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

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Manager
Joined: 22 May 2007
Posts: 211
Among 200 people, 56% like strawberry jam, 44% like apple jam, and 40% [#permalink]

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05 Jul 2008, 07:05
1
35
00:00

Difficulty:

75% (hard)

Question Stats:

62% (01:54) correct 38% (01:35) wrong based on 617 sessions

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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

M08-7
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Joined: 03 Apr 2007
Posts: 1242
Re: Among 200 people, 56% like strawberry jam, 44% like apple jam, and 40% [#permalink]

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Updated on: 05 Jul 2008, 10:29
1
1
Attachment:

sheetal_venn.GIF [ 12.71 KiB | Viewed 15075 times ]

Originally posted by goalsnr on 05 Jul 2008, 08:38.
Last edited by goalsnr on 05 Jul 2008, 10:29, edited 2 times in total.
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Re: Among 200 people, 56% like strawberry jam, 44% like apple jam, and 40% [#permalink]

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06 Jul 2008, 09:26
11
7
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)
Attachments

venn.jpg [ 13.93 KiB | Viewed 15022 times ]

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Re: Among 200 people, 56% like strawberry jam, 44% like apple jam, and 40% [#permalink]

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06 Jul 2008, 11:53
11
3
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
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Among 200 people, 56% like strawberry jam, 44% like apple jam, and 40% [#permalink]

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22 Jul 2014, 01:40
7
2
aaron22197 wrote:
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

M08-7

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.

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.

Attachment:

Jams.png [ 12.55 KiB | Viewed 14894 times ]

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Re: Among 200 people, 56% like strawberry jam, 44% like apple jam, and 40% [#permalink]

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22 Jul 2014, 06:30
Bunuel wrote:
aaron22197 wrote:
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

M08-7

Look at the diagram below:
Attachment:
Jams.png

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.

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.

Bunuel how did you assume in this question that there would be atleast some people liking all the three jams ?
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Posts: 46302
Re: Among 200 people, 56% like strawberry jam, 44% like apple jam, and 40% [#permalink]

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22 Jul 2014, 06:50
himanshujovi wrote:
Bunuel wrote:
aaron22197 wrote:
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

M08-7

Look at the diagram below:
Attachment:
Jams.png

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.

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.

Bunuel how did you assume in this question that there would be atleast some people liking all the three jams ?

Saying that there are no such overlap would be an assumption... Which part of my solution are you referring exactly?
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Re: Among 200 people, 56% like strawberry jam, 44% like apple jam, and 40% [#permalink]

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22 Jul 2014, 19:14
Quote:
Look at the diagram below:
Attachment:
Jams.png

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.

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.

I am referring to the venn diagram. Basically the main premise of the solution that these people comprise of three intersecting sets.

In other words , for all overlapping sets question do we assume that the distribution as per the above Venn diagram , unless ofcourse mentioned otherwise
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Re: Among 200 people, 56% like strawberry jam, 44% like apple jam, and 40% [#permalink]

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22 Jul 2014, 20:29
2
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

Attachments

rasp.png [ 9.78 KiB | Viewed 12799 times ]

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Re: Among 200 people, 56% like strawberry jam, 44% like apple jam, and 40% [#permalink]

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23 Jul 2014, 02:33
himanshujovi wrote:
Quote:
Look at the diagram below:
Attachment:
Jams.png

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.

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.

I am referring to the venn diagram. Basically the main premise of the solution that these people comprise of three intersecting sets.

In other words , for all overlapping sets question do we assume that the distribution as per the above Venn diagram , unless ofcourse mentioned otherwise

____________
Yes. How else?
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Re: Among 200 people, 56% like strawberry jam, 44% like apple jam, and 40% [#permalink]

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23 Jul 2014, 12:08
Somethin else as in say Set A and set B having some common intersection with set C being totally a sub set of A/B or set C being a altogether different set with no intersection

Sent from my iPhone using Tapatalk
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Posts: 46302
Re: Among 200 people, 56% like strawberry jam, 44% like apple jam, and 40% [#permalink]

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23 Jul 2014, 12:15
himanshujovi wrote:
Somethin else as in say Set A and set B having some common intersection with set C being totally a sub set of A/B or set C being a altogether different set with no intersection

Sent from my iPhone using Tapatalk

That's when you have some additional information. If you don't, then three overlapping sets should be represented as given above.
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Re: Among 200 people, 56% like strawberry jam, 44% like apple jam, and 40% [#permalink]

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08 Aug 2014, 02:13
Bunuel wrote:
aaron22197 wrote:
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

M08-7

Look at the diagram below:
Attachment:
Jams.png

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.

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.

HI Bunuel,

Just one query.

Cant I say

People who like only strawberry = 112-60 = 52
people who like only applejam = 88-60 = 28

so here 80 people who like either strawberry or applejam.

i did it in this way and got answer 80.

Could you please clarify why cant we use this logic?

Thanks
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Re: Among 200 people, 56% like strawberry jam, 44% like apple jam, and 40% [#permalink]

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08 Aug 2014, 03:16
PathFinder007 wrote:
Bunuel wrote:
aaron22197 wrote:
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

HI Bunuel,

Just one query.

Cant I say

People who like only strawberry = 112-60 = 52
people who like only applejam = 88-60 = 28

so here 80 people who like either strawberry or applejam.

i did it in this way and got answer 80.

Could you please clarify why cant we use this logic?

Thanks

Not Bunuel, but lets try

If 30% of the people like both strawberry and apple jam
The highlighted portion is ignored in this calculation
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Re: Among 200 people, 56% like strawberry jam, 44% like apple jam, and 40% [#permalink]

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08 Aug 2014, 03:38
HI Paresh,

here i am subtracting 30 % OF 200 = 60 FROM 112 and 88 so i am considering this highlighted statement. So What you mean that The highlighted portion is ignored in this calculation. please clarify this

Thanks
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Re: Among 200 people, 56% like strawberry jam, 44% like apple jam, and 40% [#permalink]

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09 Aug 2014, 05:20
PathFinder007 wrote:
HI Paresh,

here i am subtracting 30 % OF 200 = 60 FROM 112 and 88 so i am considering this highlighted statement. So What you mean that The highlighted portion is ignored in this calculation. please clarify this

Thanks

Hello PathFinder007,

Kindly refer to Bunuel's diagram. (Yellow shaded) I've attached herewith

30% (60) is overlap of BOTH Strawberry & Apple; so it cannot be subtracted as stated in your answer

So, only strawberry would be less than 52, only apple would be less than 28.

How much less?? Its unknown, that's why variables "a" & "b" are taken respectively (Refer my earlier post diagram)

Also common to all "c" has to be considered. That's why only Raspberry would be less than 80

In this problem, as three products are give, 3! + 1 = 7 possibilities have to be considered

1. Only Strawberry
2. Only Apple
3. Only Raspberry
4. Strawberry+Apple
5. Strawberry+Raspberry
6. Apple+Raspberry
7. Apple+Raspberry+Strawberry

All possibilities have to be considered with caution to avoid duplication

For me, Venn diagram helps a lot
Attachments

rasp.png [ 9.78 KiB | Viewed 12331 times ]

Jams.png [ 12.55 KiB | Viewed 12351 times ]

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Re: Among 200 people, 56% like strawberry jam, 44% like apple jam, and 40% [#permalink]

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08 Dec 2014, 23:54
Bunuel wrote:
aaron22197 wrote:
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

M08-7

Look at the diagram below:
Attachment:
Jams.png

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.

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.

Please confirm this...either - or implies that atleast one of the condition must hold. In other words, both condition can also be true.
either not A or not B implies only one condition needs to be false and not both. In other words, any one one condition can only be false.

Is this the logic taken in above question??
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Re: Among 200 people, 56% like strawberry jam, 44% like apple jam, and 40% [#permalink]

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09 Dec 2014, 08:45
enders wrote:
Bunuel wrote:
aaron22197 wrote:
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

M08-7

Look at the diagram below:
Attachment:
Jams.png

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.

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.

Please confirm this...either - or implies that atleast one of the condition must hold. In other words, both condition can also be true.
either not A or not B implies only one condition needs to be false and not both. In other words, any one one condition can only be false.

Is this the logic taken in above question??

_____________
Yes, that's true.
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Re: Among 200 people, 56% like strawberry jam, 44% like apple jam, and 40% [#permalink]

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16 Dec 2014, 19:36
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
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Re: Among 200 people, 56% like strawberry jam, 44% like apple jam, and 40% [#permalink]

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03 Jan 2015, 19:59
1
walker wrote:
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

walker
Shouldnt it be
280- (60+ x ) + ( All three)
why did not you count ALL THREE ?
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Re: Among 200 people, 56% like strawberry jam, 44% like apple jam, and 40%   [#permalink] 03 Jan 2015, 19:59

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