Among 200 people, 56% like strawberry jam, 44% like apple jam, and 40%

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) 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 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 \(Raspberry=80\geq{60}\), 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.

Answer: B.

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.

Refer diagram below:

We require to find the maximum value of the pink shaded region

Setting up the equation:

112 + 28-b + b + 80 - (a+b+c) = 200

80 - (a+b+c) = 60

Answer = B

Hi Bunuel,

Is my approach correct?
a is number of people who like both Strawberry and Rasberry
b is number of people who like both Apple and Rasberry
c is number of people who like all three

We have 100% = 56% + 44% + 40% - 30% -a-b +c
=> 10+c = a+ b
In order to have maximum of people who only like Rasberry we have to minimize a,b,c => a+b = 10 and c =0
=> Answer is (40% - 10% )*200 = 60
Thank you

This is great. i also got the correct answer but used a different approach :

A = no. of people who like only Strawberry
B = no. of people who like only apple
C = no. of people who like only raspberry
D = no. of people who like both strawberry and apple but not raspberry
E = no. of people who like both strawberry and raspberry but not apple
F = no. of people who like both apple and raspberry but not strawberry
G = no. of people who like all 3

A+D+E+G =112
B+D+G+F = 88
C+E+G+F = 80
D+G = 60

A+B+C+2(D+E+F) + 3G = 280
A+B+C+D+E+F+G =200

Subtracting the 2 ->

(D+E+F) +2G = 80, which can be written as -> (D+G) +(E+F) + G =80 -> 60 +E+F+G = 80

=> E+F+G = 20

Also from above -> C+E+F+G = 80 => C+ 20 = 8
=> C= 60...

Is this method correct???

The questions asks "Largest possible number of people". Hence, according to my logic, in order to maximise the number of people who like raspberry jam, we should make all the 60 people like strawberry and Apple. Hence, the answer comes as 80 rather than 60. Can someone tell if there is anything wrong with my logic??

The case you are considering is not possible because the total number of people in this case will be more than 200: 112 + 88 - 60 + 80 = 220.

There are several correct solution on previous two pages. For example, here: https://gmatclub.com/forum/among-200-pe ... l#p1385279

Hi Bunuel

I got the answer correct. I just need a little clarification. The raspberry circle consists of 80 ppl. If 60 can be the highest in the gray portion, do 20 ppl fall in that portion of the raspberry circle that overlapping with strawberry and/or apple circle?

Yes, the remaining 20 could be in strawberry and/or apple circle.

Solution is attached here.. Video as well.

Bar overlap method for me. Lines indicate percent:

------------------------------------------------
56 %
||||||||||||||||||||||||||||||||-----------------------------------
||||||||||||||||||||||||||||||||30 % overlap
||||||||||||||||||||||||||||||||||||||||||||||||-------------------
||||||||||||||||||||||||||||||||||||||||||||||||14 % left to 44
|||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||------------------
|||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||30 % remaining

30 % = 60

Edit: Wow, this post really looks like crap on a mobile device... =D

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