In a graduating class, the difference between the highest and lowest salaries is $100,000. The median salary is $50,000 higher than the lowest salary and the average salary is $20,000 higher than the median. What is the minimum number of students W in the class?  Choose one
A) A)10
B) B)12
C) C)15
D) D)20
E) E)25
the difference between the highest and lowest salaries is $100,000.   So there are at least 2 people - say one with salary 0 and the other with 100k. No salary will be outside this range.   Median = 50k more than lowest. So median is right in the center of lowest and highest since lowest and highest differ by 100k. In our example, median = 50k. Since there are more than 2 people, there would probably be a person at 50k.   Mean = 20k more than median so in our example, mean salary = 70k   On the number line,   0........50k (median)........100k   Mean = 70k   So there must be people more toward 100k to bring the mean up to 70k. Since we want to add minimum people, we will add people at 100k to quickly make up the right side deficit. 0 and 50k are (70k + 20k) = 90k away from 70k. 100k is 30k away from 70k. To bring the mean to 70k, we will add two people at 100k each to get:   0....50k.....100k, 100k, 100k   But when we add more people to the right of 70k, the median will shift to the right. We need to keep the median at 50k. So every time we add people to the right of 70k, we need to add people at 50k too to balance the median. 50k is 20k less than 70k while 100k is 30k more than 70k. To keep the mean same, we need to add 2 people at 100k for every 3 people we add at 50k. So if we add 3 people at 50k and 2 people at 100k, we get:   0, ... 50k, 50k, 50k, 50k, ... 100k, 100k, 100k, 100k, 100k   the median is not at 50k yet.   Add another 3 people at 50k and another 2 at 100k to get   0, 50k, 50k, 50k, 50k, 50k, 50k, 50k, 100k, 100k, 100k, 100k, 100k, 100k, 100k   Now the median is 50k and mean is 70k.   Total number of people is 15.   Answer (15)(70  + 20 )= 
<gadget id="calculator">(70  + 20 )</gadget>
<output>90</output>
90k away from 70k. 100k is 30k away from 70k. To bring the mean to 70k, we will add two people at 100k each to get:   0....50k.....100k, 100k, 100k   But when we add more people to the right of 70k, the median will shift to the right. We need to keep the median at 50k. So every time we add people to the right of 70k, we need to add people at 50k too to balance the median. 50k is 20k less than 70k while 100k is 30k more than 70k. To keep the mean same, we need to add 2 people at 100k for every 3 people we add at 50k. So if we add 3 people at 50k and 2 people at 100k, we get:   0, ... 50k, 50k, 50k, 50k, ... 100k, 100k, 100k, 100k, 100k   the median is not at 50k yet.   Add another 3 people at 50k and another 2 at 100k to get   0, 50k, 50k, 50k, 50k, 50k, 50k, 50k, 100k, 100k, 100k, 100k, 100k, 100k, 100k   Now the median is 50k and mean is 70k.   Total number of people is 15.   Answer (15)
<result>C</result>
In a graduating class, the difference between the highest and lowest salaries is $100,000. The median salary is $50,000 higher than the lowest salary and the average salary is $20,000 higher than the median. What is the minimum number of students W in the class?