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Set-Venn

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Senior Manager
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Set-Venn [#permalink] New post 25 Sep 2011, 03:53
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I have solved 2 out of 3. Can somebody help me with Q2.? Thanks.

Q.A survey was conducted among 500 ppl each of whom likes at least one of apple, orange , banana.The number of ppl who like apple is 240, those who like orange are 250 and those who like banana are 290.

Q1. If 60 ppl like only apple and banana, then what is the maximum possible number of ppl who like only orange?
1)120 2) 130 3)140
[Reveal] Spoiler: OA
140
Ppl who like apple = A
Ppl who like orange = O
Ppl who like banana = B
Ppl who like all three= x
We know the formula: Total=A+O+B -{Sum of Exactly 2 groups members} - 2*AnOnB + Neither

Sum of Exactly 2 groups members=Sum of ppl who like only apple and orange + Sum of ppl who like only orange and banana + Sum of ppl who like only apple and banana.

To maximize ppl who like only orange we have to minimize Sum of ppl who like only apple and orange and Sum of ppl who like only orange and banana. It will be zero.

Sum of Exactly 2 groups members= 0+0+60 =60
Also, neither=0
Total=A+O+B -{Sum of Exactly 2 groups members} - 2*AnOnB
500=240+290+250-{60} -2x
Solving for x=110.
Hence maximum number of ppl who like Orange= Total who like Orange-Total who like all three
=250-110=140


Q2. If 120 ppl like only apple, then what is the maximum possible number of ppl who like only orange and banana?
1)160 2)170 3)180
[Reveal] Spoiler: OA
160


Q3. What is the maximum possible number of ppl who like all the 3 fruits?
1)110 2)120 3)130 4)140 5)150

[Reveal] Spoiler: OA
140
We know the formula: Total=A+O+B -{Sum of Exactly 2 groups members} - 2*AnOnB + Neither
In this case Sum of Exactly 2 groups members = 0
500=240+290+250-0-2x
2x=280
x=140

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Re: Set-Venn [#permalink] New post 27 Sep 2011, 22:02
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Good questions for learning purpose.
Although seems more of a CAT type question.

2. for only orange and banana to be maximum,

number of people liking all 3 fruits = 0

also, 120(only apple)+ AOr+ABn- AOrBn = 240 (AOr= liking both Apple and orange)
(ABn - liking both Apple and Banana); (AOrBn - liking all 3)

gives AOr+ ABn = 120.

hence,
240+250+290-(120-OrB)-2AOrBn= 500

gives, OrBn= 160.
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Senior Manager
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Re: Set-Venn [#permalink] New post 27 Sep 2011, 23:08
amit2k9 wrote:
240+250+290-(120+OrB)-2AOrBn= 500


Thanks man. These are for practice purpose only. Just to get totally comfortable with these kinds of question.
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Re: Set-Venn [#permalink] New post 26 Aug 2012, 05:37
jamifahad wrote:
I have solved 2 out of 3. Can somebody help me with Q2.? Thanks.

Q.A survey was conducted among 500 ppl each of whom likes at least one of apple, orange , banana.The number of ppl who like apple is 240, those who like orange are 250 and those who like banana are 290.

Q1. If 60 ppl like only apple and banana, then what is the maximum possible number of ppl who like only orange?
1)120 2) 130 3)140
[Reveal] Spoiler: OA
140
Ppl who like apple = A
Ppl who like orange = O
Ppl who like banana = B
Ppl who like all three= x
We know the formula: Total=A+O+B -{Sum of Exactly 2 groups members} - 2*AnOnB + Neither

Sum of Exactly 2 groups members=Sum of ppl who like only apple and orange + Sum of ppl who like only orange and banana + Sum of ppl who like only apple and banana.

To maximize ppl who like only orange we have to minimize Sum of ppl who like only apple and orange and Sum of ppl who like only orange and banana. It will be zero.

Sum of Exactly 2 groups members= 0+0+60 =60
Also, neither=0
Total=A+O+B -{Sum of Exactly 2 groups members} - 2*AnOnB
500=240+290+250-{60} -2x
Solving for x=110.
Hence maximum number of ppl who like Orange= Total who like Orange-Total who like all three
=250-110=140


Q2. If 120 ppl like only apple, then what is the maximum possible number of ppl who like only orange and banana?
1)160 2)170 3)180
[Reveal] Spoiler: OA
160


Q3. What is the maximum possible number of ppl who like all the 3 fruits?
1)110 2)120 3)130 4)140 5)150

[Reveal] Spoiler: OA
140
We know the formula: Total=A+O+B -{Sum of Exactly 2 groups members} - 2*AnOnB + Neither
In this case Sum of Exactly 2 groups members = 0
500=240+290+250-0-2x
2x=280
x=140


HI everyone just wanted to bring this question out in the open

I got stumped in the very first option

in order to maximize only orange from the Diagram I can see only orange is 250 -( x+y+z)= only orange

so in order to maximize I would minimize x+y+z so I would take x+y+z= 0 so maximum only orange = 250

so what is wrong with this logic !! ( assuming actual answer is correct ) why cannot be assume people who like all three (apple . orange and Banana) to be 0?
They have to like at least one, not necessarily there must be some who like all three , so we should be able to take Z=0 in order to maximize only orange unless I am messing up somewhere. Please do help
Attachment:
A O B.JPG
A O B.JPG [ 19.88 KiB | Viewed 934 times ]

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Re: Set-Venn [#permalink] New post 26 Aug 2012, 22:07
stne wrote:
jamifahad wrote:
I have solved 2 out of 3. Can somebody help me with Q2.? Thanks.

Q.A survey was conducted among 500 ppl each of whom likes at least one of apple, orange , banana.The number of ppl who like apple is 240, those who like orange are 250 and those who like banana are 290.

Q1. If 60 ppl like only apple and banana, then what is the maximum possible number of ppl who like only orange?
1)120 2) 130 3)140
[Reveal] Spoiler: OA
140
Ppl who like apple = A
Ppl who like orange = O
Ppl who like banana = B
Ppl who like all three= x
We know the formula: Total=A+O+B -{Sum of Exactly 2 groups members} - 2*AnOnB + Neither

Sum of Exactly 2 groups members=Sum of ppl who like only apple and orange + Sum of ppl who like only orange and banana + Sum of ppl who like only apple and banana.

To maximize ppl who like only orange we have to minimize Sum of ppl who like only apple and orange and Sum of ppl who like only orange and banana. It will be zero.

Sum of Exactly 2 groups members= 0+0+60 =60
Also, neither=0
Total=A+O+B -{Sum of Exactly 2 groups members} - 2*AnOnB
500=240+290+250-{60} -2x
Solving for x=110.
Hence maximum number of ppl who like Orange= Total who like Orange-Total who like all three
=250-110=140


Q2. If 120 ppl like only apple, then what is the maximum possible number of ppl who like only orange and banana?
1)160 2)170 3)180
[Reveal] Spoiler: OA
160


Q3. What is the maximum possible number of ppl who like all the 3 fruits?
1)110 2)120 3)130 4)140 5)150

[Reveal] Spoiler: OA
140
We know the formula: Total=A+O+B -{Sum of Exactly 2 groups members} - 2*AnOnB + Neither
In this case Sum of Exactly 2 groups members = 0
500=240+290+250-0-2x
2x=280
x=140


HI everyone just wanted to bring this question out in the open

I got stumped in the very first option

in order to maximize only orange from the Diagram I can see only orange is 250 -( x+y+z)= only orange

so in order to maximize I would minimize x+y+z so I would take x+y+z= 0 so maximum only orange = 250

so what is wrong with this logic !! ( assuming actual answer is correct ) why cannot be assume people who like all three (apple . orange and Banana) to be 0?
They have to like at least one, not necessarily there must be some who like all three , so we should be able to take Z=0 in order to maximize only orange unless I am messing up somewhere. Please do help
Attachment:
A O B.JPG


Oh My!
This is my first post

This question looks really tough ! can some one help with this solution I am also confused , I Think there may be something wrong with this question !!
Re: Set-Venn   [#permalink] 26 Aug 2012, 22:07
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