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

Question

Out of 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 maximum 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

Among 200 people, 56% like Orange Juice, 44% like Grape Juice, and 40% like Milk. If 30% of the people like OJ and Grape Juice, what is the greatest possible number of people who like Milk but do not like either OJ or Grape Juice?

(A) 20
(B) 60
(C) 80
(D) 86
(E) 92

(A) 20 
(B) 60 
(C) 80
(D) 86 
(E) 92

leonidas · Accepted Answer

Like strawberry = 112
Like Apple= 88
Like Rasberry = 80
Like straberry and apple = 60

As shown in the diagram:

(52-y)+(60-x)+(28-z)+(80-x-y-z)+x+y+z=200 ----(1)

We need (80-x-y-z) = Like Rasberry but do not like either Straberry or Apple.
From (1),
(80-x-y-z) = 200-(52+60+28)
 =60

Hence (B)

walker · Answer

Fast way.

In order to transform sum 112+88+80=280 to 200 we have to exclude double counting:
280-60-x=200 --> x=20 (raspberry jam + any other jam) --> 80-20=60 only raspberry jam

Bunuel · Answer

Look at the diagram below: https://gmatclub.com/forum/download/file.php?id=23733 Notice that "30% of the people like both strawberry and apple jam" doesn't imply that none of these 30% (60 people) can also like raspberry jam. The intersection of the strawberry and apple jam groups is represented by the yellow segment in the diagram. No specific formula is needed to solve this question: 112 people like strawberry jam, 88 people like apple jam, and 60 people like both strawberry and apple jam. Thus, the number of people who like either strawberry or apple jam (or both) is 112 + 88 - 60 = 140 (the area covered by Strawberry and Apple in the diagram). Therefore, there are a total of 200 - 140 = 60 people who "do not like either strawberry or apple jam." Can all of these 60 people like raspberry jam? Since there are 80 people who like raspberry jam ( ext{Raspberry} = 80 \ge 60 ), it is possible! The maximum number of people who like raspberry jam and don't like either strawberry or apple jam is 60 (the gray segment in the diagram). In this case, the number of people who don't like any of the three jams (the area outside the three circles) would be zero. Side note: The minimum number of people who like raspberry jam and don't like either strawberry or apple jam would be zero (if the Raspberry circle is entirely inside the Strawberry and/or Apple circles). In this case, the 60 people who "do not like either strawberry or apple jam" would be those who don't like any of the three jams. Answer: B. Jams.png

PareshGmat · Answer

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

vietnammba · Answer

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

bethebest · Answer

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???

LatentProdigy · Answer

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??

Bunuel · Answer

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

priyankachhabra01 · Answer

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?

Bunuel · Answer

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

GMATinsight · Answer

Solution is attached here.. Video as well.

https://www.youtube.com/watch?v=KREPptXZnt4

Bambi2021 · Answer

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

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