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That Mean Range

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That Mean Range

by yourshail123 » Sun Sep 09, 2012 11:11 am

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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...
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by rijul007 » Sun Sep 09, 2012 11:23 am
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
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by Javoni » Sun Sep 09, 2012 11:33 am
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...
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by yourshail123 » Sun Sep 09, 2012 1:09 pm
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. :)
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by Scott@TargetTestPrep » Sun Feb 10, 2019 7:29 am
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
The sum of the integers is 8 x 23 = 184.

To maximize the range, we need the largest element to be as large as possible and the smallest element to be as small as possible. To find the largest possible value in the set, we should take the rest of the elements as small as possible. Thus, we can let the first 7 integers be 1, 2, 3, 4, 5, 6, 7, for a sum of 28, so the largest value in the set would be 184 - 28 = 156, for a maximum range of 156 - 1 = 155.

Answer: B

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