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Senior | Next Rank: 100 Posts
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by ramonsa » Thu May 07, 2009 11:46 am
Hello ... need some help to see this problem.

There are 26 students who have read a total of 56 books among them. The only books they have read, though, are Aye,Bee,Cod, and Dee. If 10 students have only read Aye, and 8 students have read only Cod and Dee, what is the smallest number of books any of remaining students could have read?

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by stevestein » Thu May 07, 2009 1:02 pm
Among the 26 students total, we have solid information about the reading accomplishments of 18 of the students:

10 students have each read exactly one book = 10 books read.
8 students have read exactly two books = 16 books read.

At this point, we know that 26 books (26 out of 50 total books) have been read by those 18 kids (18 out of 26 kids).

This means that the 8 remaining students must read the 30 remaining books.

What is the smallest number that any of these students could read?

If we wish to minimize the number of books read by one of these remaining students, we should maximize the number of books read by the others.

So, if 7 of the remaining 8 students read all 4 books, that gives us a total of 28 books between them, leaving 2 books to be read by the last remaining student.

Thus, 2 is the minimum number of books that could be read by any of the remaining students.

I hope that's helpful! Let me know.
Steve Stein
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