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
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
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Since there are 11 different integers, the median would the value of (11 + 1)/2 = 6th integer, when the integers are arranged in ascending order.
Say the smallest integer = x; thus, the largest integers = x + 50.
Since we want the greatest possible integer (x + 50), we must have greatest value of x.
Given that the median is 25, the value of x can be less than or equal to 25. Thus, we take x = 25. But this is incorrect since the 11 integers are different.
So, since the 6th integer = 25, the greatest possible value of x = 25 – 5 = 20.
So, the largest integers = x + 50 = 20 + 50 = 70.
Correct answer: B
Hope this helps!
Jay
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