Graduate Management Admission Test (GMAT) Practice Test

In a set of consecutive integers, if the total number is odd, what will the sum always be a multiple of?

1. 1

2. 3

3. 2

4. The number of integers in the set

The correct answer is: The number of integers in the set

When considering a set of consecutive integers, if the total number of integers in that set is odd, the nature of consecutive integers helps establish certain properties about their sum. For any set of consecutive integers that contains an odd number of integers, let's denote the first integer in the series as \( n \). The set will include \( n, n+1, n+2, ..., n+(k-1) \), where \( k \) is an odd integer (the total count of integers in the set). The sum \( S \) of these integers can be computed by using the formula for the sum of an arithmetic series: \[ S = \frac{k}{2} \times (\text{first term} + \text{last term}) \] Here, the first term is \( n \) and the last term is \( n + (k - 1) \), leading to: \[ S = \frac{k}{2} \times (n + (n + (k - 1))) = \frac{k}{2} \times (2n + k - 1) \] Since \( k \) is odd, \( \frac{k}{2} \) will result in