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# According to a survey, at least 70% of people like apples, a

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According to a survey, at least 70% of people like apples, a [#permalink]

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03 Apr 2009, 22:12
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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%

OPEN DISCUSSION OF THIS QUESTION IS HERE: according-to-a-survey-at-least-70-of-people-like-apples-140725.html
[Reveal] Spoiler: OA

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rampuria

Last edited by Bunuel on 13 Aug 2014, 23:50, edited 2 times in total.
RENAMED THE TOPIC.
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Re: According to a survey, at least 70% of people like apples, a [#permalink]

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04 Apr 2009, 22:37
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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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Re: According to a survey, at least 70% of people like apples, a [#permalink]

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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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rampuria

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Re: According to a survey, at least 70% of people like apples, a [#permalink]

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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: According to a survey, at least 70% of people like apples, a [#permalink]

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06 Apr 2009, 10:35
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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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Re: According to a survey, at least 70% of people like apples, a [#permalink]

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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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Re: According to a survey, at least 70% of people like apples, a [#permalink]

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08 Apr 2009, 13:27
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: According to a survey, at least 70% of people like apples, a [#permalink]

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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?

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Re: According to a survey, at least 70% of people like apples, a [#permalink]

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23 Oct 2009, 23:52
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100 - (30 + 25 + 20) = 25
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Re: According to a survey, at least 70% of people like apples, a [#permalink]

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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: According to a survey, at least 70% of people like apples, a [#permalink]

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05 Dec 2009, 11:22
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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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Re: According to a survey, at least 70% of people like apples, a [#permalink]

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12 Jan 2010, 10:57
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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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Re: According to a survey, at least 70% of people like apples, a [#permalink]

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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?
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Re: According to a survey, at least 70% of people like apples, a [#permalink]

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13 Aug 2014, 16:14
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Re: According to a survey, at least 70% of people like apples, a [#permalink]

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13 Aug 2014, 23:51
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%

First of all, let's simplify the question: say there are 100 people. So, we have that at least 70 people like apples, at least 75 like bananas and at least 80 like cherries. Since we want to minimize the group which likes all three, then let's minimize the groups which like each fruit:

80 people like cherries;
75 people like bananas;
70 people like apples.

-----(-----------)---- 80 people like cherries and 20 don't (each red dash represents 5 people who like cherries);
-----(-----------)---- 75 people like bananas and 25 don't (each blue dash represents 5 people who like bananas).

So, we can see that minimum 55 people like both cherries and bananas (11 dashes).

To have minimum overlap of 3, let 20 people who don't like cherries and 25 who don't like bananas to like apples. So, we distributed 20+25=45 people who like apples and 70-45=25 people still left to distribute. The only 25 people who can like apples are those who like both cherries and bananas. Consider the diagram below:

-----(-----)---------- 80 people like cherries and 20 don't (each red dash represents 5 people who like cherries);
-----(-----)---------- 75 people like bananas and 25 don't (each blue dash represents 5 people who like bananas);
-----(-----)---------- 70 people like apples and 30 don't (each green dash represents 5 people who like apples).

Therefore the minimum number of people who like all three is 25.

OPEN DISCUSSION OF THIS QUESTION IS HERE: according-to-a-survey-at-least-70-of-people-like-apples-140725.html
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Re: According to a survey, at least 70% of people like apples, a [#permalink]

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27 Nov 2015, 22:43
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Re: According to a survey, at least 70% of people like apples, a   [#permalink] 27 Nov 2015, 22:43
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