Hi,
Let's call:
Dorm rooms that have DVD : D
Dorm rooms that have MP3: M
Dorm rooms that have Cell: C
I didn't know which is the most convenient approach to this problem. This is just what I think:
We have three circles D, M, C which value at 75, 55, and 80 respectively. The total sum is 100. Thus there is no way these circles cannot overlap each other.
To find the max value of triple overlapped area, find the max value of double overlapped area first, then plug the third circle to it as much as possible.
Overlap between:
D and M :(75+55) - 100 = 30
D and C: (75+80) - 100 = 55
M and C: (55+80) - 100 = 35
Hey look and D and C, 55 is exactly the value of circle M. Plug circle M perfectly into the overlapped zone between D and C, we got maximum value of triple overlapped area: 55
To find the minimum, try the same, and we got D and M have the minimum overlapped area : 30
Thus the area that is NOT overlapped: 100 - 30 = 70. Try to distribute as much as possible the last circle's area to this not-overlapped-between-D-and-M area to prevent the triple overlapping among three circles. Sure, we can distribute 70 out of 80 area units of circle C. The 10 units left have no way to be distributed, but go directly into the overlapped zone between D and M. Thus, minimum triple overlapped area is 10 units.
If you try this to all the remaining cases, the results are also the same :
Not-overlapped zone between D and C: 100 - 55 = 45. Distribute circle M (55 units), we still have 10 units being triple overlapped.
Not-overlapped zone between M and C: 100 - 35 = 65. Distribute circle D (75 units), we still have 10 units being triple overlapped.
Thus, x - y = 55 - 10 = 45.
Pick C.
Correct me if I'm wrong. Awaiting for expert to give out the most convenient approach to this.
"There is nothing either good or bad - but thinking makes it so" - Shakespeare.
