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# PS-Venn Diagrams

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Senior Manager
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PS-Venn Diagrams [#permalink]  03 Apr 2009, 22:12
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Question Stats:

25% (01:02) correct 75% (01:48) wrong based on 19 sessions
According to a survey, at least 70% of people like apples, at least 75% like bananas and at least 80% like cherries. What is the minimum percentage of people who like all three?

A. 15%
B. 20%
C. 25%
D. 0%
E. 35%

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Thanks
rampuria

Last edited by rampuria on 05 Apr 2009, 08:50, edited 1 time in total.
CEO
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Re: PS-Venn Diagrams [#permalink]  04 Apr 2009, 22:37
Expert's post

1) minimum apples&bananas:
[XXXXXXXXXXXXXX------] - apples
[-----XXXXXXXXXXXXXXX] - bananas
mimimum a&b = 70 - (100-75) = 45%

2) minimum (apples&bananas)&cherries:
[XXXXXXXXX-----------] - apples&bananas
[----XXXXXXXXXXXXXXXX] - cherries
mimimum a&b = 45 - (100-80) = 25%

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Senior Manager
Joined: 04 Sep 2008
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Re: PS-Venn Diagrams [#permalink]  05 Apr 2009, 08:56
Walker, you're right. I have changed the options. Can you explain your answers.
I dont understand the maxima and minima concept in venn diagrams. Can you explain.

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Thanks
rampuria

CEO
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Re: PS-Venn Diagrams [#permalink]  06 Apr 2009, 09:36
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Expert's post
rampuria wrote:
Walker, you're right. I have changed the options. Can you explain your answers.
I dont understand the maxima and minima concept in venn diagrams. Can you explain.

My reasoning here is pretty simple:
let's we have two sets with x% and y% attributes.
What is maximum possible percentage of x&y attributes? We have to choose lesser number between x and y.
What is minimum possible percentage of x&y attributes? It is possible, when 100-x% elements have y attribute. So, for x&y y - (100-x) remains. You can see illustrations in my previous post one more time.

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Re: PS-Venn Diagrams [#permalink]  06 Apr 2009, 10:35
rampuria wrote:
According to a survey, at least 70% of people like apples, at least 75% like bananas and at least 80% like cherries. What is the minimum percentage of people who like all three?

A. 15%
B. 20%
C. 25%
D. 0%
E. 35%

least no.of people like A and B = 70+75-100=45

least no.of people like (A and B) and C = 45+80-100 =25

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Senior Manager
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Re: PS-Venn Diagrams [#permalink]  07 Apr 2009, 07:26
Very good explanation walker. Thanks.

Now, I also got stumped by the term 'at least' in the problem. What is its significance?

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Thanks
rampuria

CEO
Joined: 17 Nov 2007
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Re: PS-Venn Diagrams [#permalink]  08 Apr 2009, 13:27
Expert's post
rampuria wrote:
Very good explanation walker. Thanks.

Now, I also got stumped by the term 'at least' in the problem. What is its significance?

We should understand that minimum for apples&bananas&cherries is minimum for "at least" values. If we take 71% for apples, we will get 26% > 25%.
"at least" steals a bit of our time....

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Re: PS-Venn Diagrams [#permalink]  08 Apr 2009, 17:16
walker wrote:
rampuria wrote:
Walker, you're right. I have changed the options. Can you explain your answers.
I dont understand the maxima and minima concept in venn diagrams. Can you explain.

My reasoning here is pretty simple:
let's we have two sets with x% and y% attributes.
What is maximum possible percentage of x&y attributes? We have to choose lesser number between x and y.
What is minimum possible percentage of x&y attributes? It is possible, when 100-x% elements have y attribute. So, for x&y y - (100-x) remains. You can see illustrations in my previous post one more time.

I have read this and the illustration multiple times. The min part still seems hazy to me

What I understand is you are applying (A U B) = A + B - ( A N B )

We will have min (A N B) when we have min A and min B values. Is that what you are saying?

If my interpretation is incorrect, can you/X2suresh take another stab?

Thanks
Manager
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Re: PS-Venn Diagrams [#permalink]  08 Jul 2009, 17:58
I also am not seeing the logic here. How do you solve using a venn diagram?
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Re: PS-Venn Diagrams [#permalink]  23 Oct 2009, 23:52
100 - (30 + 25 + 20) = 25
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Re: PS-Venn Diagrams [#permalink]  03 Dec 2009, 02:51
Really need help on this one... I also need a good review about Venn Diagrams and their formulas. Completely forgot everything
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Re: PS-Venn Diagrams [#permalink]  05 Dec 2009, 11:22
Although I did solve this one correctly but when I saw walker's explanation - it took sometime get the soln in my brain as another way of solving this Q. Anyway my way here follows -

Least nos of people who like A and B = 70 +75 - 100 = 45%
Least nos of people who like B and C = 75 +80 - 100 = 55%
Least nos of people who like A and C = 70 +80 - 100 = 50%

Now using the formula
A u B u C = n(A) + n(B) + n(c) - n(A n B) - n(B n C) - n(A n C) + n( All Three)
So we get, 70 + 75 + 80 -45 - 55 - 50 + n(All Three) = 100
Which implies - n(All three) = 100 -75 = 25%

Let me know what u guys think of this approach..

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CEO
Status: Nothing comes easy: neither do I want.
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Re: PS-Venn Diagrams [#permalink]  12 Jan 2010, 10:57
1
KUDOS
Although I did solve this one correctly but when I saw walker's explanation - it took sometime get the soln in my brain as another way of solving this Q. Anyway my way here follows -

Least nos of people who like A and B = 70 +75 - 100 = 45%
Least nos of people who like B and C = 75 +80 - 100 = 55%
Least nos of people who like A and C = 70 +80 - 100 = 50%

Now using the formula
A u B u C = n(A) + n(B) + n(c) - n(A n B) - n(B n C) - n(A n C) + n( All Three)
So we get, 70 + 75 + 80 -45 - 55 - 50 + n(All Three) = 100
Which implies - n(All three) = 100 -75 = 25%

Let me know what u guys think of this approach..

This one is very gud but lengthy approach.

Min Who like all three = total - ( who doesn't like any one of all)

= 100- ( 100- 70 + 100-75 + 100-80) = 100-75 = 25/

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Manager
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Re: PS-Venn Diagrams [#permalink]  12 Jan 2010, 16:20
nice one thanks for the explanation
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Re: PS-Venn Diagrams [#permalink]  12 Jan 2010, 17:08
I3igDmsu wrote:
I also am not seeing the logic here. How do you solve using a venn diagram?

You can probably get away with using 1 venn diagram with three circles, but I found it easier to use 2.

Venn 1
cirlce 1 people who like A:70%
circle 2 people who like B: 75%
overlap: 70+75-100=45

Venn 2
circle 1 people who like both A&B 45%
circle 2 people who like C 80%
overlap: 80 + 45 - 100 = 25

Thus min =25%

that help at all?
Intern
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Re: PS-Venn Diagrams [#permalink]  26 Oct 2010, 05:12
Can someone explain this one with the help of vein diagrams ???

I understand that this will be a bit lengthy.

Thanks-V
Manager
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Re: PS-Venn Diagrams [#permalink]  27 Oct 2010, 03:38
Still Confuse??? Please some one can give me the clear ans???
Re: PS-Venn Diagrams   [#permalink] 27 Oct 2010, 03:38
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