The GRE will never lie to you—but it doesn’t always tell you what you really want to know. The GRE is a little bit like my friend in this exchange:
Me: “What do you think of this outfit?”
My friend: “Well, it’s very… creative.”
Sure, it’s not like she lied (zebra-striped leggings are pretty creative). But she also didn’t come right out and call me a fashion victim. In order to work that out, I had to crack the code.
You already know how to “crack the code” in English. Codebreaking is how we figure out what people really mean, even though we exaggerate, simplify, avoid touchy topics, and change the subject. And on the test, codebreaking is how you start to understand a GRE Math problem.
Here’s an example of a GRE Math problem that’s full of code:
What is the largest integer n such that 5n is a factor of 10!?
This problem looks fairly intimidating, but if it just said what it meant in plain English, it’d be a lot easier. The people who write GRE Math problems want to intimidate you a little, if they can—that way, they can reward people who calm down, take a deep breath, and focus on what the problem really means. Let’s do exactly that right now.
10! is pronounced as “10 factorial,” and it’s code for a very large number: the number you’d get by multiplying 10, times 9, times 8, times 7, and all the way down to 1.
If something is a factor of 10!, you can divide 10! evenly by that number. For instance, 2 is a factor of 10!. So is 20.
We really want to know whether 5n divides evenly into this large number. 5n is code too. An exponent just refers to a number such as 5, 5×5, 5x5x5, 5x5x5x5, or any number of 5s multiplied together. Since the problem asks about the largest integer n, you’re looking for the largest number of 5s that you can possibly divide evenly into 10!.
So, here’s what the problem says now:
10x9x8x7x6x5x4x3x2x1 can be evenly divided by 5x5x…x5. What is the largest number of 5s that can be evenly divided into the larger number?
“Divisible” or “evenly divided” is code as well. If you want to know if one number is divisible by another number, here’s a great way to do it. Write a fraction, with the bigger number on the top and the smaller number on the bottom. Start simplifying that fraction, a little bit at a time. If you can cross off the entire bottom of the fraction, you know the number is divisible. If you can’t, it isn’t divisible.
If we were solving this problem, we’d write our fraction like this:
How many 5s can be crossed off on the bottom? As many 5s as there are on the top. Notice that 10 can be rewritten as 5 times 2.
So, there are exactly two 5s on the top of the fraction. The answer to the problem is 2: 10! is divisible by 5².
Here’s what the GRE Math problem really said, ignoring all of the code:
In total, how many 5s can be divided out of the numbers 10, 9, 8, 7, 6, 5, 4, 3, 2, and 1?
You aren’t supposed to go through all of that codebreaking on GRE test day. There just isn’t time. If you see a GRE Math problem that has code you don’t know how to translate, consider guessing and moving on. But, here’s why codebreaking is still important: if you do it ahead of time, you’ll recognize the code quickly when you see it on the test.
If anything about the problem we just did was surprising or challenging for you, take a moment to make some flashcards. On the front of the flashcard, write a piece of code you could see in a problem. On the back, write out what it really means. Here are the flashcards that I’d make for this GRE Math problem:
Let’s practice some codebreaking and get a few more flashcards made. Here are some snippets of “GRE code.” Take your time and work out what they’re really saying, in plain English. Then, make a flashcard or two for each one.
- xy ≠ 0
- x is divisible by 6, but not by 12
- x² + 1 is odd
- p has exactly two factors
- p has an odd number of factors
- a²/b < 0
Try it out, and let us know what you think in the comments!
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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 170Q/170V on the GRE. Check out Chelsey’s upcoming GRE prep offerings here.
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