GRE Arithmetic - Integers and Absolute Value

You need to understand the various properties of numbers because many GRE math questions will use words such as integer, whole number, and ratio, and you’ll need to be familiar with these and similar concepts.

Integers are whole numbers on the number line, and can be either negative or positive. For every positive integer, there is an equivalent negative integer. Zero is a special integer, and it is neither positive nor negative. Examples of integers are -3, -2, -1, 0, 1, 2, 3. All numbers on the number line to the left of the zero are negative integers, while all numbers to the right of the zero on the number line are positive integers. That said, here is a sample GRE quantitative comparison integer question:

Column A    Column B
The number of integers
that are less than -10
but greater than -34,645,734,654
The number of integers
that are greater than 9
but less than 34,645,734,654

First, you'll need to know that there are as many negative integers as there are positive integers, because for every positive integer, there is an equivalent negative integer*. However, the set of numbers in Column B is greater than the set of numbers in Column A because Column B also includes positive 10, while Column A does not include negative 10.

Although the concept of positive and negative numbers is straight-forward to those that routinely use math in their work or who routinely used math in college, you might find it a bit confusing, in which case, feel free to quickly draw a number line if you are given a positive/negative integer question on the GRE. That way, you'll be able to easily see how one number relates to another.

Consecutive integers are two or more numbers that are written in sequence, where the numbers are ordered according to size. For example, the consecutive integers from -2 to 1 are -2, -1, 0, and 1. So, a simple GRE consecutive integer question might be the following:

How many consecutive integers are
larger than -5 and smaller than 6?

Again, this is a straight forward GRE question, but ONLY if you know the definition of consecutive integers. The consecutive integers greater than -5 and smaller than 6 include -4, -3, -2, -1, 0, 1, 2, 3, 4, and 5, for a total of 10 integers.

The absolute value of a number is the distance to the number from 0 on the number line. The symbol for absolute value is | |, and the absolute value of a number is always positive. For example, the absolute value of -5, which is written as |-5|, is 5, and the absolute value of 6, written as |6|, is 6. Two different numbers are opposite if they have the same absolute value, so -6 and 6, and -22 and 22 are opposite numbers.


*Keep in mind that the GRE General Test is meant to measure your BASIC math skills. If, while reading the above referenced statement, you were conjuring up proofs and theorems that depend on concepts such as Kantor's degrees of infinity, the cardinality of infinite sets, or, God-forbid, you ventured so far as to begin thinking about Godel's Incompleteness Theorems as a way to address the relation of infinite sets to Hilbert's posed problems (see, we know our math!), then you have over-analyzed the problem. Remember; think SIMPLE! If you catch yourself performing tedious calculations, or you are employing advanced mathematical techniques in an attempt to answer a question, then stop! and look for an easier solution.