sunita123 wrote:
median-5=25-5=20 -
why did we subtract 5 from median?Bunuel wrote:
Official Solution:
A set of 11 different integers has a median of 25 and a range of 50. What is the greatest possible integer that could be in this set?
A. 65
B. 70
C. 75
D. 80
E. 85
Consider 11 numbers in ascending order to be \(x_1\), \(x_2\), \(x_3\), ..., \(x_{11}\).
The median of a set with odd number of elements is the middle number (when arranged in ascending or descending order), so the median of given set is \(x_{6}=25\);
The range of a set is the difference between the largest and the smallest numbers of a set, so the range of given set is \(50=x_{11}-x_{1}\) \(\rightarrow\) \(x_{11}=50+x_{1}\);
We want to maximize \(x_{11}\), hence we need to maximize \(x_{1}\). Since all integers must be distinct then the maximum value of \(x_{1}\) will be \(median-5=25-5=20\) and thus the maximum value of \(x_{11}\) is \(x_{11}=50+20=70\).
The set could be {20, 21, 22, 23, 24, 25, 26, 27, 26, 29, 70}
Answer: B
2 things to be noted here
We need to find the largest number possible in the list and that number is x1
Option C,D and E can be ruled out because if median is 25 and range 50 that means number x1 to x5 will be 25 but we are told there are 11 different integers so this case is not possible.Likewise D and E not possible.
Now to maxmimize X11,you need to minimize other numbers..
Thus when you subtract from 5 median to get 20 as the smallest number then largest possible number will be Range (50)+20= 70..
Mind you even 65 can be an option but since we need to find largest integer possible 70 will be the answer
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