DVD, Cell phones, and MP3 players in village

shulapa wrote:Hi all,

In a village of 100 housholds, 75 have at least one DVD player, 80 have at least one cell phone, and 55 have at least one MP3 player. Every villager has at least one of these three devices. If X and Y are respectively the greatest and lowest number of house holds that have all three of these devices, X-Y is:

a. 65
b. 55
c. 45
d. 35
e. 25

OA: C

clearly greatest possible nuber = 55


Overlap of DVD AND Cell Phone with least possible numbe r= 75+80 -100= 55

Overlap of (DVD AND Cell Phone with least possible number) and MP3 PLAYER least possible nuber = 55+55-100 = 10



Answer = 55-10=45

Look at these other explanations. For someone like myself, who needs to use visuals, there's a post by a user named "calgmatter" who makes it a bit more intuitive.

https://www.manhattangmat.com/forums/vie ... &view=next

The least number of households than can have ALL 3 is:

|----------------------100 households--------------------|

<--------------------80 cell---------------------->20 no cell

25 No DVD<-------------------75 DVD------------------->

<25MP3--><10 MP3>..................................<20MP3>

...............|overlap3|.................................................

How many households overlap for all 3? 10. So Y=10.

55-10 = 45.

This is a tough question.

It's easy to figure out the maximum no. of households with all three devices (55) but difficult to figure out the minimum number of households with all three.

Can some experts pls explain the quickest way to solve this?