16 members, 4 won medals on front stroke, 8 won medals on back stroke, 7 members didn't win. How many won medals in both categories?

Question

I think its three but I am really having problems with the logic arghhhh!

Answer 1

There are a few ways to do this. Draw your 2 circles inside a rectangle, a Venn diagram. Outside the circles is 7. This leaves the 3 sections inside the circles which must add to 9, 16-7.

Now we know, 8 people has to be in the 2 section s that make up the back stroke circle. Although we don't know how many are in each of these sections, we DO know that we had 9 people to place in the 3 sections and 2 of the sections add to 8, so the missing section must have 1 person. In this case, we have 1 person in the front stroke only section. This leaves 3 in the both section, 4-1 =3. That means there are 5, 

8-3, in the back stroke only section.

 

Let's check

1+3+5+7 = 16 for all 4 sections.

1+3 =4 for the front stroke section.

3+5 = 8 for the back stroke section.

 

So everything works.

 

Hope you could follow the logic.