Venn Diagrams

glenn101 · 2008-04-03 14:58:09

Hi, I am having trouble with these 2 particular venn diagram questions. My venn diagrams are correct but I am uncertain of how you get the answers.

Here is question 1:

Fifty people are interviewed. Twenty-three say they like Brand X, 25 say they like brand Y, 19 say they like brand Z. Eleven say they like X and Z. Eight say they like Y and Z. Five say they like X and Y. Two like all three. How many like none of them.

Here is question 2:

Three rectangles A,B and C overlap(intersect). Their areas are 20cm², 10cm², and 16cm² respectively. The area common to A and B is 3cm², that common to A and C, is 6cm², that common to B and C is 4cm². How much of the area is common to all three if the total area is covered is 35cm².

If you do get answers could you please describe in detail how you derived that answer.

Thank you in advance,
Glenn.

Last edited by glenn101 (2008-04-03 15:12:22)

Daniel123 · 2008-04-04 00:05:05

1. Once you have drawn the diagram, start from the centre (i.e. the intersection of X, Y and Z). You know that is 2. Then take the intersection of X and Z. You know that should total 11, so the section, exlcuding the centre, must be 9. Use the same reasoning for (X and Y), and (Y and Z), and then again for the whole X, Y and Z circles individually. If you then add up all the individual sections, you should get 45, meaning 5 like none.

Last edited by Daniel123 (2008-04-04 00:07:11)

John E. Franklin · 2008-04-04 05:23:04

Click picture for visual aid I made!

mathsyperson · 2008-04-04 09:54:50

2. Looking at the given values, I guessed that the intersection of all three rectangles had an area of 2cm². Putting that value in the middle of the Venn diagram, all the rest of the information could be filled in and the total area worked out as 35cm², so that guess was right.

(Then I felt like I'd cheated, so I put x in the middle and did it again. )

What I'm interested in is what those three rectangles actually look like. I've got a sheet of paper full of failed attempts, but all I've ended up with is a piece of cubism.

Edit: >_<
That's what I get for assuming the side lengths were integers. Thanks John.

John E. Franklin · 2008-04-04 11:43:25

2.)
For MathsyPerson!
a way I found.
Click picture.
Overlapping little squares
are dimensions of
the square root of 2
and half of that for the
skinny "1".

Last edited by John E. Franklin (2008-04-04 11:44:31)

glenn101 · 2008-04-04 11:46:30

I can't thank you guys enough, your all Brilliant!
and yes my venn diagrams did look similar and now I see how you resulted with the answer, thanks for that, many thanks to everyone!

John E. Franklin · 2008-04-04 11:59:23

Thanks!! It makes me very happy to help someone!

Also 46 was 20 + 10 + 16
and
46 + center - 3 - 6 -4 = 35 (when you subtract off the double-thick parts once, and the middle got erased 3 times, then add the center back in)

40 + center = 42

center = 2 in area.

Last edited by John E. Franklin (2008-04-04 12:01:35)

glenn101 · 2008-04-04 13:06:57

thank you again for your thourough explanation it really makes the difference.

John E. Franklin · 2008-04-04 13:18:13

No prob!, and I see it is light out where you live on this
sunlight chart MathIsFun made:
http://www.mathsisfun.com/time-zones-world.html
I'm going to bed soon, as you can guess from the eastern US being dark now.

Math Is Fun Forum

#1 2008-04-03 14:58:09

Venn Diagrams

#2 2008-04-04 00:05:05

Re: Venn Diagrams

#3 2008-04-04 05:23:04

Re: Venn Diagrams

#4 2008-04-04 09:54:50

Re: Venn Diagrams

#5 2008-04-04 11:43:25

Re: Venn Diagrams

#6 2008-04-04 11:46:30

Re: Venn Diagrams

#7 2008-04-04 11:59:23

Re: Venn Diagrams

#8 2008-04-04 13:06:57

Re: Venn Diagrams

#9 2008-04-04 13:18:13

Re: Venn Diagrams

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