Number properties are all about categories and rules. Certain kinds of numbers behave the same ways in all cases. When discussing number properties, don’t assume that they apply exclusively to integers. Integers are one subset of numbers: namely, positive and negative whole numbers and zero. The concept of number properties is perfect fodder for the GMAT test makers because it allows them to reward you for using the Core Competencies of Pattern Recognition and Critical Thinking to draw inferences about how numbers behave, based on certain characteristics they possess. That’s why number properties questions appear on the Quant section with greater frequency than other topics: these questions constitute approximately 20 percent of GMAT Problem Solving questions and nearly 30 percent of Data Sufficiency questions.
Distinct simply means “different.” So in this question, all 600 integers are different—there are no integers that show up more than once in the set. Don’t assume that a set of integers always contains only distinct integers. This concept often comes into play with questions dealing with variables. Just because x and y are different letters does not necessarily mean that they represent different values.
All integers are either odd or even. Students often forget that 0 is an even number. All integers ending with the digit 0, 2, 4, 6, or 8 are considered “even numbers,” and all integers ending with the digit 1, 3, 5, 7, or 9 are considered “odd numbers.” When a number is classified as even or odd, it must also be an integer; non-integers are not considered odd or even.
Basically, the only difference is the number zero. Zero is the only number that is neither positive nor negative. This is a great example of how number properties questions test your Attention to the Right Detail. A question that asks about negative numbers does not include zero as a possibility, but a question that asks for non-positive numbers does include zero. You can bet that considering zero when it shouldn’t be considered, or vice versa, can lead to a wrong answer on Test Day.
As mentioned earlier, because number properties deal with the expected behavior of numbers based on certain rules, Pattern Recognition is an essential Core Competency for these questions. Also, you should use Critical Thinking in two ways: by remembering the abstract rules of number properties and by using the Kaplan strategy of picking numbers to make those properties more concrete in your mind on Test Day.
Here are the main topics we’ll cover in this chapter:
Now let’s apply the Kaplan Method to the number properties question you saw earlier:
This is a Value question. To have sufficiency, you need a single value for the number of positive odd integers in Set X. The question stem tells you that the total number of integers in the set is 600 and that they are all distinct, or different from each other.
Once you are sure you understand the information in the question stem, move on to the statements. Statement (1) tells you the number of even integers in Set X, from which you could determine the number of odd integers in Set X. But you don’t know the number of these odd integers that are positive. Statement (1) is insufficient. Eliminate (A) and (D).
Statement (2) tells you the percentage of the odd integers in Set X that are positive. But Statement (2) tells you nothing about the number of odd or even integers in Set X. Statement (2) is insufficient. Eliminate (B).
Now combine the statements. From the two statements together, you could determine the number of odd integers and the percentage of those odd integers that are positive. Together, the two statements are sufficient. Choice (C) is correct.
Now let’s look at each of the six areas of number properties that show up on the GMAT Quantitative section, starting with integers and non-integers.