Graduate Management Admission Test (GMAT) Practice Test

If an odd number is raised to a positive integer power, what will the result be?

1. Even

2. Odd

3. Neither

4. Cannot be determined

The correct answer is: Odd

When an odd number is raised to a positive integer power, the resulting value remains odd. This is rooted in the properties of odd numbers. An odd number can be expressed in the general form of \(2n + 1\), where \(n\) is an integer. When you raise this expression to a positive integer power, you effectively multiply the odd number by itself multiple times. For example, if you have an odd number like 3 and raise it to the power of 2, the calculation is: \[ 3^2 = 3 \times 3 = 9, \] which is still odd. This multiplicative property continues for any positive integer power. Moreover, the product of any two odd numbers is also odd. Therefore, no matter how many times you multiply an odd number by itself, the product will never result in an even number. Thus, raising an odd number to any positive integer power will consistently yield another odd number.