Explanation

Since , it is equally true that



We can apply this fact multiple times. First, we can write it twice for each of the given averages:





Then, we can write for the group of items overall:





Then we can bust out our long-division skills to determine the right side of this equation.



We can actually pause here, since 14 point something leaves only one possible answer. The correct answer is (E). Another way to solve this question is to consider that the average of the two groups will be substantially above the midpoint between the numbers 12.40 and 15.25, but less than 15.25. This is because there are 3 numbers in each group evenly balancing each other out on either side of that midpoint, with then three items remaining in the higher group pulling the average upward.