100 people, 85 carry a phone, 80 carry a beeper, 75 speak 2 languages, 70 wear suits. What is the minimum number of people who must have all of the above?

Guest Jun 13, 2015

#1**0 **

70 suit wearers - 25 unable to speak two languages - 20 with no beepers - 15 with no phone = 10 (minimum number of people who have all four)

Guest Jun 13, 2015

#2**+10 **

Here's a pictorial representation. The dotted lines enclose the overlap of all four criteria and cover 10 people (from 25 to 35 on the diagram).

.

Alan Jun 15, 2015

#3**0 **

Thanks Alan, that is really neat.

I have been thinking about that problems since it was first posted.

Melody Jun 15, 2015

#4**+10 **

Best Answer

with Alan's pictorial representation:

void red (suits) = 100 - 70

void blue (language) = 100 - 75

void green (beeper) = 100 - 80

void black (phone) = 100 - 85

100 - (100-70) - (100-75) - (100-80) - (100 -85) = 100 - 30 - 25 - 20 - 15 = **10**

heureka Jun 15, 2015

#5**0 **

I have added this inot this probability/counting thread.

http://web2.0calc.com/questions/probability-melody#rr0

This thread is also referenced from the "Great answers to learn from" sticky thread

Melody Jun 22, 2015