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

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Intern
Joined: 21 Sep 2009
Posts: 7

Kudos [?]: 7 [0], given: 1

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

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06 Oct 2009, 12:32
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Question Stats:

61% (01:41) correct 39% (01:06) wrong based on 83 sessions

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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

OPEN DISCUSSION OF THIS QUESTION IS HERE: in-a-class-of-30-students-2-students-did-not-borrow-any-101980.html
[Reveal] Spoiler: OA

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Manager
Joined: 06 Oct 2009
Posts: 68

Kudos [?]: 35 [0], given: 5

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

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06 Oct 2009, 21:05
2 students didn't borrow, so total students who borrowed is 28

Average number of books per student is 2

So total books borrowed is 28x2=56

12 students borrowed each 1 book, so total book these students took= 12 book
10 students borrowed each 2 books, so total book these students took= 20 book

Total book borrowed by above two group of students= 12+20=32

Remaining books available= 56-32= 24
remaining students=28-22=6

6 students borrowed atleast 3 books
to calculate max books one student could have take, let's assume all other 5 students took 3 book each
so 5x3= 15 books

So the 6th student will have 24-15= 9 books(ans)

I hope the explanation is detailed enough

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Senior Manager
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Posts: 318

Kudos [?]: 351 [0], given: 13

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

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06 Oct 2009, 21:26
appuamar wrote:
In a class of 30 students, 2 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 number of books per student is 2, what is the maximum number of books that any single student could have borrowed?

plz explain wid exlanation..

Total # of students = 30
Avg # of books per student = 2
Total # of books = 30*2 = 60
# of student borrowed at least 3 books = 30-2-12-10 = 6
# of books borrowed by above 6 students = 60-(12*1)+(10*2) = 28
Considering that 5 out of above 6 students borrowed only 3 books, # of books borrowed = 5*3 = 15
So maximum # of books borrowed by any single student = 28-15 = 13

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Manager
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In a class of 30 students, 2 students did not borrow any books from [#permalink]

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20 Aug 2010, 02:05
1
KUDOS
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

[Reveal] Spoiler:
Attachment:

Untitled.jpg [ 98.4 KiB | Viewed 1886 times ]

Kudos [?]: 62 [1], given: 15

Math Expert
Joined: 02 Sep 2009
Posts: 42270

Kudos [?]: 132811 [1], given: 12378

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

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20 Aug 2010, 07:35
1
KUDOS
Expert's post
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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Kudos [?]: 132811 [1], given: 12378

Manager
Joined: 01 Jul 2010
Posts: 53

Kudos [?]: 62 [0], given: 15

Schools: LBS, Harvard, Booth, Stanford, ISB, NTU
WE 1: S/W Engineer
Re: In a class of 30 students, 2 students did not borrow any books from [#permalink]

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20 Aug 2010, 08:18
Wow, Couldn't ask for a better explanation!! Thanks a ton!

Kudos [?]: 62 [0], given: 15

Math Expert
Joined: 02 Sep 2009
Posts: 42270

Kudos [?]: 132811 [1], given: 12378

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

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23 Sep 2010, 06:04
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Expert's post
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prashantbacchewar wrote:
I am getting 7. Please post OA.

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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Kudos [?]: 132811 [1], given: 12378

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

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27 Feb 2016, 05:36
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Re: In a class of 30 students, 2 students did not borrow any boo   [#permalink] 27 Feb 2016, 05:36
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