Why do you want to do something else than plugging?
I find it efficient here, you solve the question in a very few time.

jc114 wrote:Set M has 15 numbers while Set K has 17 numbers. If one number from set K is taken and moved into set M, is the average of K larger than M?
(1) after moving a number into M, the median of M is smaller than the median of K.
(2) after moving a number into M, the average of M and the average of K both increased.

OA is B

Is there a better way to solve this than plugging #s??

You can plug in #'s but for me that would be really time consuming and I'd probably make a mistake along the way. Just by understanding how mean and median relate to each other, you can solve the problem without any calculation.

1. So we move a number from K to M and M's median is smaller than K's. I don't think this tells us much other than exactly what's stated. We don't know if K's was smaller before... we definitely don't know anything about the average. Insufficient

2. We move a number from K into M and both averages increase. From this we know that this number was below K's mean and above M's mean. So, K's mean is larger than M's. Sufficient.

I guess but who wants to plug in 15 and 17 #s?
I just want to understand the theory behind medians and averages..