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Overlapping Sets

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Overlapping Sets [#permalink] New post 15 Jul 2010, 23:45
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A
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C
D
E

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Among 200 people, 56% like strawberry jam, 44% like apple jam, and 40% like raspberry jam. If 30% of the people like both strawberry and apple jam, what is the largest possible number of people who like raspberry jam but do not like either strawberry or apple jam?


A. 20
B. 60
C. 80
D. 86
E. 92
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Re: Overlapping Sets [#permalink] New post 16 Jul 2010, 05:01
Hi,

I am sure you are pretty familiar with the attached.

Attachment:
Set.JPG
Set.JPG [ 7 KiB | Viewed 1847 times ]


Assume Set A is Strawberry, B is Apply and C is Raspberry.
The largest possible of people who like Raspberry jam but do not like either Strawberry or Apple jam is
C + y + z.
40% like Raspberry jam. This is C + y +z + o.
C + y + z is maximum when o is 0 ie there aren't any people who like all the three jams.
So we can say C + Y + z = 40% of 200 = 80 people.

Hope my answer is clear.

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Jack
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Re: Overlapping Sets [#permalink] New post 16 Jul 2010, 05:51
Expert's post
Hussain15 wrote:
Among 200 people, 56% like strawberry jam, 44% like apple jam, and 40% like raspberry jam. If 30% of the people like both strawberry and apple jam, what is the largest possible number of people who like raspberry jam but do not like either strawberry or apple jam?


A. 20
B. 60
C. 80
D. 86
E. 92


Above solution is not right.

Good discussion: m08-q-68236.html?hilit=strawberry
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Re: Overlapping Sets [#permalink] New post 16 Jul 2010, 11:32
I believe the answer is 60 (B), Here's why:

56%+44%-30%=70% who like either Strawberry, Apple, or both.

That means 100%-70% = 30% do not like either Apple of Strawberry jam.

30% is the most possible that like raspberry jam but do not like either strawberry or apple (assuming nobody in the group does not like any)
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Sets!!!!!Cab anybody help me solve thi susing venn diagram? [#permalink] New post 25 Jul 2010, 11:37
Among 200 people 56% like strawberry jam, 44% like apple jam, and 40% like raspberry jam. If 30% of people like both strawberry and apple jam, what is the largest possible number of people who like raspberry jam but do not like either strawberry or apple jam?
1.)70 2.)80 3.)60 4.)120

Any help in demystifying the above problems with venn diagram shall be highly appreciated ?
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Re: Overlapping Sets [#permalink] New post 15 Dec 2010, 17:42
The correct answer is B (60), right?
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Re: Overlapping Sets [#permalink] New post 15 Dec 2010, 20:38
Please see the Venn diagram below
Attachments

Venn.PNG
Venn.PNG [ 17.45 KiB | Viewed 1346 times ]

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Re: Overlapping Sets [#permalink] New post 16 Dec 2010, 04:31
Expert's post
Re: Overlapping Sets   [#permalink] 16 Dec 2010, 04:31
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