## 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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### 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

by sambati » Tue Aug 04, 2020 1:58 pm

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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

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### Re: A set of 11 different integers has a median of 25 and a range of 50. What is the greatest possible integer that coul

by [email protected] » Tue Aug 04, 2020 11:53 pm
sambati wrote:
Tue Aug 04, 2020 1:58 pm
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
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.