That Mean Range

yourshail123 wrote:The average (arithmetic mean) of a list of 8 different positive integers is 23. Which of the following is the greatest possible range of this list of numbers?

(A)149
(B)155
(C)156
(D)168
(E)183

Please explain...

The range of the set is from smallest to the greatest positive integer in the set

You can get the greatest possible value in the set if the remaining values are the least,

Average of 1,2,3,4,5,6,7,x is 23
Find the value of x
23*8- 28 = 184-28 = 156

Range = Highest value - lowest value = 156-1 = 155


Option B

Since the question stem is asking for the Greatest possible range of the list, here we go:
List of 8 different positive integers: 1, 2, 3, 4, 5, 6, 7, X.
We didn't consider 0 above as 0 doesn't have sign, i.e. neither positive nor negative.
So we need to find Range = X-1. From question stem we know that the arithmetic mean of the list is 23, hence we get X+ 28 (sum of integers from 1 to 7) = 23*8, from here we get that X = 184-28 = 156.
Thus, our Range =X-1=156-1=155, so I guess (B)

Please, correct me if I went awry.

yourshail123 wrote:The average (arithmetic mean) of a list of 8 different positive integers is 23. Which of the following is the greatest possible range of this list of numbers?

(A)149
(B)155
(C)156
(D)168
(E)183

Please explain...

Oohhh damn!! I was just looking why the numbers are selected as 1,2,3,4,5,6,7,X only. Little that I noticed question says 'different' positive integers. Thanks guys.. that was silly on my part.