Explanation

Start by plugging in a set of consecutive integers that encompasses the full spectrum of integers, such as −2, −1, 0, 1, 2. The average and median of the set are both 0.

In any set of consecutive integers, the average will always equal the median. Performing the operations in choices (A), (B), (C), and (F) results in sets of numbers that are still consecutive.

Thus, while in choices (B), (C), and (F) the averages change, the medians also change to those same values.

Eliminate choices (B), (C), and (F). In choice (A), neither the average nor the median changes, so you can eliminate it as well. For choice (D), the new average is −1.64 and the new median is −8.2. Again, both values change, so you can eliminate choice (D). In choice (E), the new average is .4, but the median hasn’t changed; choice (E) works. You can eliminate choice (G) based on the other calculations, and the only correct answer is choice E.