GMAT Math's Favorite Numbers
October 03, 2006
Believe it or not, some numbers show up on the GMAT Quantitative section a lot more than others. I'm not just talking about little numbers that the test can't avoid, like 2, 3, and 5. Consider the following:
- Many GMAT questions deal with number properties, such as factors and multiples.
- Most GMAT word problems "work out": after doing the algebra, the answer will be a round number, not 17.832.
- Most numbers in algebra and number properties questions are small–usually less than 100, almost always less than 250.
- The GMAT actively tests concepts such as exponents and square roots.
- As questions get harder, the GMAT likes to mix all of these things together, testing multiple concepts in one question.
Because the numbers are often small, that limits the possibilities. Because the test focuses on factors, multiples, and exponents, it needs numbers that have lots of factors, including occasional squares. And because problems usually result in round numbers, they need numbers that can be reached in a number of ways, whether by adding or subtracting other round numbers, or some other method.
Really, it doesn't matter very much to you why the GMAT relies so much on a handful of numbers. I'm sure you're wondering what they are, and how you can use your knowledge of them to your advantage. Well, here you go:
- Squares, especially of non-primes. The key numbers here are 16, 36, 64, and 81.
- Multiples of 12: 12, 24, 36, 48, 60, 72, 84, and 96.
- Numbers under 100 with several prime factors: 30, 42, 60, 78 (occasionally), and 84.
The most important thing you can do is learn to recognize these numbers as fitting into these categories. If you see 84, know that it has 2, 3, and 7 as factors–it's not just some random integer in the 80s. If you see 96, know it's 8*12–again, not some number the GMAT randomly tossed out there.
Beyond that, become familiar with the various ways expressions can result in these numbers. Of course you know that 16 = 4^2 and 48 = 12*4, but do you know the following?
- 64 is the only number (besides 1) under 100 that is the square of an integer and the cube of an integer.
- 16 and 81 are the only numbers (again, besides 1) that are both the square of an integer and the square of a square.
- 30 and 42 are the smallest integers with at least three prime factors.
- The only integers with exactly three factors are the squares of prime numbers.
Those factoids will come in handy again and again, as will recognizing each of the numbers as members of the groups I've listed them as. If nothing else, seeeing these numbers and realizing that they are notable in some way may give you an idea of how to do a question, or a notion of what the test is after, that you wouldn't have otherwise.
Best of all, knowing these frequently-tested concepts will save you valuable time on the test, and help you avoid the careless mistakes that result when you rush through a simple division problem or a factorization. There isn't a lot to memorize here, but all of it will reap benefits come test day.
About the author: Jeff Sackmann is a GMAT tutor based in New York City. He has created many resources for GMAT preparation, including the popular Total GMAT Math and Total GMAT Verbal, as well as 1,800 practice GMAT math questions.