swerve wrote: ↑

Tue Jun 16, 2020 4:49 am

8, 5, x, 6

The median of the list of positive integers above is 5.5. Which of the following could be the average (arithmetic mean) of the list?

A. 3
B. 5.5
C. 6.25
D. 7
E. 7.5

The OA is B

Solution:

Since the median is 5.5, which is (5 + 6)/2, we see that x must be the smallest number in the list, i.e., x ≤ 5. However, we are also given that x is a positive integer, so x ≥ 1. We can create the following inequality for the average:

(1 + 5 + 6 + 8)/4 ≤ (x + 5 + 6 + 8)/4 ≤ (5 + 5 + 6 + 8)/4

5 ≤ (x + 5 + 6 + 8)/4 ≤ 6

Since only 5.5 is between 5 and 6, we see that choice B is the correct answer.


Answer: B