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A number of students have recently told me that they struggle with “problem recognition,” particularly in the Quant section of the GRE. What many mean by this is that when they look at a problem, they don’t immediately see how to get to the solution. They might recognize some of the concepts involved, but the problem as a whole has aspects that make it look unfamiliar and difficult. When this happens on the test, in a high-pressure, time-sensitive environment, the resulting feeling can be paralyzing.
I have a different idea of what “problem recognition” means, though. Here’s the secret: when I see a difficult GRE Quant problem for the first time, I often have the same reaction—I have no idea! I don’t see the whole solution right away. I may not even feel confident I really do know how to solve it. I have to fight the reaction, honed by many years of math-aversion, to panic and give up.
However, having spent a lot of time learning GRE Quant best practices, I’ve trained myself to take a different, more deliberate approach, regardless of my instinctive reaction. First, I remember two things:
- The makers of the GRE design problems that look intimidating. But this doesn’t mean that they’re all terribly difficult. Sometimes the problems that look the messiest end up being relatively straightforward.
- There’s a finite amount of math content on the test. I reassure myself that I know the topic this problem is testing, even if I don’t yet understand how it’s being tested. (And if I see a topic that I’m not familiar with, then I remind myself that skipping a problem or three is often a smart test-day strategy).
Next, I take a deep breath and get started. I pick an entry point and start doing something. Precisely what I do depends on the topic and the format of the problem. For example:
- On a difficult geometry problem, I’d start by drawing or re-drawing and labeling the figure.
- On a difficult divisibility problem, I’d start by making factor trees for the numbers involved.
- On a difficult word problem, I’d start by translating the text into formulas or notes.
Notice that each of these opening tasks is fairly mechanical. I’m doing something that I know how to do, which builds confidence. I’m also doing something that doesn’t take a whole lot of brain power. Instead of banging my conscious mind against the problem, I’m absorbing the information in it and letting my sub-conscious, problem-solving brain get to work.
Solving any difficult problem is a dialogue between conscious, directed work and unconscious processing— think, for example, of people who report having worked on a difficult task unsuccessfully all day only to find the solution to the problem in their dreams. To solve hard problems effectively on the GRE, you want to allow space for this unconscious processing to help you out. This is why starting each problem with a routine task is so useful. It minimizes anxiety, because you’re doing something that’s likely to be helpful while giving your mind room to make intuitive connections.
As for how to know which task to start with, fortunately this is a skill that can be trained. I find the “see this/do this” format really helpful for developing this skill. Here’s how it works.
After I solve a tricky problem, I go back and think about what the ideal approach would have been. What task should I have started with? What clues in the problem point to that task as the right entry point?
Once I’ve answered these questions, I make a flashcard. On the front, I’ll write:
WHEN I SEE A DIFFICULT DIVISIBILITY PROBLEM…
And on the back, I’ll write:
I WILL START BY PRIME FACTORING.
Over time, as you build a stack of these, you’ll find that, in addition to the content on the GRE being finite, there are a limited number of problem “types.” While you’ll probably still see problems that contain unfamiliar or surprising elements, you’ll have a go-to starting place for anything that might come up. This is what problem recognition means to me—not necessarily knowing exactly how to solve every problem, but having a good plan for where to start, and confidence that, if I know my content, this strong start will help me find my way to the right solution. 📝
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Cat Powell is a Manhattan Prep instructor based in New York, NY. She spent her undergraduate years at Harvard studying music and English and is now pursuing an MFA in fiction writing at Columbia University. Her affinity for standardized tests led her to a 169Q/170V score on the GRE. Check out Cat’s upcoming GRE courses here.