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The Reason Behind Reasoning – Based Study

by Veritas Prep on April 6th, 2012
Learn more about Veritas Prep's GMAT course or read Veritas Prep articles on BTG.
Posted in
  • Arithmetic
  • Geometry
  • GMAT Math
  • Powers and Roots

If you’re a regular reader of Veritas Prep articles, you’ve likely seen us comment on the importance of recognizing the GMAT as a reasoning-based test, and not merely one that tests content. Why is that so important and why are we so emphatic about it?

At Veritas Prep headquarters, we are  fortunate to be able to see quite a bit of that upper echelon of GMAT scorers, as we have had hundreds of instructors with 99th percentile scores and have trained thousands of 700+ scorers. And particularly as we talk with our instructors, the following themes emerge about those who score in that top percentile on the test:

  • Most will admit that they are  almost ashamed of some of the content gaps they had when they took the GMAT, particularly now that they have  had to master all the content to teach it (but remember – they did score way, way above 700!)
  • Most will also sheepishly admit that they kind of enjoyed studying for the test, and that they thought of it as more of a brain-teaser than as a chore of memorization or “practice”
  • And with all of that said, most tend to agree with our following estimate…

Of any group of 100 people who score in the top percentiles of the GMAT, we would estimate that:

2-3 of them did so based purely on content knowledge. They know every fact, formula, and rule that the test could present so well and from so many directions as to make the questions obsolete. To do so requires a nearly photographic memory – these folks can recite dozens of digits of pi and have memorized three- and four-digit multiplication problems. Most people will never think this way.

15-20 of them did so with admittedly weak content knowledge*, but could reason their way through questions in ways that bridged those knowledge gaps and leveraged the ways in which problems were written to gain unique insight into the test. These are the folks who are annoying to watch Jeopardy with: they may not know the information cold, but they will  pick up on the hints in the clues and category names to seemingly know everything.

Everyone else had to do a combination of both – they mastered the bulk of the content and had to learn some reasoning and problem solving skills to know how to employ that information. And here is  why reasoning-based learning is so critical: everyone with the capacity to do well on the GMAT already knows how to study content.  They’ve pored over notes the week leading up to midterms and jotted down the clues that the TA mentioned in the review session about what would be on the test. Studying content isn’t a groundbreaking concept – if you are  even eligible to sit for the GMAT you’ve done enough content study in your life that you almost intuitively do this before any event in which knowledge would be important.

Few, however, intuitively know to study reasoning. For example, consider this geometry rule:

The lengths of the sides, respectively, in a 45-45-90 degree isosceles triangle follow the ratio: x : x : x * squareroot(2)

And this question:

In isosceles triangle ABC, the length of line AB is 2 and the length of line BC is 2*squareroot(2). What is the perimeter of triangle ABC?

The answer? It’s not possible without further information. Why? We don’t know which side AC matches because we don’t know whether it is a right triangle. It only appears to be a right triangle because two of the sides match the formula, but in an isosceles (but not necessarily right) triangle the third side could be either 2 or 2*squareroot(2). And here is the takeaway: most students who miss this question will simply categorize this as a “triangle mistake.” But that’s not why they missed it! In order to miss this question, one actually needs to know quite a bit about triangles…one will usually only miss this because they think, erroneously, that they can employ the 45-45-90 triangle ratios.

It’s not at all that they “don’t know triangles,” but rather that the test baited them into thinking that they had more information than they really did. In fact, one could argue that in order to fall into the trap on that question, a student actually has to be pretty well-versed in geometry. Someone who does not know that triangle ratio wouldn’t think to use it. But they’d never see that question on the test…the CAT algorithm would be feeding them much simpler questions that don’t require nuance. Once you’re above that “are you smarter than a fifth grader?” threshold, however, the questions require more than just knowledge, and they’ll be designed to trap you if all you’re looking to do is show off your short-term memory.

Reasoning-based curriculum teaches students how to think like the testmaker – to anticipate and avoid traps, to pay attention to subtlety in wording where it tends to occur most, and to think critically when assessing which knowledge to use to solve a problem. But students do not  usually think this way on their own – their years of education have taught them that when they get a question wrong, they should go back and “study that information.”

Content-based curriculum is incomplete if not unnecessary – students will study content on their own because that’s what they’ve always done. But without reasoning, that content knowledge is not enough. Remember this: The GMAT is not a pass/fail exam. It is graded on a curve – its job is to take the entire pool of MBA candidates and break them into a bell curve, showing schools which students are the most likely to succeed. At a certain point, everyone above that level (say, for sake of argument, 540) has proven that they “know” algebra, geometry, etc. The test has to separate on reasoning, and that’s why so many students will complain that they studied for 100+ hours but only scored in the 500s. Knowledge can only take you so far on a test that seeks to determine your analytical abilities.

For these reasons, reasoning is crucial. Content is only about a third of the GMAT, with the rest of the test dependent on your reasoning ability. But your inclination when you study is to study content – it’s up to you to recognize that you need to stay conscious of reasoning and not just knowledge. We’ll continue to be emphatic about the need for reasoning, in large part because we know that it’s the portion of the test that just doesn’t come naturally to most.

*-a postscript about gaps in content knowledge: Your author, believe it or not, completely blanked on what most GMAT students would consider a remedial piece of knowledge. When multiplying x^y * x^z, what do you do with the exponents? Not immediately having this rule (you add the exponents) memorized constitutes a pretty big content gap, but with reasoning he was able to prove it using something else (if you multiply x^2 * x^3, that’s xx * xxx, so there are five x’s…of course you add the exponents!). You would be surprised at how many little gaps like that many 700+ scorers had when taking the test, but they were able to overcome them through reasoning. Similarly, you’d be surprised at how often someone knows every one of those formulas/rules cold, but doesn’t perform well. Why? Because the test requires reasoning, and those who have not made that a central part of their study regimen are often easy prey for trap answers.

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