Question

In a group of 50 patrons, 12 patrons like lattes and espressos, 9 patrons like espressos and cappuccinos, 8 patrons like lattes and cappuccinos, and 4 patrons like all 3 coffee drinks. Altogether, 20 patrons like lattes, 22 patrons like espressos, and 17 patrons like cappuccinos. How many patrons don't like any of these coffee drinks?
a. 18
b. 14
c. 12
d. 16

Answer 1

Answer: 16

Step-by-step explanation:

A P E X

Answer 2

I used a Venn Diagram which I attached.
Think of it as a flower and work your way from the center out to the doubles (two kinds of coffee) and finally the singles (only one kind of coffee)
I place 4 in the center to represent the people that like all three.
Then I put 8 in the Latte Espresso group since they along with the 4 who like all three, make up the 12 who like lattes and espresso.  I put 4 in the Latte & Cappuccino group since they and the 4 who like all coffees, make up the 8 who like lattes and cappuccinos. And then I put 5 in the Espresso Cappuccino group who along with the 4 in the middle make up the 9 who like both of those.
In all 20 like lattes and my latte circle already has 16 so I added 4 (who only like lattes).  22 like espresso and I have accounted for 17 (8+4+5) so that means there are 5 who only like espresso.  Finally out of the 17 who like cappuccinos, 13 are already accounted for so I will add 4 who like only cappuccinos.
Since there are 50 people and I can account for 34 of them (add all the numbers in all three circles), there must be 50-34 people who don't like any.  The correct answer is d.16

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