don’t give yourself bigger strategies to attack plenty of future problems. And let’s be frank here – the last few steps (going from 9/y = 0.12 to solving for y) aren’t where the difficulty lies…if you can’t perform that math by the time test day comes around, you’re not getting anywhere near your goals. Basic linear algebra and multiplication/division are muscle memory…there’s no shame in being rusty at first, but you need to get that up to speed through repetition and practice.
What makes this problem difficult is its abstract setup and the reasoning required to make it concrete and get it going – precisely the portion that the written solution glosses over, and sadly the portion that many students fail to notate when they’re learning the problem, in favor of copying down the steps to finish the calculation at the end.
The most valuable thing that you can do as you study is learn strategies and concepts – not mere skills and formulas. But we’ve been trained through schooling that you can typically copy down what the teacher did, repeat those steps over and over again, and spit them back on the test and do well. That’s what successful people have often done to succeed – it’s just that the GMAT is different. Everyone taking the GMAT has already demonstrated that they can memorize and regurgitate – they’ve all graduated high school with solid grades and gotten at least almost done (if not totally done) with college doing much of the same.
So how should you study?
-Of course brush up on your basic skills, but don’t leave it there
-Look for bigger-picture takeaways every time you do a problem. What made the problem difficult? How was it similar to other problems you’ve seen? What strategies would help to set it up properly or avoid the trap answer? This is where good instructors and lessons can make a huge difference.
-Focus your notetaking and energy on the takeaways and strategies, and then worry about the steps through practice.
-Use the written solutions as references, not as how-to manuals. Written solutions often have to choose between “technically accurate” and “practically helpful” and usually choose accuracy; they’re very often not the best way to think about a problem, or the most scalable way to do multiple problems.
Watching many GMAT students study, it’s striking how often they copy down steps or flip to the back of the book, memorizing and copying instead of thinking and conceptualizing. The GMAT is a reasoning/concept test, not a fact/skill test. Make sure that you focus on the takeaway and not just the steps, and your next step will be to take away that unofficial score report with a big number on it.