Quick GRE Math Tricks
Mastering GRE math means challenging yourself to improve your executive reasoning, on top of re-learning math rules you may not have seen for years. It’s not always an easy process, but there are a few quick math tricks that might earn you some points!
Memorize your squares (and primes, and decimals)
“Why would I memorize the perfect squares if I get to use a calculator on the test?” Because of problems like this one:
If (x – 17)² = 361, which of the following could be the value of x?
(A) -36
(B) -16
(C) -2
(D) 2
(E) 16
This problem isn’t asking you to square a number. If it was, you would just use the calculator. Nonetheless, if you know your perfect squares up to 20², you might see a quick way to solve this one. The not-so-quick way is to FOIL the expression on the left side, subtract 361, then try to figure out some way to solve the quadratic. The quick way? If you know that 361 is 19², take the square root of both sides!
x – 17 = ±19
x = 17 ± 19
x = -2 or 36
The same goes for the prime numbers (up to 50) and the decimal forms of ⅛, ⅙, ⅕, ¼, and ⅓. It isn’t about calculating them, since you’ve got a calculator for that. It’s about recognizing them when they could save you time on a challenging problem.
Check the total
When you do a Data Interpretation problem that divides up a population into groups, always check to see how large the total population is. Here’s an example from the 5lb. Book of GRE Practice Problems:
If you don’t notice the 557 in the title of the graph, you could waste time adding up the households unnecessarily. Look for the total when you first read the graph! On harder problems, missing the total can make you fall for trap answers as well as wasting time.
Put the answer in a box
This GRE math trick requires you to adopt two new habits. First, on every single GRE math problem, read all the way through to the very end before you start solving. In particular, read the part of the problem that tells you what you’re solving for.
A lot of the time, you’ll be solving for something totally ordinary:
What is the value of x?
How many donuts did May purchase?
But sometimes, you’ll be solving for something trickier:
What is the probability that it will rain on Thursday but not on Wednesday?
What fraction of the students who passed the final exam had perfect attendance?
How much greater is the cost of a muffin than the cost of a donut?
Here’s the second new habit: every time the “question” part of a GRE math problem is even a little bit complicated, write down exactly what you’re solving for, and put a box around it, before you start solving. If you can, you might even simplify a bit:
prob(rain Thurs)*(1-prob(rain Weds))
perf. attendance AND passed exam / passed exam
muffin $ – donut $
This serves a few purposes. First, it makes sure you’re reading thoroughly. Second, it can get you unstuck if you’re stuck on a problem: if you aren’t sure what to do next, check what you still need to solve for in order to answer the question. It’s also a useful part of your guessing strategy. If you can’t articulate exactly what you’re solving for, you should probably bail out on the problem and move on to the next one.
Avoid QC calculations
A lot of Quantitative Comparisons GRE problems, like this one, have an easy number as one of the two quantities:
You can solve this problem by calculating the exact value of the other quantity, but the trick here is that you don’t have to. There’s often a way to decide whether the harder quantity is bigger or smaller than the easier one, without calculating its exact value. When you see a problem where just one quantity is a number, take a moment to consider whether you can get away with just comparing.
It’s possible on this problem, by the way! Since there are more juniors than seniors, the average score should be closer to the juniors’ average than the seniors’. Thus, the average is closer to 88 than to 92, which means it must be lower than 90.
Write what you put into the calculator
Once you plug something into your calculator, it’s gone! You can’t look back at it and double-check that you entered all of the numbers right. So, unless you’re entering something exactly as it’s written in the problem (and maybe even then), jot down exactly what you’re going to plug into the calculator before you calculate. Then you can at least double-check your work for mistakes and make changes later on if you need to. This is especially true for Data Interpretation problems, where I like to write down what I’m calculating twice: once in plain English, then once with the numbers I’ll be using.
What next?
If you’re looking for a more methodical approach to studying for the GRE, check out this article on how to study. Want more math tricks? Try “GRE Math for People Who Hate Math,” where we break down some of the more obscure-looking things on the GRE quant section into easier terms. And as you accumulate helpful math tricks, write them down! Add a column to your error log for strategies like these, and review it just before test day to refresh your memory.
Don’t forget that you can attend the first session of any of our online or in-person GRE courses absolutely free. We’re not kidding! Check out our upcoming courses here.
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 170Q/170V on the GRE. Check out Chelsey’s upcoming GRE prep offerings here.