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the laregst possible number of people!

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by Ozlemg » Wed Jun 29, 2011 8:03 am
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?

A.50
B.60
C.70
D.80
E.100
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by vikram4689 » Wed Jun 29, 2011 8:37 am
Answer is 60, draw the diagram for 3 sets. You will get it easily. You have to find the area that only Rasberry covers. Given info will help you calculate the Area(apple OR strawberry). Now subtract it from total to get ONLY RASBEERY =30%

Note: for largest area assume that all of 200 people like at least one jam.
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by pemdas » Wed Jun 29, 2011 8:49 am
S=56
A=44%
R=40%
S&A=30% <> S+A-(S&A)=56+44-30=70%
So 30% may not like either S,A jams or 200*30%=60
Ozlemg wrote: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?

A.50
B.60
C.70
D.80
E.100
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by winniethepooh » Wed Jun 29, 2011 8:53 am
The total % of people given :
SB= 56% + AP= 44% + RB= 40% = 140 %
Out of 140%, 30% people like SB and AP, therefore, the remaining people(110%) like only one of three jams + SB or RB + SB or AP + SB OR AP OR RB
110% - 100% = 10% = SB or RB + SB or AP + SB OR AP OR RB
Therefore, only SB = 40% - 10% = 30%.
Therefore, B.
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by Ozlemg » Wed Jun 29, 2011 9:25 am
the point I could not get it this: what happens to the ones who like S+A+R? should not we subtract it from the total number, too?
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by winniethepooh » Wed Jun 29, 2011 10:21 am
@ Ozlemg: That's included in the 10%. Our aim is to get full 100% of people. That is (S and A and R) - [(S or A or R) + (S or A) + (S or R) + (R or A)].
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by amit2k9 » Thu Jun 30, 2011 3:31 am
s+a+r-sa-sr-ar-2sar = 100 %

thus r-sr-ar-2sar = 100-[56+44-30] = 30

thus 30% of 200 = 60.
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by chawlavinu » Sun Jul 03, 2011 5:48 am
I am unable to understand why 2SAR is there?

I guess formula should be:
S + A + R - 2SA - 2SR- 2AR - 3SAR + N = 100%

where N= people who dont like any of the Jam item.

Also, help me to understand how do you calculate the 30% exactly?

Thanks
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