In a village of 100 households, 65 have at least one DVD player, 75 have at least one cell phone, and 35 have at least one MP3 player. If x and y are respectively the greatest and lowest possible number of households that have all three of these devices, x – y is:  Choose the correct choice from the following answers
A) 60 B) 55 C) 45 D) 35 E) 25
Am I missing something here??? it seems straightforward......   The obvious maximum that have all 3 is 35, because you are limited by the SMALLEST number.   The minimum is simply the sum of the max of each people who DONT have the product, so:    100-75= 
<gadget id="calculator"> 100-75</gadget>
<output>25</output>
25 don't have Cell    100-65= 
<gadget id="calculator"> 100-65</gadget>
<output>35</output>
35 don't have DVD   and  100-35= 
<gadget id="calculator"> 100-35</gadget>
<output>65</output>
65 don't have MP3   SO a total of   25+35+65= 
<gadget id="calculator">  25+35+65</gadget>
<output>125</output>
125 combined who might NOT have SOME combination of the 3 products. So subtract that from 100, to give you the minimum of the people who COULD have all 3 and you get 100-125= -25.   35+25= 
<gadget id="calculator">35+25</gadget>
<output>60</output>
60   60
<result>A</result>
In a village of 100 households, 65 have at least one DVD player, 75 have at least one cell phone, and 35 have at least one MP3 player. If x and y are respectively the greatest and lowest possible number of households that have all three of these devices, x – y is: