mathewmithun wrote:Five offices have an average of 8 people per office and a median of 7 people per office, and none of the offices are vacant. What is the maximum number of people who can be in the largest office?
A. 23 B. 24 C. 25 D. 26 E. 27
although OA is 24, I think 23 will also fit this scenario
Pls help...
There are 5 offices with an average of 8 people per office, so there are 5*8=40 people. To maximize the number of people in one office, we need to minimize the number of people in the other four offices while staying within the restrictions stated in the problem.
1. We know the median is 7, so the list of number of people in the offices, in ascending order, looks like this : ___, ____, 7, ____, ____.
2. We know that no offices are vacant, so there must be at least 1 person in each office. Nothing in the problem states that there is a different number of people in each office, so both of the numbers to the left of 7 could be 1: 1, 1, 7, _____, _____.
3. The fourth number of the list must be greater than or equal to 7 because 7 is the median. The smallest possible value in this range is 7: 1, 1, 7, 7, _____.
4. So far, we have 1+1+7+7=16 people. We know the office has 40 people total, so the largest office has [spoiler]40-16=24 people[/spoiler]
