20 burger lovers were asked if they like tomato or lettuce. 12 like tomato, 12 like lettuce, and 7 like both. How many Do Not like tomato or lettuce?

Question

20 Burger lovers were asked.

12 like tomato

12 like lettuce

7 like both

 

how many Do Not like tomato or lettuce?

Answer 1

Here's how I'd do it. I don't think that there's a standard process for this, I just worked it out in my head.

 

You've go your 20 burger lovers:

 

A B C D E F G H I J K L M N O P Q R S T U

 

7 of those 20 can be removed immediately. We know that that group of 7 cannot be in the "do not like tomato or lettuce" group, but we don't know how the 12 tomato people and the 12 lettuce people overlap with each other. So we can remove the "both" (B) people like so:

 

A B C D E F G H I J K L M N O P Q R S T U

B B B B B B B B

 

Since we removed 7, we know that there 5 people who like lettuce only (L), and 5 people who like tomato  only (T). The thing is -- these cannot overlap, otherwise you would have another "both" person. So you can distribute them like so:

 

A B C D E F G H I J K L M N O P Q R S T U
B B B B B B B B L L L L L T T  T T  T

 

That means there are only 3 people left who don't like either.

 

DOUBLE-CHECK: with the way the answer is now, there are 7 people who like both, 7 + 5 = 12 people who like lettuce, and 7 + 5 = 12 people who like tomato.

Answer 2

I think of the solution as two intersecting circles (a 2-circle venn diagram)

On the left is tomato likers

On the right is lettuce likers

In the middle is those who like both

Put 7 in the middle since you're given this information in the problem

Now, how do you get to 12 tomato likers in the left circle when there are already 7 who like tomato (+ lettuce) in the middle/intersected space?

5 like just tomato

Same thing with lettuce; since 7 already like lettuce (+ tomato) in the middle space, 5 like lettuce alone

Add 5 (only tomato likers) + 7 (both likers) + 5 (only lettuce likers) and you have 3 remaining "don't likers"