The GMAT will never lie to you. But, it doesn’t always tell you what you really want to know. The GMAT 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 GMAT, codebreaking is how you start to understand a Quant problem.
Here’s an example of a problem that’s full of GMAT code:
What is the largest integer n such that 10n is a factor of 40!?
The people who write GMAT 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.
The term ‘factor’ is our first piece of GMAT code. If you’ve been studying for the GMAT for a while, you probably know what the term means: a factor of a number is another number that divides into it evenly. But that sort of definition isn’t quite what I mean when I talk about GMAT code. On the GMAT, when you see the term factor, especially combined with large numbers, that’s actually code for “look at the prime factors.”
Or, as a flashcard:
We have a little more decoding to do before we can rewrite this problem in plain English. That largest integer n thing is making the problem complicated. What does it mean? It’s code.
When you raise 10 to the nth power—or when you raise any number to the nth power—what happens to its prime factors is predictable. The prime factors of 10¹, or 10, are 2 and 5. The prime factors of 10², or 100, are 2, 5, 2, and 5. The prime factors of 10³ are 2, 5, 2, 5, 2, and 5. In other words, n is code for the number of twos and fives you have!
Combine those two pieces of GMAT code. If you want to find the largest integer that n could possibly be, then you want to find the largest number of twos and fives that could be prime factors of 40!. So, we need to take a look at the prime factors of 40!. Let’s break that down with another code flashcard.
To find the number of twos and fives in the prime factorization of 40!, work your way through the list of numbers from 1 to 40. The number 5 has a five in its prime factorization; so do 10, 15, and 20. Since 25 = 5×5, there are actually two more fives there. 30, 35, and 40 have one more five apiece. In total, there are 9 fives.
We don’t actually have to count the number of twos! That should save some time. There are definitely more than 9 twos; since we need the same number of twos and fives in order to make powers of ten, the limited number of fives will be the bottleneck.
Let’s see how we translated the entire problem, from GMAT code into plain English. If you don’t have a flashcard that looks like this yet, make one!
The version on the back of the flashcard looks much simpler—because it is. By translating GMAT code into simple terms, we’ve turned a seemingly complex Number Properties problem into a Counting problem.
Let’s practice some codebreaking and get a few more flashcards made. Here are some snippets of “GMAT 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 170/170 on the GRE. Check out Chelsey’s upcoming GMAT prep offerings here.