Sucking All the Juice Out of GMAT Quant Problems
Remember how you’d finish off a Capri Sun pouch by twisting it up, trying to get out every precious drop of those 6 ounces of happiness? Capri Sun always left you wanting more… something never said about a Judd Apatow movie.
Let’s do the same thing with OG GMAT Quant problems. In order to extract all the potential value from doing an OG problem, you’re going to need to deeply review it, and then (in the vast majority of cases), you’re going to need to redo it once or twice a later date. Why?
The learning process usually flows in this 4-stage continuum:
Exposure → Partial Ability → Effortful Competence and Functional Understanding → Effortless Competence and Total Understanding
Stage 1: We feel clueless and don’t know what to do or think.
Stage 2: We recognize some aspects or know some related moves/properties/formulas, but can’t seem to solve this one.
Stage 3: We solved this one, but we did so with low confidence or only after taking well over 2 minutes.
Stage 4: Let’s discuss.
Effortless Competence refers to the calmness and confidence you feel within 30 seconds of reading the problem: you understand what sort of problem this is and have in mind at least one plan for how you could attack it. You can execute the mechanical steps quickly and easily.
Total Understanding means that you recognize any traps the test writers had in mind. You can connect this problem to some other problem you’ve done. You could write your own version of this problem, in which the details could all be changed but the concept being tested would be the same.
GMAT Quant problems vary a great deal in terms of what content knowledge is needed to get the correct answer on that problem, but you can usually harvest all the available GMAT skill points available in a problem by running down this checklist:
The Recipe for Mastery
- I know how to simplify / re-frame the question being asked (if possible).
- I know any underlying formulas/properties being tested.
- I am aware of all constraints in the problem and know what inferences (if any) could be drawn from them.
- I can make any applicable GMAT vocab translations.
- I know what clues signify the Topic, and what my First Move / First Thought (if any) is for that Topic.
- I can execute the arithmetic involved swiftly, accurately, and easily.
- I can recognize any answer choices that would be savvy to eliminate if I’m guessing.
- I can recognize the potential thinking traps or mechanical missteps involved in this problem.
- For Problem Solving, I can recognize multiple ways of doing this problem (if they exist).
- For Data Sufficiency, I can recognize any easy eliminations we get.
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Every time we review a GMAT Quant problem, we want to do an inventory of all its stats. Pick your metaphor:
If you’re an outdoor kid, think of each problem as a baseball card or basketball card. You gotta break down where that problem went to school, how tall/heavy that problem is, what season of its career that problem is in, and, of course, what that problem’s slugging average was last year.
If you’re an indoor kid, think of each problem as a Magic: the Gathering or Pokemon card. You gotta break down that problem’s hit strength, defense rating, available potions, and special spells.
If you’re a fashionista, think of each problem as an outfit in an editorial shoot. Who designed that problem’s jumpsuit? What ankle-length boots is that problem wearing? How much does that problem’s handbag cost?! Who can afford that? Who are these problems that are wearing $5000 outfits?! Sorry, I… I lost myself there for a second.
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Wanna hear another cool learning science term? T h e f l u e n c y i l l u s i o n. This refers to the idea that in the moment of learning how to do something, we understand how to do it. This gives us the illusion of being fluent at the task.
Imagine you’re a teenage driver with his first flat tire. You watch your mom or the driver from AAA replace your tire and feel like now you understand how to replace a flat. Maybe in the case of your parent, it’s even you who replaces the tire, with your parent’s instructions. You feel pretty good about yourself. You think, So what if you can’t grow facial hair yet, Patrick—I mean, Hypothetical Character. You just changed a tire. ADULT looks good on you, sir!
Now for the thought experiment: let’s say your next flat tire doesn’t come until two years later. You’ve seen it done once before. Are you going to be able to remember how to fix the flat?
Probably not! You thought you knew how to fix it, but that was the fluency illusion. In reality, you have Partial Access (stage 2). You’re definitely better than clueless, but you can’t quite get the job done on your own.
So what if the flat tire had only been one year later? Still pretty doubtful for me that I’d recall it. One day later? Sure. One week later? Sure. One month later? Yeahhhh?
Our goal is to schedule ourselves redo appointments around the fringe of when we think we’d probably start to forget something we’ve learned. The most efficient way to build strong retrieval strength for a memory is to ‘wake it up’ right when it’s getting close to having decayed so much that it’s hard to access anymore.
If I had that 2nd flat tire about two months after I had changed my first flat, I would probably still possess enough memory of the first exposure that if I really struggled I could remember all the things I was supposed to do (stage 3).
When we connect back to the past like that (like closing the loop in the movie Looper, but not involving self-murder), we basically create a long-term, rather than a short-term, memory. Having that 2nd flat tire a couple months after the first one would probably allow me to remember how to change a flat for the next five years.
So what is the decay-rate we expect of GMAT Quant problems? How long should we wait to schedule our redo appointments?
If the problem was at stage 1, you could do it 2-4 days later.
If the problem was at stage 2, you could try it 5-7 days later.
If the problem was at stage 3, you could try it 15-20 days later.
How are you going to remember to perform all these erratically-timed redo problems?
YOU’RE GOING TO START A REDO CALENDAR, and it’s going to be the most important habit you have in your GMAT practice. As you’re reviewing GMAT Quant problems, you should always have this calendar handy. Evaluate for yourself what stage of learning you feel like you’re at for this problem, and set an appropriate redo appointment on your calendar.
A redo appointment just looks like this: PS147
If I put PS147 on my calendar for May 25th (and a 2nd redo 15-20 days later on June 12th), then when those dates roll around and I look at my calendar for the day, I know that Problem Solving #147 is one of the problems I’m scheduled to redo that day.
The Redo Calendar is for revisiting the holistic experience of doing that problem. However, there is a much more obvious and famous tool for drilling down on the discrete bytes of content from each problem: FLASHCARDS.
The first five ingredients in the Recipe for Mastery were all about the Recognition stage. If we try a problem and find that we were lacking on any of those first five questions, then we need to make a flashcard (hard copy or virtual one on our phone/computer).
The sixth ingredient was about mechanical mastery of arithmetic / algebra / breaking down to primes / performing exponent rules / etc. Some of those moves are definitely flashcard-friendly, but often having a deficiency here means less about memorizing one specific move and more about assigning ourselves some foundational “rinse and repeat” practice on whatever topic / operation we were struggling through. The Foundations of Math question banks in the Manhattan Prep Student Center (click on the circled “?” icon, if you have Atlas access) are a great source of 10Q drill sets on a variety of mundane but important topics.
The last four ingredients were more about our overall savvy when it comes to GMAT Quant problems. To drill down on these big-picture awareness skills, put down your pencil. Take about 15-30 minutes and flip through PS and DS problems, focusing only on questions like these:
Problem Solving:
– Could I Make Up My Own Numbers on this problem?
– Could I Work Backwards from the numbers in the answer choices?
– Are the Answers Spread Apart so much that estimation would be good enough?
– Are any answer choices just repeating a number in the problem or showing me one-move mental math using numbers in the problem? (These are good answers to avoid when guessing.)
Data Sufficiency:
– Does it seem like there is some rephrasing / simplifying / or other upfront organizing we would do with this problem, or would we just dive into the statements?
– Does either statement on its own seem obviously insufficient?
– Is this a C trap? Is it too obvious that if we had both statements, we would have enough info?
In conclusion, your goal is to harvest all the available value from every OG Quant problem you try. So make sure you’re performing these steps:
- Assessing which stage of the learning continuum this problem currently is for you
- Asking the 10 Questions about each problem you try (many will not be applicable, that’s fine)
- Creating flashcard quizzes to circle back on any of the missing observations/translations you had when you tried the problem
- Setting one or two redo appointments at appropriate intervals so that you will remember to circle back to this problem when you’re “due” to start forgetting it
In Part 2 of this article (coming next month), we’ll take a handful of OG GMAT Quant problems and subject them to the 10 Questions together. ?
Want some more GMAT tips from Patrick? Attend the first session of one of his upcoming GMAT courses absolutely free, no strings attached. Seriously.
Patrick Tyrrell is a Manhattan Prep instructor based in Los Angeles, California. He has a B.A. in philosophy, a 780 on the GMAT, and relentless enthusiasm for his work. In addition to teaching test prep since 2006, he’s also an avid songwriter/musician. Check out Patrick’s upcoming GMAT courses here!