Integers

Though not explicitly tested, the concepts of integers and whole numbers are important to solving GRE math problems.

Rules

An integer is a number without any fraction or decimal behind it.

1, 3, -5, and 268 are integers, while 1.77 and ${\tfrac {-2}{7}}$ are not.

A whole number is a non-negative integer.

0, 1, 2, and 3 are whole numbers; .62, -8, and ${\sqrt {56}}$ are not.

Practice

Determine whether each of the following is an integer, a whole number, or neither.

1. -2

2. 113.7

3. ${\tfrac {5}{6}}$

4. 593

Comments

The GRE isn't going to ask questions such as “which of the following is an integer?” but the concept is important for solving other questions. For instance, if 1 < x < 5, x could have an infinite number of values, from 1.00001 to 3.0065. But if x is an integer, its values are now limited to 2, 3, and 4.

Answers to Practice Questions

1. -2 is an integer – it does not end in a fraction or decimal. However, it is not a whole number. Whole numbers are positive.

2. 113.7 is not an integer because it ends in a decimal. Because it is not an integer, it is not a whole number either. Remember, whole numbers are positive integers.

3. ${\tfrac {5}{6}}$ is not an integer – it is a fraction. Integers, remember, are numbers which do not end in fractions or decimals. Because it is not an integer, it is not a whole number either, since whole numbers are positive integers.

4. 593 is an integer because it does not end in a decimal. It is also a positive (non-negative) integer so it is also a whole number. Remember, all whole numbers are integers but not all integers are whole numbers, only if they are non-negative.