Graduate Management Admission Test (GMAT) Practice Test

How is the sum defined for an average of a set of integers?

1. Sum = (Maximum + Minimum)/2

2. Sum = (Average)(Number of elements)

3. Sum = (Number of elements)/2

4. Sum = Maximum + Minimum

The correct answer is: Sum = (Average)(Number of elements)

The correct choice is derived from the fundamental relationship between the average of a set and the sum of its elements. The average of a set of integers is defined mathematically as the sum of all the integers divided by the number of integers in the set. To express the sum in terms of the average, one can rearrange the formula for the average: Average = Sum / Number of elements. Multiplying both sides by the number of elements, we arrive at the equation: Sum = Average × Number of elements. This demonstrates that the sum of the integers in the set can be obtained by multiplying the average value by the total number of integers. In contrast, the other options relate to different mathematical concepts or give incorrect forms. For instance, calculating the average using maximum and minimum values can only provide a midpoint and doesn't accurately reflect the sum of integers in the set. Thus, understanding the basic relationship of average, sum, and the count of elements is essential for interpreting these concepts correctly.