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# overlapping sets

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Manager
Joined: 31 Aug 2009
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19 Sep 2009, 22:28
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Question Stats:

50% (02:06) correct 50% (01:42) wrong based on 17 sessions

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According to a survey, at least 70% of people like apples, at least 75% like bananas and at least 80% like cherries. What is the minimum percentage of people who like all three?

A. 15%
B. 20%
C. 25%
D. 0%
E. 35%

I got this wrong. Here's my work. Where did I go wrong?

Let A&B&C = X

A&B (excl. C) = A+B-100-X = 45-X
B&C (excl. C)= B+C-100-X= 55-X
C&A (excl. C= C+A-100=50-X

Overlapping elements (ie everything that is in more than one set) = A+B+C - 100= 125

A&B+B&C+C&A+A&B&C= 125 => 45-x+55-x+50-x + x = 125. Solved it. Wrong answer.

Or Method 2:

A&B= A+B-100= 45
B&C= B+C-100=55
C&A= C+A-100= 50

Let X equal overlap of A&B&C

Overlapping elements (ie everything that is in more than one set) = A+B+C - 100= 125

A&B+B&C+C&A + (-3x+x) = 125

Since X is counted 3 times in the calculation above you need to take it out but you need 1 X that represent A&B&C thus:

A&B+B&C+C&A -2x = 125

Solving em. Wrong.
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20 Sep 2009, 00:16
ps-venn-diagrams-77473.html
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Manager
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20 Sep 2009, 01:14
thanks but i dont understand that solution. it is a very intuitive answer and i'm not at that level. i need some formulas. build from the ground up first then i'll try to understand it at a highlevel.

i guess A+B has to have some minimal overlap since it has to be max 100. But why not 40 or 35 etc.. because it only has to be less than 100 it doesn't have to add to 100.

unless you can explain that please feel free.
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20 Sep 2009, 05:17
I'm getting the min as 25.

I wud go with option C
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15 Oct 2009, 02:46
70% like A
75% like B
80% like C

If 70% like A and 75% like B then the ones which like them both are 70+75-100 = 45%
80% like C so all the C lovers plus the ones which like A an B both are: 45+80 = 125
so the ones which like A + B + C are 125- 100= 25%
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21 May 2011, 23:21
is using the formula correct:

100=70+75+80-(45+50+55)+all+ 0 ( neither)
all=100-75 hence 25%
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23 May 2011, 23:21
so it goes

70+75 -100 = 45
45 + 80 -100 = 25 %
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25 May 2011, 18:49
amit2k9 wrote:
so it goes

70+75 -100 = 45
45 + 80 -100 = 25 %

So far the posts are just answers. Can anyone provide a solid explanation?
Re: overlapping sets   [#permalink] 25 May 2011, 18:49
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