I Hate Venn Diagrams.

2,000 people take part in a survey to determine the preferences of the public in terms of pizza toppings. 632 say that they like pepperoni on their pizza, 339 like bacon, and 477 like sausage. 223 like both pepperoni and sausage, 112 like pepperoni and bacon, and 66 like bacon and sausage. If 22 like all 3 toppings, how many people do not like any of the toppings on their pizza?


The answer is 931.

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5 solutions

Finn Hulse
Sep 24, 2014

2 , 000 ( 632 + 339 + 477 223 112 66 + 22 ) = 931 . 2,000-(632+339+477-223-112-66+22)=\boxed{931}.

Very good trick! I liked it. Now I do not need more to make the confused diagram.

Victor Paes Plinio - 6 years, 8 months ago

Done the same way Finn. This type of problem is coming in my exam this month. Thanks for making me practise!!!😃😊😆 LOL.

Yash Singhal - 6 years, 8 months ago

exactly the same , it is P.I.E

math man - 6 years, 8 months ago

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It is PIE, however I've simplified it a bit. Do you see why?

Finn Hulse - 6 years, 8 months ago

nice.................................

PUSHPESH KUMAR - 6 years, 8 months ago
Venture Hi
Sep 24, 2014

I usually use Venn diagram to solve this type of problems but have a feeling your method is quicker.

Venn diagrams are confusing and impractical (in my opinion). I like to look at numbers, not circles.

Finn Hulse - 6 years, 8 months ago

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i agree, venn diagram < P.I.E

math man - 6 years, 8 months ago

Same here.

Yash Singhal - 6 years, 8 months ago
Benjamin Hilliard
Apr 26, 2019

2000 - ((632 + 339 + 477) - ((223 + 112 + 66) - 22)) = 2000 - (1448 - (401 - 22)) = 2000 - (1448 - 379) = 2000 - 1069 = 931

Let x x be the number of people who do not like any of the toppings. Then,

x = 2000 ( 319 + 201 + 22 + 90 + 44 + 183 + 210 ) = 2000 1069 = x=2000-(319+201+22+90+44+183+210) = 2000 - 1069= 931 \color{#D61F06}\boxed{931}

Pooja Hariharan
Sep 27, 2014

Using n( AUBUC) formula we can find the number of people who liked either of the 3 toppings so subtracting it from 2000 we get 931

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