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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

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 #4
avatar+18715 
+10

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
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 #1
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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
avatar+26329 
+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).

 

 overlap

.

Alan  Jun 15, 2015
 #3
avatar+91053 
0

Thanks Alan, that is really neat.     

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

Melody  Jun 15, 2015
 #4
avatar+18715 
+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
avatar+91053 
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

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