books from the library

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books from the library

by Xbond » Fri Aug 14, 2009 12:40 am
Hi there,

I would like to know the simplest process to resolve this PS. Explanation is requested.

In a class of 30 students, 2 students did not borrow any books from the library, 12 students each borrowed 1 book, 10 students each borrowed 2 books, and the rest of the students borrowed at least 3 books. If the
average (arithmetic mean) number of books borrowed per student was 2, what is the maximum number of books that any single student could have borrowed?

a) 3
b) 5
c) 8
d) 13
e) 15
Source: — Problem Solving |

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by tohellandback » Fri Aug 14, 2009 1:34 am
IMO D

total number of books borrowed=30*2=60

12 students borrow 1book eachi.e 12 books
10 students borrow 2 books each i.e. 20 books

these are fixed, we cannot do anything about them

To maximize the number for any one kid, we need to minimize for the others.
12+10=22. so 28-22=6 students left.
minimize it for 5 kids. they borrow at least 3. let them all borrow 3. total =15

books left=60-12-20-15=13 books
The powers of two are bloody impolite!!

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by Xbond » Mon Aug 17, 2009 5:24 am
many thks guys

OA is D

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by imhimanshu » Mon Aug 17, 2009 6:33 am
@ hell and back..Bingo..!.same aproach followed by me :D