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In a class of 30 students, 2 students did not borrow any

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In a class of 30 students, 2 students did not borrow any [#permalink] New post 25 Mar 2012, 10:30
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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 each 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
[Reveal] Spoiler: OA
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Re: Word problems [#permalink] New post 25 Mar 2012, 10:33
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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 borrowed at least 3 books. If the average number of books per student was 2, what is the maximum number of books any single student could have borrowed?

A. 3
B. 5
C. 8
D. 13
E. 15

"The average number of books per student was 2" means that total of 2*30=60 books were borrowed;
2+12+10=24 students borrowed total of 2*0+12*1+10*2=32 books;
So 60-32=28 books are left to distribute among 30-24=6 students, these 6 are "the rest who borrowed at least 3 books";

To maximize the number of books one student from above 6 could have borrowed we should minimize the number of books other 5 students from 6 could have borrowed. Minimum these 5 students could have borrowed is 3 books per student, so total number of books they could have borrowed is 5*3=15 books. So the 6th student could have borrowed is 28-15=13 books.

Answer: D.

Hope it's clear.
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Intern
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Joined: 30 Nov 2011
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Kudos [?]: 10 [0], given: 23

Re: In a class of 30 students, 2 students did not borrow any [#permalink] New post 26 Mar 2012, 00:05
thanks Bunuel, explanation very clear.
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Re: In a class of 30 students, 2 students did not borrow any [#permalink] New post 14 Jun 2013, 04:27
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Bumping for review and further discussion*. Get a kudos point for an alternative solution!

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Re: In a class of 30 students, 2 students did not borrow any   [#permalink] 14 Jun 2013, 04:27
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