Here’s How to Always Know What to Do on Any GRE Problem
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“When I See This, I Will Do This”: A GRE Study Tool
“I know all of the rules, but I’m nowhere close to my goal score.”
“When I study, I understand everything right away. But when I took the actual GRE, I couldn’t make it happen.”
“I never know what to do when I see a Quant problem for the first time. If somebody tells me how to set the problem up, I can do it perfectly, but I can’t get started on my own.”
“I get overwhelmed by Verbal questions. I’ll think that my answer makes sense, but then I’ll review the problem and realize that there were a dozen different things I didn’t notice.”
If any of those statements ring true for you, you’re not alone. You’ve probably been studying for a while, or you at least have a good grasp on the basic math, logic, and vocabulary. But getting a great GRE score isn’t just about knowing the content. It’s also about always knowing what to do next on any GRE problem. That’s what the “When I see this, I will do this” technique is for.
Before your next review session, create a new spreadsheet, or open your notebook to a fresh page. In the leftmost column, you’ll record clues. In the middle column, you’ll record responses.
Clue: Any feature of a problem that stands out to you. Before your next review session, create a new spreadsheet or open your notebook to a fresh page. In the leftmost column, you’ll record clues. In the middle column, you’ll record responses.
Response: The right thing to do when you notice a particular clue.
For each problem you review, regardless of whether you got it right or wrong, record at least one clue and response. Make your clues general enough that they’ll be useful to you on other problems, but don’t make them too general. The perfect clue is one you’ll always react to in the same way, no matter where you see it. Here are some examples for Quant:
These are useful clues, since they’re neither too specific nor too general. You’ll probably see exponents with non-prime bases in many problems, and you’ll generally react to them in the same way, even though you might never see the specific equation 25x = 5y + 1 again.
Here’s an illustration of how you’d identify useful clues while reviewing a Quant problem. First, do the following problem:
If t is divisible by 12, what is the least possible integer value of a for which t²/2ˆa might not be an integer?
(A) 2
(B) 3
(C) 4
(D) 5
(E) 6
The solution: if t²/2ˆa might not be an integer, then t² might not be divisible by 2ˆa. Since t is divisible by 12, its prime factors include 2, 2, and 3. So, the prime factors of t² include 2, 2, 2, 2, 3, and 3. That makes it divisible by 2ˆ4, but it might not be divisible by 2ˆ5. So the right answer is (D) 5.
That’s a bit of a whirlwind solution, right? And knowing it well, even memorizing it, will do absolutely nothing for you on test day. To improve your understanding of the solution and provide yourself with takeaways for other problems, break it down into clues and responses. At each step of the solution, what was the right thing to do next, and why?
The first step was to recognize the relationship between “t²/2ˆa might not be an integer” and divisibility. That comes up in a lot of problems, because it’s a handy way for the GRE to disguise divisibility problems to make them harder. Here’s how you’d generalize it into a clue and response:
Whenever you see “a/b is an integer”, the right first step is to start thinking about divisibility.
The next step was to determine whether t² was divisible by 2ˆa. The solution jumped immediately to finding the prime factorization of t², but why? Here’s the clue:
Questions about divisibility are actually questions about prime factorization.
There was another trick involved in finding the prime factors of t². You might remember it from earlier in this article!
That’s how you knew that t² contained the prime factors 2, 2, 2, 2, 3, and 3. (You could add another row to your own spreadsheet, to remind yourself that t² might contain other prime factors as well!)
Finally, how did you know that t² was divisible by 24, but not by 25? Another clue:
Since t² can be divided by 2 four times, it must be divisible by 24. You don’t know whether it can be divided by 2 a fifth time, so it might not be divisible by 25. That makes (D) 5 the correct answer.
Now, try using the clues from this problem to solve these micro-problems:
- Is 280³ divisible by 2ˆ12?
- a/20 is an integer, and 20/b is an integer. Is a/b an integer?
- If 3ˆ10/y is an integer, is y/9ˆ8 an integer?
The more clues you add to your own list, the more you’ll notice that GRE problems test the same skills over and over. It’s not possible to see every problem—that’s one good reason not to adopt a ‘quantity over quality’ approach to studying! But it is possible to learn which features are used over and over, and how to react to them. If you feel like you already know the content, but you can’t bring it together, then stop thinking so much about content and start thinking about knowing what to do next. That’s how you take control of the GRE. ?
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Chelsey Cooley
is a Manhattan Prep instructor based in Seattle, Washington. Chelsey always followed her heart when it came to her education. Luckily, her heart led her straight to the perfect background for GMAT and GRE teaching: she has undergraduate degrees in mathematics and history, a master’s degree in linguistics, a 790 on the GMAT, and a perfect 170/170 on the GRE. Check out Chelsey’s upcoming GRE prep offerings here.