Hi sns,
a) Timing each problem is a great first step. You definitely want to get a feel for 2 minutes. The next step is doing problems in timed sets--for instance, 5 problems in 10 minutes. This forces you to budget your time. If you're going to have a colossal timing failure (5 minutes on one problem), you want it to happen now, not on the test. This is also a great way to practice letting the hardest problems go in advance.
b) Long response below . . .
c) It is very useful to recognize problems by specific type, because there is often a specific strategy that fits a specific type. If I lump all rate/work problems together, for instance, I won't be able to respond very quickly to the specifics of the problem. It's much better if I recognize that an average speed problem requires a different approach from a combined work problem. You mentioned stats: that includes simple averages, weighted averages, finding the median, etc. Again, knowing what the challenge is makes it much easier to respond. It's like being a doctor who recognizes a certain set of symptoms and says "Ah, I've seen this before." That doctor is much better equipped to respond than one who simply says "This patient has stomach trouble."
Okay, now for b). There are many things you want to do in your review process that could end up pushing the time per problem to 30 minutes or more. Here's a rough outline:
1. Start by doing a timed set of problems. Answer all problems no matter what. If you guess and move on because a problem looks too hard, note that so you can determine later if the problem was as hard as it looked (and why).
2. DO NOT check the answers. Go back through these problems (now or in your next study session) UNTIMED. Here are a few things to look at:
*What type of problem is this, and how can I tell?
*Are there particular problems or strategies associated with this problem type that I should keep in mind? (For instance, on a problem involving percentages, I always want to ask myself “percent of what?”)
*Do I feel confident about my work on this problem? Why or why not?
*How else might I have approached the problem?
*(Once you’ve examined different approaches): What is the optimal approach to this problem (for me), and how can I tell? Are there cues in the problem that make one approach clearly preferable to another? (For instance, if I see variables in the answer choices, I might want to pick numbers. However, if the relationship between the variables is not very clear, picking numbers might be difficult or impossible to do.)
*Were there tricks or traps in this problem? How did/could I notice and avoid them?
*Did I correctly interpret what the question was asking for? Did I successfully provide that answer at the end? (In other words, if the question asked for x+1 and I gave x, or the question asked me to infer and I tried to strengthen, I need to notice that problem and make plans to avoid it in the future.)
*(For verbal): Why is each answer choice right or wrong? If you were down to two tempting choices, what is the difference between them? If you didn’t like any of the choices, what made the one you chose better (or the least bad)? In RC (or CR conclusion), can you find support for your choice? In SC, can you cite a rule or identify a meaning issue that this choice violates or resolves? In CR assumption-based, does this choice address an assumption or “gap” in the argument?
The point here is to get the most out of every problem. Often, we get a problem right and move on without learning from the experience. If we did the problem well, it’s useful to study why we were successful. If we just got lucky, we need to notice that and figure out how we might perform at this level more consistently. Checking the answers too early prevents a lot of these insights by focusing our attention only on our obvious errors, or on the most difficult problems. This is not a great way to build up a consistent, accurate problem solving method.
3. Check your answers and re-review as needed. Any big surprises? If so, what did you miss in the last stage? Did you misinterpret the question? Did you keep making the same arithmetic error? Is this a content area that you don’t understand well? Try to sort the problem out for yourself before checking the explanation.
4. Check the explanation. If you have access to our
OG Archer, you may want to use those quant explanations in place of the sometimes-laborious explanations in the
OG itself. Compare the explanation to what you’ve discovered. Are there any additional insights? Does it validate your approach or raise more questions? Maybe you like your approach better—that’s fine as long as it works!
5. Take some notes (ideally organized by topic/type.) What trends do you notice within individual topics, or across the test? What makes a problem easier or harder for you? What are some signs that a problem is too difficult? What are you doing when you make a careless error? (Doing too much in your head? Skipping steps? Misreading the prompt?)
6. If you’re studying topic-by-topic, use your notes to develop a plan of attack for each topic you’ve studied. What are my weaknesses? What approaches work best for which subtypes? When do I need to guess and move on? Is there any content for which I need to do further reading or basic skills practice?
Of course, you want to apply this process flexibly, not just go through the motions because some crazy teacher in San Diego said to do this. On some problems, this whole process might not take long at all. For instance, if you’re reviewing Problem Solving #5 from OG13, and you correctly identified which #s to add up, you probably got the right answer very quickly. In reviewing, you’d just ask “Is there a faster way I could have identified those numbers or added them up?” The answer might well be no. If you found this problem easy, the ENTIRE process, from doing the problem through reviewing and checking the explanation, might take less than 2 minutes. If you solved the problem inefficiently, or if you missed it because you got overconfident and rushed, you still might learn a thing or two in that 2 minutes. If you solved the problem correctly and systematically, you might think about how you could have that same experience on a more complicated problem.
In short, doing every problem in the
OG is only helpful if you’re able to get something tangible from each of those problems. You’re not going to see any of them on the real test, but you are going to see problems that have a lot in common with them. If you just have a passing familiarity with each problem, that won’t serve you well. However, if you can say “Hey, this reminds me of a problem I solved this way,” you can use your past experience to respond quickly, effectively, and flexibly to the demands of the test.
I hope this helps. Let me know if you have questions on any part of the process.
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Updated on: 30 Mar 2013, 20:15
I am curious about your statement that each problem review can take upto 20-30 minutes. What exactly are we supposed to review? When I revisit problems that were wrong in the first attempt, it normally doesn't take more than a quick perusal of the solution for me to 'get it'. What is it that I'm doing wrong?
