Least value registered=5
Highest value registered=30
Mean number of people for the past 6months=20
Let the total number of people registered for all the 6 month=P
thus, p/6 =20 ; P=120
Various possible values of x for the 6 month are as shown below
1.X = [5,5,20,30,30,30]
absolute value x-m =[15,15,0,10,10,10]
Sum of the absolute values= 15+15+....+10=60
2.X=[15,10,25,20,20,30]
x-m=[5,10,5,0,0,10]
Sum of x-m =30
3. X=[20,15,25,20,20,20]
x-m=[0,5,5,0,0,0]
Sum of x-m=10
Sum of the values are 60,30 and 10
Hence ans is C,D,E

However, you would observe that all the values of X in the 3 cases sums up to 120
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Thanks for the explanation. Please, how do you determine that the 3 lists of x values are exhaustive and how do you intuitively establish the lists?

20, 20, 20, 20, 20, 20, the absolute deviation of each number from 20 points is 0, sum=0

5, 5, 20, 30, 30, 30, each data is as far away as possible from 20, and the guaranteed sum is 120, at this time, the maximum sum of absolute deviation is 60

With such extreme analysis, the lock answer falls within 0 and 60

Next, quickly verify that the options in the range [0, 60] can actually be made up.

For example, 10, in order to ensure that the average does not change, 20, 20, 20, 20 are reserved, one 20 minus 5, one 20 plus 5, and the absolute deviation sum is 10

For example, 30, in order to ensure that the average does not change, a 20 minus 5, a 20 plus 5, a 20 plus 10, a 20 minus 10, the absolute deviation sum is 30

Not sure this is a real GRE question.

For example: usually the answer choices are in ascending order and not in decreasing order.

But aside this, Not sure this would be an official question.

I arrived at an intuitive demonstration of the solution. Unfortunately, I have posted less than ten times; thus, I cannot attach the image of my work.

Usually images on a scratch paper are not allowed.

The answer should be typed as all the students, moderators, and admins do