Graduate Management Admission Test (GMAT) Practice Test

What type of set results in a sum that is always a multiple of the number of elements in the set?

1. Oddly spaced set

2. Evenly spaced set

3. Randomly spaced set

4. Uniformly spaced set

The correct answer is: Evenly spaced set

The correct answer is that an evenly spaced set results in a sum that is always a multiple of the number of elements in the set. In an evenly spaced set, the elements are arranged in regular intervals, meaning that the difference between consecutive elements is constant. To understand why the sum of an evenly spaced set is a multiple of the number of elements, consider the formula for the sum of an arithmetic series. The sum of a set of numbers can be calculated as follows: 1. Identify the first term and the last term in the set. 2. Count the number of terms in the set. 3. Use the formula for the sum of an arithmetic series, which is: \[ \text{Sum} = \frac{\text{Number of terms}}{2} \times (\text{First term} + \text{Last term}) \] Since the first term and the last term are defined by the common difference, both the first term and last term are linear combinations of the common difference. Therefore, the sum will always be evenly divisible by the number of terms, ensuring that it is a multiple. In contrast, with oddly spaced, randomly spaced, or uniformly spaced sets, the gaps between the numbers vary,