Graduate Management Admission Test (GMAT) Practice Test

Why is the sum of an even number of consecutive integers never a multiple of their count?

1. Because the average is always an integer

2. Because the average is never an integer

3. Because they are not whole numbers

4. Because the sum is always greater than zero

The correct answer is: Because the average is never an integer

The rationale behind why the sum of an even number of consecutive integers is never a multiple of their count lies in the properties of averages and the characteristics of even integers. When you calculate the sum of an even number of consecutive integers, you are essentially looking at pairs of integers that are symmetric around a central point. This means that the average of these integers will always yield a fractional value. For example, consider four consecutive integers: 1, 2, 3, and 4. Their sum is 10, and there are four of them, but the average, which is the sum divided by the quantity, is 2.5. Here, while 2.5 is not an integer, this means that the sum is not divisible by the number of integers, which confirms the concept in question. By extension, because the average of an even count of integers results in a non-integer value, the sum will inherently not be a multiple of the count of those integers. Each pair contributes to a total that, when split evenly among the total count, does not yield a whole number. Thus, the correct understanding solidifies why the sum behaves in this manner with respect to being a multiple of the count. Being aware of properties of