Graduate Management Admission Test (GMAT) Practice Test

The sum of an even number of consecutive integers is never a multiple of:

1. The number of elements in the set

2. The average of the integers

3. The highest integer in the set

4. The sum of the integers

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

To understand why the correct answer is that the sum of an even number of consecutive integers is never a multiple of the number of elements in the set, consider the nature of consecutive integers and how their sum is calculated. When you have an even number of consecutive integers, you can express them as \( n, n+1, n+2, \ldots, n+k-1 \), where \( k \) is the even count of integers. The sum of these integers can be calculated as: \[ \text{Sum} = n + (n+1) + (n+2) + \ldots + (n+k-1) \] This simplifies to: \[ \text{Sum} = k \cdot n + \frac{k(k-1)}{2} \] In this case, \( k \) is even. Now, if you divide the sum by \( k \) (the number of elements), you’re essentially calculating the average of your integers. The resulting average will yield a value that is not an integer because: 1. The term \( k \cdot n \) is divisible by \( k \). 2. The term \( \frac{k(k-1)}{