BN1989 wrote:
A set of 25 integers has a median of 50 and a range of 50. What is the greatest possible integer that could be in this set?
A. 62
B. 68
C. 75
D. 88
E. 100
Consider 25 numbers in ascending order to be
x_1,
x_2,
x_3, ...,
x_{25}.
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_{13}=50;
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_{25}-x_{1} -->
x_{25}=50+x_{1};
We want to maximize
x_{25}, hence we need to maximize
x_{1}. The maximum value of
x_{1} is the median, so 50, hence the maximum value of
x_{25} is
x_{25}=50+50=100.
The set could be {50, 50, 50, ..., 50, 100}
Answer: E.
Now,
in order the answer to be 88, as given in the OA, the question should state that "A set of 25
different integers has a median of 50..."
In this case since all integers must be distinct then the maximum value of
x_{1} will be
median-12=50-12=38 and thus the maximum value of
x_{25} is
x_{25}=38+50=88.
The set could be {
38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49,
50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61,
88}
Answer: B.
Hope it's clear.
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41% (01:46) correct
