karthikpandian19 wrote:Set consists of five integers that sum to 89. If the median is distinct from the other integers, what is the smallest possible value of the range of ?
A. 0
B. 1
C. 2
D. 3
E. 4
Let m=median.
Since m must be distinct from the other integers, all 5 integers cannot be the same.
To minimize the range, the other integers must differ from m as little as possible.
The smallest possible difference between m and the other integers is 1.
Thus, the smallest possible range will be achieved if the 5 integers are:
m-1, m-1, m, m+1, m+1.
Given that the sum=89, we get:
(m-1) + (m-1) + m + (m+1) + (m+1) = 89
5m = 89.
m = 89/5.
Doesn't work, since m must be an integer.
To minimize the range, we want to change the values in our list as little as possible.
Thus, we need 5m to be equal to the nearest multiple of 5, which is 90.
For the right-hand side of 5m=89 to INCREASE by 1, the left-hand side must DECREASE by 1.
Thus, the smallest value in our list must decrease to m-2:
m-2, m-1, m, m+1, m+1.
With these values, we get:
(m-2) + (m-1) + m + (m+1) + (m+1) = 89
5m - 1 = 89
5m = 90
m = 18.
Thus:
The least value = m-2 = 18-2 = 16.
The greatest value = m+1 = 18+1 = 19.
Range = 19-16 = 3.
The correct answer is
D.
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