# Tag Archives: GMAT psychometrics

## Go ahead, roll your eyes… but it’s GMAT quantitative reasoning, not GMAT math

If you’ve struggled with the GMAT quant section more than you think you should, this blog post is for you. If you’ve ever said, “I’ve always been a really good math student, but I can’t understand why the GMAT quant is so hard for me!” – then this post is definitely for you.

In my former life as a PhD student, I spent far too much time learning about the statistical science underneath standardized testing, known as psychometrics. My nearly three-year PhD odyssey didn’t result in much other than some grey hairs and a “thank you for playing!” Master’s degree in education, but I did experience a few things that probably helped me become a better GMAT and GRE tutor.

This is a story about one of those things – and at the time, I never would have guessed that it would be useful for my GMAT and GRE students.

In my first year as a PhD student, I went to a psychometrics conference, populated by academics and employees of major standardized testing organizations, including ETS (makers of the GRE and TOEFL) and GMAC (creators of your beloved GMAT). I attended a presentation by a high-ranking GMAT psychometrician, who discussed… well, nevermind that part, I’ll put you right to sleep if I start talking about it.

Anyway, here’s the useful bit: somebody in the audience asked a question about the “math section of the GMAT.” The GMAT psychometrician interrupted him politely: “Excuse me,” he said, “there is no math section on the GMAT. There’s only quantitative reasoning.”

I probably rolled my eyes. “What a dick,” I thought, “why would he make a big deal out of that? It’s math. S#!t, I’ve been teaching it for a decade. Whatever, dude.”

Sure, maybe the GMAT psychometrician wasn’t picking the best moment to make a big deal out of it, but he absolutely had a point. In the few years since I attended that conference, I’ve realized that my students – particularly Americans – actually perform better on the quant section of the GMAT when they stop thinking of it as “math” and start thinking of it as “quantitative reasoning.”

Here’s the thing: in the United States, “math” knowledge – at least through the high school level – is typically taught as sequences of mechanical steps that you need to memorize and follow. Throughout much of my public school education, our daily homework would consist of 10 or 20 nearly identical math problems. The problems were usually so similar that there was no reason to think about what any of it meant. If you could follow instructions, you’d get an A – even if you had absolutely zero understanding of the underlying mathematical concepts.

As a result, most Americans think that the word “math” just refers to a boring series of steps that you follow. Sadly, we don’t think of mathematics as a way of thinking, or as a set of useful tools for reasoning our way through useful problems. There are, of course, plenty of exceptions, but the overwhelming majority of Americans have learned math in a way that strips it of its logic, meaning, and intuition.

So it’s no surprise that I hear this over and over from GMAT test-takers, especially Americans: “I’m a really good math student, but I can’t understand why the GMAT is so hard for me!”

Obviously, there are a ton of reasons why somebody might struggle with the GMAT quant section, but plenty of GMAT test-takers make the subtle mistake of trying to learn too many formulas, memorize too many steps, and drill too many mechanical aspects of mathematics. The GMAT, for all of its flaws, brilliantly twists 10th-grade math into a hard-to-penetrate – or at least a hard-to-quickly-penetrate – tangle of logic.

In other words: if you’re trying to blindly apply mechanical techniques to GMAT quant questions above the 500 or 600 level, the exam will eat you for breakfast.

Let’s look at an example (with apologies for the blurry fractions):

Which of the following is greatest?

If you think of this as a mechanical “math question,” you’ll follow some well-worn steps here: find some common denominators, add the fractions, and THEN compare the sums.

Go ahead and try it if you’d like. If you can correctly solve the question that way in two minutes or less, I’ll give you a cookie.

But if you’re thinking of the GMAT as “quantitative reasoning” – with or without the eye-roll – then maybe you’ll try something quicker, smarter, and less arithmetic-intensive. In this case, we’re just looking for the greatest value – and we don’t care what that value actually is, as long as we know that it’s larger than the other four answer choices.

So since the question is just asking for the greatest of the five answer choices, you can just compare pairs of answer choices, and knock off anything that’s the smaller of the two. Let’s start with D and E. It’s easy to see why E is larger than D once you notice that 1 – ½ = ½, so D is gone.

Similarly, B looks a lot like E, except that the denominators in B are squared – and since larger denominators mean that the fractions must be smaller, we can cross off B. The same argument holds for C – it’s clearly smaller than E as well. And then A has smaller denominators than E – so A is your answer.

No computation required, right? If you’re approaching this wisely, you barely need to lift your pen.

So if you’re thinking of the GMAT quant section as a set of narrow mathematical tasks – formulas that need to be memorized, or boring-ass steps that need to be followed – then you’re barking up the wrong tree, at least if you want an elite GMAT quant score. Once you start looking for opportunities to apply flexible logic and identify multiple solution paths, then you’re on the right track.

If any of this strikes a nerve, then it might not be a bad idea to stop yourself whenever you start thinking about the GMAT “math section.” Roll your eyes at yourself if you’d like, but thinking of the GMAT quant section as “quantitative reasoning” might help you embrace the flexibility and logic you’ll need for a top GMAT quant score.

## How lucky was Mr. Fat Pants?

If any of you are expecting a practical, useful article about GMAT tutoring, I apologize in advance:  this is going to be a pretty useless, vaguely technocratic article about standardized testing.  Consider yourself warned.

A couple of years ago, I wrote a blog post about a fellow named Mr. FP (Mr. “Fat Pants”), who once wrote a brilliant MBA application essay about his lunchtime festivities at the office.  Mr. FP deserves to be a legend simply because he actually used the phrase “fat pants” in his MBA admissions essays, but he’s also notorious (in my little GMAT world, anyway) for springing a huge test-day surprise on both himself and his GMAT tutor:  he scored a 680 and then a 640 on his only two full-length GMATPrep practice tests, then nailed a 720 on the actual GMAT—just a few days after the 640.  Mr. FP is a great guy who kicked all sorts of ass at a top-10 business school… but we agree that he got a little bit lucky.

But how lucky did he get?  And can we somehow quantify his luck?

The quick answer is that Mr. FP was pretty darned lucky.  If you dive deep into the bowels of your GMAT score report (sorry for the image; do you really want to dive “deep into the bowels” of anything?), you’ll see some mumbo-jumbo about something called the standard error of measurement, and the score report will tell you that the standard error of measurement is about 30 points on the GMAT.

To understand the idea of a standard error of measurement, imagine for a moment that you have something called a “true” GMAT score.  There are two ways to think about a “true” GMAT score.  First, you could imagine that it’s the score you would receive if the GMAT always did a 100% perfect, 100% consistent job of measuring your verbal and quantitative reasoning skills (or whatever it is that the GMAT actually measures).  If that doesn’t seem intuitive, imagine this:  you’ll take the GMAT, I’ll wipe out your memory of the exam using the “flashy thingy” from the Men in Black movies (so that you don’t remember any of the questions), then I’ll send you back to the very same GMAT test appointment using a time machine from the Back to the Future movies.  I’ll do this an infinite number of times.  Assuming that you don’t get brain damage, your average score on your infinite number of GMAT exams would be your “true score.”

Of course, you wouldn’t always get exactly the same score on every single test appointment, even if we conjure some Hollywood magic to eliminate all day-to-day variations in your test-taking behavior.  The truth is that GMAT scores are a little bit random.  Or maybe a lot random.  Even if you behaved exactly the same way every single time you took the test, you’d still get slightly different GMAT scores from one day to the next.  That’s an inevitable part of standardized testing, especially on an adaptive exam that spits out somewhat randomized questions.

Back to the technical crap:  the standard error of measurement is basically a measure of that random variation in your scores from one GMAT exam to the next, even if we assume that you’re a robotic test-taker who always behaves the same way.  If you’ve taken a few statistics courses, you could think of the standard error of measurement as the rough equivalent of a standard deviation for your GMAT score:  since the GMAT’s standard error of measurement is around 30 points, roughly 2/3 of all test-takers will score within 30 points of their “true” GMAT score, and roughly 95% of test-takers will score within 60 points of their “true” GMAT score.

In other words, your GMAT score could plausibly fluctuate by around 30 points from day to day, but you aren’t terribly likely to gain or lose 60 points simply by random chance.

With this in mind, Mr. FP seemed to be a very lucky man.  We’ll never know Mr. FP’s “true” GMAT score, but based on his homework and GMATPrep test results, I would have wagered that he was in line for a 660 or so—halfway between his two GMATPrep scores.  If we pretend that 660 really was his “true” GMAT score, then Mr. FP scored 60 points—or two standard errors of measurement—above his “true” score.

If you’re a statistics geek, you’re welcome to bust out your favorite z-chart and do the calculations yourself, but the bottom line is that there was roughly a 1 in 40 (2.5%) chance that Mr. FP would receive a random gift of 60 or more points from the GMAT gods.  And keep in mind that any random, luck-based deviation from your “true” GMAT score could work in your favor—but it’s equally likely that it will work against you:  if 1 out of every 40 test-takers will earn at least 60 “measurement error points” that they don’t “deserve”, then 1 out of every 40 test-takers will lose at least 60 points on their GMAT score, just from bad stinking luck.  The gods of random chance are sometimes very kind, but they’re also randomly very cruel.

So if you’re still 60 or so points away from your ideal GMAT score and you want to roll the dice, go for it.  But your odds of a Mr. FP-esque stroke of good luck aren’t all that good, and it’s probably better to hit the GMAT books hard and make your own luck.