“Just tell us the answer!” a student demanded of me in a recent class. She wasn’t rude, but she definitely wasn’t happy. And I understand—I wasn’t being an easy teacher. I try not to be. I don’t want to be an explanation parrot, because my explanations don’t really transform into my students’ learning. Learning is harder than that. It requires active thought and wrestling with difficult concepts. So even when my students give a right answer, I ask them the often-feared question, “Why do you think that?”
This is a teaching tactic called the “Socratic Method,” named after the infamous inquisitive nuisance, Socrates. Socrates asked ‘Why do you think that?’ so often that his fellow countrymen finally just put him to death to shut him up. Fortunately, I don’t think my students keep hemlock handy.
But many of Socrates’ teachings come with some great advice for GMAT test takers. The one I’d like to talk about today is a famous paradox. When someone asked an oracle who the wisest man in Athens was, she responded “Socrates.” Socrates himself made such claims, and often, but when asked why it was so, he replied, “I know that I know nothing.”
Elsewhere in the world, a similar phrase is attributed to Buddha: “The fool who knows he is a fool is that much wiser. The fool who thinks he is wise is a fool indeed.”
When such a similar thought crops up in both Western and Eastern philosophies, it’s probably worth paying attention to.
Socrates was being, in many ways, humble. He was arrogant about his humility, yes, which is a lovely contradiction, but he made his point: I’m not smart because I think I’m smart. I’m smart because I know how dumb I am.
This is GMAT wisdom, in multiple ways.
We’ve spoken before about how you need to admit when you’re not going to know how to answer a question and need to move on. We’ve also pointed out how this is a feature of the test—practically everyone misses many, many questions, even very high scorers. But those very high scorers virtually always guessed on questions they realized weren’t going well—they acknowledged what they did not know. You cannot be too proud on the GMAT. You have to be comfortable missing questions, and you have to admit to yourself that you don’t know everything, and be proud of that self-realization.
But there’s another way that humble thinking can be useful.
The other day I was working with a student on a 600-level GMAT word problem. It was something similar to this:
“A toy maker is filling 9 bags with marbles. 8 of the bags hold the same number of marbles, the other holds two times that amount. In each of the first 8 bags, he makes 1/4 of the marbles red, and in the final bag he puts in X times as many red marbles as he put in each of the other bags. If 3/8 of the total marbles are red, what is X?”
It wasn’t terribly easy, but it wasn’t terribly hard, either—at least conceptually. Conceptually, this is just fractions of totals and, basically, reading comp.
He missed the question, and I asked him, “What do you think makes this problem difficult?” He thought for a moment and said, “The setup.”
“Why?” I asked, predictably.
“It’s complicated. There are bunch of moving parts, we have fractions of different totals, we’re multiplying a bunch of numbers by different things, it’s just complicated and easy to mix up.”
“So what do you think went wrong for you?”
“Probably the setup.”
I pointed out to him that he was 2/3 ‘done’ with the problem before I had even finished the setup. Why? Because I knew the setup was a nightmare. It was subtle and required pinpoint accuracy. So I told him something I don’t think he expected to hear: “Don’t be so arrogant.”
I got the problem right and he didn’t, not because I’m smarter than him. I got it right because I knew how likely I was to mess up that setup if I wasn’t incredibly careful. He had no such self-doubt. He knew the problem looked tough, but flew through the setup anyway. And though he was 2/3 ‘done’ before I’d felt convinced I had set up the problem correctly, I was able to work quickly through the rest of my work, and his last ‘third’ was a nightmare, because it was wrong. His answer was hard to come by (because the numbers didn’t work out, because they’d been set up incorrectly), and when he finally got an answer, it wasn’t one of the choices, so he had to start looking back, scanning for a mistake, reworking arithmetic, rereading the problem… He was dead in the water.
(Here’s a tip: you don’t move fast by “moving fast.” You move fast by moving carefully and correctly, in discrete, understandable steps).
The same student also missed another question that looked something like:
10 – [ -8 + 5*3 – 2(3-4) -1] = ?
Again, I got it right. Is it because I know what 5*3 is better than that student? I might be somewhat faster at arithmetic, due to how often my job requires it, but there’s no difficult calculation to be found there. It’s just care. I told myself, “Okay, be really, really specific about the order of operations here, and keep good organization, or I’ll mess things up.” He told himself, “This is just arithmetic, I got this.”
Take one statement of a DS problem:
If all angles are right angles, what is the perimeter of the polygon above?
1) x = 12, y = 6
Pretty much everyone’s instinct is the same on this statement. “Well, that’s not sufficient. I don’t know anything about the measurements of the corner that’s cut out.” What would a more humble test taker do, though? They would probably say, “But let me just check for anything funny.” Try that. How might you check?
Maybe you’d assign some variables for the other sides. You might realize you could label those opposite side y as “a” and “6-a,” and across from side x as “b” and “12-b.” And then you might add all the sides together and realize that the ‘a’ and ‘b’ cancel out, and you have a perimeter of 36. What?! Weird. It definitely felt not sufficient, but I guess… Ah, I see! I always go 12 ‘over,’ and I always go 6 ‘up,’ even if it’s in ‘pieces,’ so the perimeter is always 36. But if you go by what seems obvious at first, without any self-doubt, you’d never make this realization.
Good test takers know how fallible they are. They know where the difficulties in a problem lie. They know that the test makes things that ‘seem’ or ‘feel’ a certain way but that still need to be investigated. They are, in the end, humble—they know they mess up.
They don’t do work in their heads because they know how hard it is to remember something you’ve just done and try to take the next step forward, they don’t jump to conclusions because they know their conclusions are often wrong, they don’t presume they can just handle a difficult thing because they’re good at the test. I’ve said something like “-10 > -9” or messed up math like “(-3) – 7 = ?” so many times in my life, I’ve finally started to tell myself, “You’ll mess this up if you’re not careful, so be careful” whenever negatives crop into a problem. And I am. I take a few extra seconds to make sure I don’t mess it up.
Start taking pride in a healthy chunk of self-doubt as you work on the GMAT. Admit you don’t know what you don’t know, admit that difficult things are difficult and might require specific care, admit that you’re not good at the test and you might find yourself getting better at it. It’s a bizarre paradox, but the recognition of fallibility will make you less fallible.
And then we can all drink the hemlock together and become one with everything, finding the self-aware ignorance of nirvana. 📝
Want some more GMAT tips from Reed? Attend the first session of one of his upcoming GMAT courses absolutely free, no strings attached. Seriously.
Reed Arnold is a Manhattan Prep instructor based in New York, NY. He has a B.A. in economics, philosophy, and mathematics and an M.S. in commerce, both from the University of Virginia. He enjoys writing, acting, Chipotle burritos, and teaching the GMAT. Check out Reed’s upcoming GMAT courses here.