SOLUTION: Out of 100 persons surveyed ,75% had a personal computer ,68% had a dishwasher, 85% had a refrigerator and 80% had a video recorder. How many people had all four items?

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Question 1155837: Out of 100 persons surveyed ,75% had a personal computer ,68% had a dishwasher, 85% had a refrigerator and 80% had a video recorder. How many people had all four items?
Answer by ikleyn(52821)   (Show Source): You can put this solution on YOUR website!
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There is no enough data to answer the question.


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Hello, I got your message (as a comment).

Let me repeat it again: the problem formulation does not bring enough information to be solved.

I found and saw precisely this formulation in other sites in the Internet: I made my own search and research.

Again: all these posts are DEFECTIVE.

Your "solution", which you presented in your comment, is INCORRECT (both solutions).

To disprove it, let consider more simple problem.

    Out of 100 people surveyed, 75 had a PC and 68 had a dishwasher.
    How many people had all these items ?


Let assume that these 100 people are numbered from 1 to 100 and lined in a row.

Let's consider two cases.

    Case 1. These 68 are those with numbers from 1 to 68,

            and these 75 are those with numbers from 1 to 75.


            Then the number of those who has both items is 68.



    Case 2. These 68 are those with numbers from 1 to 68,

            but these 75 are those with numbers from 100 to 26.


            Then the number of those who has both items is from 26 to 68, i.e.  68-25 = 43.

Thus in these different cases we have two different answers.

It means that the problem does not allow to get a UNIQUE answer --- exactly as I stated.


Next.

This forum works THIS WAY:

    The visitor posts the problem.

    If the problem is posed correctly, in a right way, the tutor solves it.

    If the problem is posed INCORRECTLY (as in your case), the tutor NATURALLY does not solve it.

    In this case, the tutor may say to the visitor, that the problem has deficiencies (is DEFECTIVE), 

     but the tutor is not obliged to explain, what the deficiencies are and so on. Such explanation IS NOT the tutor's duty.


    These are VERY NATURAL rules, and it is assumed, that the visitor is so smart and so much educated, that 

    does understand it without repeating explanation.


    Otherwise, this forum would die after one week of work.


These rules are presented somewhere in the special section of the forum,
but they are so OBVIOUS that it would be strange to repeat them again and again.

In each regular day, I serve 10 - 15 - 20 posts/problems from visitors, and, NATURALLY,
have no an opportunity to make so extended explanations.

Next.

To complete my post in positive mode, I will refer to the lessons in this site, which are close to your "problem".

These lessons are
    - Counting elements in sub-sets of a given finite set
    - Advanced problems on counting elements in sub-sets of a given finite set
    - Challenging problems on counting elements in subsets of a given finite set

First of them is introductory lesson.

The other two are advanced.

After reading these lessons, you will understand the subject MUCH BETTER.

And PLEASE, post me some message, confirming that you saw and have read these lines.

If you will post your words to me, then PLEASE REFER to the problem's ID number 1155837.


Happy learning (!)




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