Number Properties in GMATPrep
What are number properties? This concept covers things that we often call basic topics that we learned in middle school (or earlier): divisibility, factors and multiples, odds and evens, positives and negatives, and so on. Its also true, though, that this material can become quite complex. For example, fundamental counting principles are included in number properties, and the more complex problems of this type are something called Combinatorics which most of us hate. :) In addition, we've all come up against very challenging problems testing a supposedly "simple" concept, such as divisibility.
We face two big challenges in dealing with number properties:
(1) On the one hand, we think of most number properties concepts as basic concepts, things that we learned before we ever learned the more advanced algebra and geometry. The test writers purposely find ways to test the truly basic material in disguised ways this is how they make the material harder.
(2) On the other hand, number properties concepts can be quite complex and we may not have learned all of the more complex material in school because most of us learned number properties at a younger age / lower school level.
I talk to students all the time who struggle with Number Properties, in particular with topics centered around divisibility and prime numbers, two commonly tested topics on the test. Students also struggle with recognizing that a problem is about number properties, because the test writers have been able to disguise what the problem is really testing.
So Ive pulled together links to a bunch of number properties articles that Ive written in the past, with a little commentary on what you can learn from the different articles. Enjoy!
Start with this article, Disguising and Decoding Quant Problems. We talk about how the test writers disguise material that you probably do already know, and how we can learn to decode the problem or strip away the camouflage.
As you study, keep an eye out for problems on which, at some point, you think to yourself, Oh, thats what this problem is about? I didnt see that coming! (Note: this could happen in any content area, but it tends to happen quite a bit with harder number properties questions.) When that happens, ask yourself: Okay, so whats the code here? What was the clue (or clues) in the original problem that could have tipped me off as to the disguise?
Then pull out a blank flash card and write When I see <fill in the blank with the clue> on one side and Ill think / do <fill in the blank with the action to take> on the other. When I see clue ABC, Ill know that this is really telling me XYZ in disguise, and then Ill take the necessary steps to answer. One more tip: for the clue, also think about alternate wording. How else could they give me this same clue? On a future question, I might see different specific words that ultimately mean the same thing.
You may also want to read this article about Translating Words Into Math. Its a two-part article and the second part, in particular, talks about how the test-writers disguise things. (To read the second part, scroll down to the bottom of the first part, linked above, and click on the link to read the second half!)
Our first article above started us off with the concepts of divisibility and primes, so lets continue down that path. In Patterns in Divisibility, we examine two GMATPrep problems that share some interesting characteristics. In this article, we discuss some interesting topics related to prime numbers.
Many questions address basic characteristics of numbers, such as whether theyre positive or negative, odd or even, integer or fraction / decimal. These can be disguised in various ways; two of the most common are inequalities and absolute values (which we normally associate more with algebra).
Here are two that use inequalities as a disguise, one article from 2010 and another from earlier this year, as well as a third one that plays around with absolute value. All three of these are generally hiding issues that deal with positive and negative properties of numbers.
And finally here are two more: a Number Line problem and one dealing with Consecutive Integers. The former tests positive and negative properties, as well as some others, and the latter covers a less-commonly-tested but still important number properties category.
The above articles are not a comprehensive treatment of number properties principles and theory if you are using our Number Properties book, I recommend that you work through all of the general chapters first before you start to use the above. The above articles all touch on ways in which the GMAT can disguise questions, making it very difficult for us to tell in the first place that were dealing with this topic in general, so theyll be valuable resources for you as you try to put into practice what youre learning from the book. Happy studying!