survey on the food preferences of pupils at a school found that 70% of the pupils like pears, 75% like oranges, 80% like bananas and 85% like apples. what is the smallest possible percentage of pupils who like all four of these fruits?

A at least 10% B at least 15% C at least 20%

D at least 25% E at least 70%.

Question

survey on the food preferences of pupils at a school found that 70% of the pupils like pears, 75% like oranges, 80% like bananas and 85% like apples. what is the smallest possible percentage of pupils who like all four of these fruits?

A at least 10%   B at least 15%   C at least 20%

D at least 25%    E at least 70%.

cwrw238 · Answer

nobody can answer this one by the look of it

hero · Answer

It's possible to do it and there are several approaches to it. You can use a counting method to do it but it would take a while. If you consider a class list of 20 people, you could by name create a list of pupils who liked certain fruits in accordance with the percentages and count the number of students who appear in each group. Nothing is impossible if it can be solved using math.

asnaseer · Answer

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I have tried to solve this by imagining that I have 4 strips of paper with markings on them to represent 70%, 75%, 80% and 85%. I have then marked on each paper the region that represents pupils that do NOT like a particular fruit by shading in that region. e.g. for pears, 70% like them and 30% do NOT like them so on the top strip, the 30% region is shaded.
I then tried to arrange the other strips to get worse case scenario - e.g. for the next fruit (oranges at 75%) I assumed that the 30% of pupils that do NOT like pears happen to like oranges. I repeated this process for the other two fruits.
so the common region which represents pupils that like all four cannot be less than 15%.
I don't think I have used any well known method here - just thinking through the problem lead me to this approach. I hope it helps - and also hope it is correct ;-)

interesting problem.