In a class of 30 students, 2 students did not borrow any : GMAT Problem Solving (PS)
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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]

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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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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.

Hope it's clear.
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Re: In a class of 30 students, 2 students did not borrow any [#permalink]

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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]

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14 Jun 2013, 04:27
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]

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29 Dec 2014, 03:40
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Re: In a class of 30 students, 2 students did not borrow any [#permalink]

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16 Jun 2016, 08:35
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Re: In a class of 30 students, 2 students did not borrow any [#permalink]

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18 Dec 2016, 16:07
Amazing Official Question.
Here is what i did in this Question =>

12*1=> 12
10*2=> 20
So 32 books are borrowed by 22 students
Sum(30)=2*30=60

Hence 6 students borrow 60-32 = 28 books
Now the least books borrows by them => 3
So for the maximum number => 3,3,3,3,3,3,x => x= 28-15 = 13

Hence D

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Re: In a class of 30 students, 2 students did not borrow any   [#permalink] 18 Dec 2016, 16:07
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