Graduate Management Admission Test (GMAT) Practice Test

What is the property of the sum of an evenly spaced set with an even increment?

1. It is always odd

2. It is a prime number

3. It is always a multiple of the number of elements in the set

4. It cannot be determined

The correct answer is: It is always a multiple of the number of elements in the set

The sum of an evenly spaced set with an even increment exhibits a characteristic that relates closely to the number of elements in that set. When you have an evenly spaced set, this means that the numbers follow a consistent pattern of increments, and in the case of an even increment, all differences between consecutive terms are equal and are even numbers. When you add together a series of evenly spaced numbers, the result (or sum) can be observed to relate significantly to the total count of those numbers. If the increment between terms is even, then regardless of how many terms are included, the overall result will be a multiple of that number of terms. This is due to the fact that each pair of terms contributes evenly to the sum and maintains that even sum across the entire set of numbers. For example, consider a set of numbers like 2, 4, 6, 8, and so forth. The increment here is even, and if you count the numbers (say there are 4), their total will always yield a sum that is even and divisible by 4, reinforcing the idea that the sum behaves consistently in this manner. Thus, it can be concluded that the property of the sum of an evenly spaced set with an even increment