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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?

Answer: The general equation is where denotes the number of people who like none of the three jams (draw the Veinn diagram). To maximize the number of people who like raspberry but not strawberry or apple jam has to be 0. The new equation can be rewritten as follows: S + R + A - SA - AR - SR + SAR + N = 100% ........

I am not convinced with the formula given here: Shouldn't the formula be: S + R + A - SA - AR - SR - 2SAR + N = 100%

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.

My answer is 80. As per Tejal's venn diagram, if there are no one like Rasberry+Apple, Strawberry+Rasberry and Strawberry+Rasberry+apple, then the number for Rasberry will be greatest = 80.

Please tell me where I am missing.

tejal777 wrote:

I have drawn a venn diagram.Please see where my error lies: We need to find the shaded area= 80-x-y-z =??

Applying formula: 200=112+88-60+80-y-z+x 80-y-z+x=60 Hmm..Should'nt that be "-x"... Shocked

This approach is wrong because if you assume all sections mentioned by you (x, y and z in tejal777's diagram) to be zero than the sum would be more than 200: 140 who like either Strawberry or Apple (or both) plus 80 who like ONLY Raspberry (as you proposed) = 220>total.

By the way tejal777's diagram is wrong as he assumed that 60 is the # of people who like ONLY strawberry and apple.

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??

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

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?? _________________

True # of items = (total # in group 1) + (total # in group 2) + (total # in group 3) - (# in only 1/2) - (# in only 1/3) - (# in only 2/3) +(# in 1/2/3)

I have always always used this formula!! _________________

My answer is 80. As per Tejal's venn diagram, if there are no one like Rasberry+Apple, Strawberry+Rasberry and Strawberry+Rasberry+apple, then the number for Rasberry will be greatest = 80.

Please tell me where I am missing.

tejal777 wrote:

I have drawn a venn diagram.Please see where my error lies: We need to find the shaded area= 80-x-y-z =??

Applying formula: 200=112+88-60+80-y-z+x 80-y-z+x=60 Hmm..Should'nt that be "-x"... Shocked