GMAT Tip of the Week: Three Essential Steps To Learning From Mistakes

“You can learn a lot more from a few seconds of pain than from a few hours of glory.”

We all want to breeze through our GMAT homework getting every question right in under two minutes, but absolutely no one does that. And if you’re in a GMAT class, do you really want to get every answer right the first time? Sure, that might mean that “you’re great”, but in reality what it probably means is that the class is going through problems that are too easy. The beauty of mistakes – and the reason that Veritas Prep classes emphasize “Learning by Doing” with challenge-level problems throughout – is that they’re the best learning opportunities out there. Every time you make a mistake, you’re adding another lesson to the pile and finding a new hole to plug. Every mistake you make in practice is a chance to make sure you learn to avoid that mistake for when it really matters.

But mistakes should sting – your goal is perfection even while your reality is flawed. So the lesson here isn’t “everyone makes mistakes” but instead “everyone makes mistakes, but those who learn from them are the ones who become great”. And the more pertinent GMAT lesson is that there are three essential steps you should take every time you miss a GMAT question:

1) Understand why your wrong answer was wrong.

2) Understand why the right answer was right.

3) Understand why your wrong answer was tempting.

And note – if you happened to guess correctly after narrowing it down to two answer choices, you should still go through these steps.

Let’s take a look at a Data Sufficiency problem from the Veritas Prep Question Bank as an example of using this strategy:

What is the area of right triangle XYZ?

(1) Side YZ is 9 inches long.

(2) Side XZ is 15 inches long.

Here’s the thought process that about 50% of all test-takers use to answer this question:

“I memorized that a common side ratio for right triangles is 3-4-5, and since 9 is (3)(3) and 15 is (3)(5), the middle side should then be 3(4) so 12. And that lets me find the area since 9 and 12 are the sides next to the right angle, so it’s (1/2)(9)(12). C is the answer!”

And those students – take a look at the graphic here to see the official stats – are wrong:

So let’s run though the steps to make sure we learn from the problem:

1) Why was our wrong answer wrong?

The question never specified that 15 was the hypotenuse, the longest side of the triangle. And if it isn’t – if 9 and 15 are the short sides, sides a and b in the Pythagorean Theorem – then the long side can be found using (9)^2 + (15)^2 = c^2, and the area is instead (1/2)(9)(15). And more specifically, our wrong answer was wrong because we assumed something that wasn’t explicit in the problem.

2) Why was the right answer right?

The right answer is E, and it’s right because it takes into account multiple variations of triangle XYZ. XYZ has three sides: 9, 15, and one other side, XY. And since XY is a variable, you have to consider three places it could land with regard to 9 and 15: it could be the smallest of the three, the middle side, or the longest. Now, because it’s a right triangle you have a quick test with the Pythagorean Theorem, and since a and b perform the same function in that formula you can test for “shortest” and “middle” side at the same time (and realize that if it’s (XY)^2 + 9^2 = 15^2, XY has to be 12, so it can’t be the shortest). But XY *can* be either the middle or the long side, allowing for two different triangles with two different areas. By playing *all* the possibilities by “Playing Devil’s Advocate” (could this triangle look any different from the original way I drew it up?), you can avoid the trap.

3) Why was our wrong answer tempting?

This is the most important of the three questions and the one people do the least. If you wrote this one off as “I need to study geometry more”, you missed the point entirely. Our wrong answer was tempting precisely because it rewarded our understanding of geometry – it let us use the 3-4-5 rule; it satisfied our intellect and released some dopamine by letting us think “nailed it: 3-4-5!”. Our answer was tempting because you do have to know a thing or two about triangles to see that 3-4-5 (POTENTIAL) relationship.

In terms of the Veritas Prep “Think Like the Testmaker” approach, consider how the author of the question created the trap answer. He recognized that you’re likely in a hurry to use the information you memorized; he set up a question that would seem to reward you for using it; and he banked on the fact that once your mind had been satisfied that you “got it” you’d immediately call off the search for other answers. C is tempting because it shows you a reward for having studied – it sells you one possibility and in doing so encourages you to stop thinking of other possibilities. What you can learn from that is “if an answer seems too obvious or tempting in the first 45 seconds, I should play devil’s advocate for another 20-30 seconds to make sure I’m not getting trapped – are there any other possibilities other than a 3-4-5 triangle here?”.

As you should see, finding out why the trap answer was tempting is a crucial part to learning from your mistakes. On a standardized test like the GMAT, the mistakes are fairly standardized too – as you can see from the graph, there’s one trap answer that gets half the test-takers. This is true of most GMAT questions – 2-3 choices are there just to let you “feel smart” when you eliminate them and go for the trap. When you make mistakes, learn from them. You can learn a lot more from a few seconds of pain than from a few hours of glory – embrace your mistakes in practice and you won’t make nearly as many on test day.

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