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Re: Among 200 people, 56% like strawberry jam, 44% like apple jam, and 40%
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27 Mar 2015, 22:26

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.

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.

Hi Bunuel

Can I use Gclub formula & is this approach correct

Total = S + A + R - (Sum of Exactly 2 group overlaps) - 2 (All 3)

Re: Among 200 people, 56% like strawberry jam, 44% like apple jam, and 40%
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17 Mar 2016, 00:43

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.

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.

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...

Re: Among 200 people, 56% like strawberry jam, 44% like apple jam, and 40%
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06 Feb 2017, 20:24

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

If we can find the total number of people who like either strawberry jam or apple jam or both and subtract it from total number of people, it gives us the number of people who like only raspberry jam. No equation is required but a Venn diagram could be a great help to solve this.

Total number of people who like either strawberry jam or apple jam or both = 112 + 88 - 60 = 140 (60 being common in both strawberry and apple so we subtract it ) No of people left ie. No of people who don't like strawberry jam or apple jam = 200 -140 = 60 B

Re: Among 200 people, 56% like strawberry jam, 44% like apple jam, and 40%
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14 Jul 2017, 03:24

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

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??

Attachments

IMG_20170714_163737_01.jpg [ 19.19 KiB | Viewed 972 times ]

Re: Among 200 people, 56% like strawberry jam, 44% like apple jam, and 40%
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14 Jul 2017, 03:35

LatentProdigy 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

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.

Re: Among 200 people, 56% like strawberry jam, 44% like apple jam, and 40%
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26 Jul 2017, 07:47

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?

Re: Among 200 people, 56% like strawberry jam, 44% like apple jam, and 40%
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26 Jul 2017, 07:58

priyankachhabra01 wrote:

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.
_________________

Among 200 people, 56% like strawberry jam, 44% like apple jam, and 40%
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10 Aug 2017, 10:47

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:

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.

Among 200 people, 56% like strawberry jam, 44% like apple jam, and 40%
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01 Feb 2018, 11:59

First let us find number of people either strawberry or apple or both = 56 + 44 - 30 = 70%

Line diagram should help us find the answer.

S + A (from left) |<------------70---------------><---30--->| |<------------60-----><-10><--30--->| 40 (raspberry from right), as we can see minimum overlap can be 10%, 30% of people can like rasp but neither S nor A. 30% of 200 = 60 => (B)

Re: Among 200 people, 56% like strawberry jam, 44% like apple jam, and 40%
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11 Oct 2018, 20:49

1

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

Solution is attached here.. Video as well.

Attachments

File comment: www.GMATinsight.com

Screenshot 2018-10-12 at 10.14.42 AM.png [ 502.5 KiB | Viewed 245 times ]

_________________

Prosper!!! GMATinsight Bhoopendra Singh and Dr.Sushma Jha e-mail: info@GMATinsight.com I Call us : +91-9999687183 / 9891333772 Online One-on-One Skype based classes and Classroom Coaching in South and West Delhi http://www.GMATinsight.com/testimonials.html

Re: Among 200 people, 56% like strawberry jam, 44% like apple jam, and 40%
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12 Oct 2018, 14:49

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:

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.

Bunuel, hope all is well. I figured this one out using intuition, and I would like to know if I got the right answer by coincidence or if its actually an alternative method:

56% like Strawberry + 44% like Apple = 100%. Take out the 30% that like them both then you have 70% of total that like either Strawberry or Apple.

If 70% likes Strawberry or Apple, then that must mean that the other 30% dislikes them, which gives you the answer: 30%. Multiplied by 200 people, you have 60 people (200 x 30%) that dislike Strawberry or Apple, and prefer Raspberry. _________________

Practice GMAT Scores: Test 1 09/25/2018 Q40 V27 560 Test 2 10/02/2018 Q45 V30 620 Test 3 10/08/2018 Q40 V34 610 Test 4 10/13/2018 Q39 V35 620

Test Date: 12/03/2018

gmatclubot

Re: Among 200 people, 56% like strawberry jam, 44% like apple jam, and 40%
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12 Oct 2018, 14:49