Clearly the maximum number that could have all three devices is 55; that is, the 55 people who own an MP3 player could also each own a DVD player and a cell phone. So x = 55.

To find y, we need to minimize the number of people who own all three devices. If 80 people own a cell phone, and 75 own a DVD player, let's find the smallest possible number that might own both. We'd want to be sure that all 20 people who do *not* own a cell phone *do* own a DVD player. We'd then have:

own cell, do not own DVD: 25
own DVD, do not own cell: 20
own DVD and cell: 55

Now we have 55 who own both a DVD and a cell. We also know that 55 own an MP3 player. Again, to find the smallest number who own an MP3, a cell and DVD, we want to be sure that all 45 people who do *not* own an MP3 *do* own a cell+DVD. So we have:

owns cell+DVD, but no MP3: 45
owns MP3, but no cell+DVD: 45
owns all three: 10

So at least 10 people must own all three devices, and y = 10.

Finally, x - y = 45.