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

The answer to this question is indeed B (60), but here is an interesting thing: everyone made mistakes either in formulas or in word translation (unfortunately the formula in OE is also incorrec).

First of all: "30% of the people like both strawberry and apple jam" doesn't mean that among these 30% can not 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 tejal777 posted it's the section x plus the section above it (the one 60 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 S+A). 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 R=80\geq{60}, then why not! So maximum # of people who like raspberry and don't like either strawberry or apple jam is 60.

Side note: min # of people who like raspberry and don't like either strawberry or apple jam would be zero (circle R is "inside" of two circles S and A). In this case these 60 people (who "do not like either strawberry or apple jam") will be those who like none of the 3 jams.

Answer: B.

There is a confusion about the formulas of 3 overlapping sets, hope my post at: formulae-for-3-overlapping-sets-69014.html#p729340 would help to clear this issue.
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It should be R+S+A-RS-RA-SA-2RSA+N=100%

R-RS-RA-2RSA=100%-N-S-A+SA

R-RS-RA-2RSA=100%-0-56%-44%+30% N is 0 because we want to maximize R

R-RS-RA-2RSA=30%

R-RS-RA-2RSA= people who only like R

30%*200people= 60 people

agreed.

But in all honesty, i drew a Venn to solve this one

Wee bit confused here:
Should'nt the number of people who like raspberry jam but do not like either strawberry or apple jam be:
R-S-A-SAR instead of R-S-A+SAR??
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countdown-beginshas-ended-85483-40.html#p649902

My bad . Promised to edit the typo and didn't do it. It's corrected now. The answer stays the same though.
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Can you please elaborate how did u solve this through Venn diagram?

I think N is the number of people who dont like any JAM. Though, are we considering each person at least like one jam?
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My debrief: done-and-dusted-730-q49-v40

Bunuel,

This is great explaination. Thanks.
Can you please tell me where above in my explaination, I am missing?
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