A set of 15 different integers has a median of 25 and a range of 25. What is the greatest possible integer that could be in this set?
32
37
40
43
50
Correct answer 43
Please explain how?
Range = biggest - smallest.
Thus:
25 = biggest - smallest.
Smallest = biggest - 25.
We can plug the answer choices into the equation above.
Since we need the greatest possible integer that could be in the set, we should start with the greatest answer choice.
Answer choice E: 50
Smallest = 50-25 = 25.
Since all the integers must be different, the smallest integer cannot be equal to the median.
Eliminate E.
Answer choice D: 43
Smallest = 43-25 = 18.
Thus, the 7 integers below the median of 25 could be {18,19,20,21,22,23,24}.
The 6 integers between 25 (the median) and 43 (the biggest) could be any 6 different integers between 25 and 43.
This works.
The correct answer is
D.
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