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Among 200 people, 56% like strawberry jam, 44% like apple jam, and 40% [#permalink]

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15 Jul 2010, 23:45

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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?

Re: Among 200 people, 56% like strawberry jam, 44% like apple jam, and 40% [#permalink]

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16 Jul 2010, 05:01

Hi,

I am sure you are pretty familiar with the attached.

Attachment:

Set.JPG [ 7 KiB | Viewed 3021 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.

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?

Re: Among 200 people, 56% like strawberry jam, 44% like apple jam, and 40% [#permalink]

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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 ?

Re: Among 200 people, 56% like strawberry jam, 44% like apple jam, and 40% [#permalink]

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01 Nov 2014, 10:53

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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

M08-7

Look at the diagram below:

Notice that "30% of the people like both strawberry and apple jam" doesn't mean that among these 30% (60) cannot be some people who like raspberry as well. Both strawberry and apple jam is the intersection of these two groups, if we refer to the diagram it's the yellow segment in it.

Next, no formula is needed to solve this question: 112 like strawberry jam, 88 like apple jam, 60 people like both strawberry and apple jam. So the # of people who like either strawberry or apple (or both) is \(112+88-60=140\) (on the diagram it the area covered by Strawberry and Apple). So there are TOTAL of \(200-140=60\) people left who "do not like either strawberry or apple jam". Can ALL these 60 people like raspberry? As \(\text{Raspberry}=80 \ge 60\), then why not! So, maximum # of people who like raspberry and don't like either strawberry or apple jam is 60 (grey segment on the diagram). Notice here that in this case the # of people who like none of the 3 jams (area outside three circles) will be zero.

Side note: minimum # of people who like raspberry and don't like either strawberry or apple jam would be zero (consider Raspberry circle inside Strawberry and/or Apples circles). In this case those 60 people (who "do not like either strawberry or apple jam") will be those who like none of the 3 jams.

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