Choose Your Own GRE Math Adventure
(Vince's 2 main options to help you with your GRE prep are HERE.)
GRE Math Tips and Tricks
hi GRE mathletes,
To be good at GRE math, you've gotta speak the language. In other words, you have to know the concepts the GRE is going to use in its math questions and you have to be fluent in those concepts.
I've got a free guide to learning GRE math concepts here - be sure to check it out, since my new math practice app, GRE Math Knight, is available there!
However, you'll also greatly benefit from having some GRE-specific math strategies to use to make certain types of questions easier to do. Good news - I've made short videos to demonstrate my favorite strategies using official ETS quant questions.
My #1 GRE Math Strategy
First, I want to tell you about my most important math strategy of all. If you remember nothing else for GRE math strategies, remember this:
It's unlikely you'll instantly know what to do when a new GRE question pops up on the screen, so ease into it. Most questions will require multiple steps and a little bit of thinking.
These three tips should help with almost any question:
- Close your eyes long enough to take a deep breath. Do not skip this step!
- Read the question, but then give yourself about 10 seconds to consider your options. Do not skip this step!
- Start working on the question by doing whatever you can first, then pause to reflect, then work on another step, pause again, etc., until you either solve it or become stuck. If you're stuck, guess and move on!
The magic is in the pauses. They'll give you the chance to notice the best way to proceed.
GRE Math Strategy Videos
The point of all this is to:
1. Teach you cues that you can recognize to try certain GRE math techniques that give you alternate ways of solving problems than "the math teacher way".
2. Explain those techniques using real GRE questions.
3. Urge you to focus on one of these strategies at a time, in a series of deliberate practice sessions. By that, I mean to work on a block of 20 questions, UNTIMED, and to find problems on which you can apply the strategy you're focused on.
For example, let's say you're focused on the strategy for simplifying quantitative comparison questions. Look at about 20 quantitative comparison questions, perhaps from the ETS Big Book, and simplify any of the quantities you can. Do not solve any other questions! Just drill that strategy.
(Hat tip to Gregmat for the above idea.)
Below are 12 math scenarios you might encounter on the real GRE. Click each scenario's link to scroll to the strategy description for that scenario. You'll also be able to watch a video of me doing a real GRE question using that strategy.
- It's a Quantitative Comparison with variables.
- It’s a word problem with numerical answers.
- The problem is abstract, with few or no numbers in it.
- There are variables in the answer choices.
- These calculations would literally take 10 minutes to do.
- It’s one of the “pick ALL correct answer choices”.
- You see language like “maximum” or “minimum”, “least”, or “greatest”.
- Crap, I’m not sure if I’m remembering this exponent / root rule correctly.
- Wow, that’s an ugly-looking bunch of numbers.
- I wonder if I can reduce or simplify this Quantitative Comparison…
- These calculations are doable but look time-consuming.
- You have the freedom to choose one of several ways a situation could take place.
- The easiest numbers to test are 0, 1, and 2.
- Insert your number into the quantities for the variable and see which is bigger.
- Now think about how might you make the OTHER quantity bigger with trial #2. Do that trial.
- If you still aren’t sure of the answer, do a third trial (but then analyze the problem to see how it might’ve been possible to figure out with just two trials).
(Testing...1, 2, 3.)
Backsolving can be the easiest way to do a word problem with numerical answer choices!
- Test the middle choice (this may tell you whether to go higher or lower if it’s not the right answer).
- By “test the choice”, I mean answer the question as if that choice is right, and see if all the other numbers in the question remain valid.
- Try testing another choice if the first one didn’t work (see step 1).
(Don't try this at home.)
- Make up a number to replace the variable in the question with.
- Figure out the answer using that number so things seem more concrete.
(Abstract problems can be easier with concrete numbers in them!)
(Another adding numbers example.)
- Invent weird (non-divisible with any number you see in the problem) numbers for the variables in the answer choices.
- Answer the question numerically using your made-up numbers. Ignore phrasing like “in terms of x”.
- Test each answer choice using the numbers you invented. The right answer will be the one that produces the numerical answer you got in step two.
(I bet you can't solve this one algebraically - you gotta use V.I.C.)
- Just start doing the problem. Finding the pattern is much easier by beginning to calculate than by just staring at it.
- Once you see the pattern, it will probably be a shortcut to the right answer.
(Spoiler: the above video is from ETS Powerprep Online Test 1.)
(Another "solve until you see a pattern)
Some “pick ALL correct answers” questions can be easier if you find out the minimum possible number and the maximum possible number - this may allow you to pick those, and every choice between them.
(Solve this "pick ALL that apply" through finding the range.)
If the question says something like “pick ALL correct answers” or you see language like “minimum” or “maximum”, it’s probably more about minimizing and / or maximizing the scenario as opposed to solving.
How big or small can you make the answer?
This is similar to what we do when testing numbers in quantitative comparison questions.
(This house was minimized.)
Don’t remember an exponent or root rule - or maybe some other rule? Solving a simpler version of a problem can confirm whether you’re remembering it correctly.
Ugly problems are often begging to be simplified. Reduce fractions, factor things out, and the problem may become easier.
(Thoreau famously said "Simplify, simplify".)
Some Q.C. questions are much easier to solve if you simplify the quantities.
- Make sure you perform the same operation on each quantity.
- That operation has to be reversable.
- Number testing might be much easier once the quantities are simpler, or the answer might already be apparent!
(Let's work as little as possible, people.)
Stop to think every so often to see if you notice a way to avoid laborious calculations.
(Your brain is a computer.)
The act of trying something may feel directionless and futile at first, but some GRE problems are best solved this way since there isn't a clever way to do them.
(If at first you don't succeed...)