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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%

_________________

Thanks rampuria

Last edited by rampuria on 05 Apr 2009, 08:50, edited 1 time in total.

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.

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.

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

_________________

Your attitude determines your altitude Smiling wins more friends than frowning

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....

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?

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%

Re: PS-Venn Diagrams [#permalink]
12 Jan 2010, 10:57

1

This post received KUDOS

rathoreaditya81 wrote:

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. What about the following approach.

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