The Mistake High GMAT Scorers Make

by Brian Galvin on

In the recent, revered book Thinking Fast & Slow, Princeton professor and Nobel laureate Daniel Kahneman fits the “Law of Least Effort” to intellectual tasks (such as, say, the GMAT).  As the notion goes, our minds – like nearly all living things – want to accomplish the most with the least amount of effort expended, and so we are often fooled into faulty conclusions or decisions once our minds have been satisfied by just enough information to let down their guard.  The reason isn’t necessarily that we’re lazy, but in a way because we’re efficient.  We’ve trained ourselves to note the effect that tends to come from each series of causes, so that when the scary music begins in a movie we know to expect the appearance of the villain, and when the customer starts nodding and agreeing we know to ask for the sale.

This efficiency is most pronounced in the highest-levels of thinkers.  Have you ever watched your math teacher skip the last two steps and just do them in her head?  Or your friend in finance react to a seemingly unimportant piece of news by predicting a rise or drop in an entire industry’s stock prices as a result?  In many ways, the “smarter” an individual is, the more their mind succumbs to the Law of Least Effort.  And this is one of the things that can doom an otherwise-high GMAT score.

Why?  The most academically successful among us have learned over time when we can stop thinking.  We know that hard questions usually have a “catch”, and that once we’ve caught it we can turn our minds back to autopilot.  We know to look for a trap answer, and once we’ve found it we’re ready to play it straight again.

The only problem is that the GMAT knows that about us, too. And so many of its hardest problems are designed precisely to exploit this tendency.  Sentence Correction questions, for example, often bait examinees into trying to remember the obscurest of rules by offering a choice between five idiomatic phrases, each within the first few words of an answer choice…but in doing so they distract your mind from the much more basic decision toward the end of each choice.  Because you’re looking for “difficulty”, the test shows it to you as a way to throw you off the scent of simplicity.

Perhaps the most common usage of this “Law of Least Effort” trap comes in the form of what we at Veritas Prep call the Shrumbuster in honor of arguably our smartest employee, Scott Shrum.  A Shrumbuster has two distinct features:

1)     It involves one difficult step or identification that satisfies the intellect of the highest-performing test-takers.

2)     Its trap is one so basic that that high-achiever, having already been satisfied by something “difficult”, falls right into it without noticing.

Consider this example:

The product of consecutive integers j, k, m, and n is 5040.  What is the value of j?

(1)   j is prime

(2)   j < k < m < n

Now, the math behind this one isn’t terribly easy, but elite test takers should arrive at the fact that 7, 8, 9, and 10 multiply together to form 5040.  To get there you typically need to employ a few divisibility shortcuts – that it ends in 0 means it’s divisible by 10, and that its digits sum to 9 means it’s divisible by 9. So with all that in mind you can find that its factors include 7, 8, 9 and 10, and that you can’t increase any of those numbers without decreasing another.  So most high performers will see that statement 1 guarantees that j = 7, the only prime number in that set.

That’s the “Shrum” part of the Shrumbuster…but here comes the “buster”.  For statement 2, most are still only thinking about 7, 8, 9, and 10, so they will think “j is the smallest, so it must be 7”.  But wait – one of the most common of all Data Sufficiency warnings is “don’t forget about negative numbers”.  And these four consecutive integers could also be -7, -8, -9, and -10…in which case j would be -10, the smallest of that set.  Statement 2 is actually not sufficient, and the reason behind that is “page one” stuff.  But the Shrumbuster element comes from the Law of Least Effort – by the time you have to make that decision about “are they trapping me into only thinking about positive numbers”, your intellect has already been satisfied so most test-takers are apt to relax.

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  • Frederick Alfredo

    psh. -10 is not prime

  • http://chronicphilomathy.blogspot.com Neil

    Frederick:

    That’s right. BUT when we’re just evaluating condition two alone, we don’t yet have the information that j is prime. It’s only when we go to the “evaluate all information together” condition (answer choice “C” in written books) that we ‘learn’ that fact and can accurately discard -10 as a possible alternate solution.

  • jd

    J need not be prime. its condition of statement 1 and not of question.

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