Set Q contains 14 distinct numbers. Which of the following operations would decrease the average of set Q while leaving the median unchanged?
A. Decreasing all 14 numbers by 2 each
B. Increasing the 3 smallest numbers by 4 each and decreasing the 4 largest numbers by 3 each
C. Increasing the 2 smallest numbers by 2 each and decreasing the 3 largest numbers by 1 each
D. Decreasing the 7 smallest numbers by 2 each and increasing the 7 largest numbers by 1 each
E. Decreasing the 2 smallest numbers by 5 each and increasing the 3 largest numbers by 3 each
I could let set the first number as 1 and make my way to 14 and do the operations but that would be tedious and because this is a standardized test question I'm afraid I'd mess up if I were to do that on the test. Is there a better way to solve this problem? can you notice any patterns? take advantage of the multiple choice format of the test