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

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Joined: 21 Sep 2006
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In a class of 30 students, 2 students did not borrow any  [#permalink]

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Updated on: 02 Oct 2006, 13:34
1
1
00:00

Difficulty:

45% (medium)

Question Stats:

63% (01:26) correct 37% (01:08) wrong based on 121 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

Originally posted by $uckafr33 on 02 Oct 2006, 10:39. Last edited by$uckafr33 on 02 Oct 2006, 13:34, edited 1 time in total.
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Posts: 631
Re: In a class of 30 students, 2 students did not borrow any  [#permalink]

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02 Oct 2006, 11:57
Intern
Joined: 21 Sep 2006
Posts: 42
Re: In a class of 30 students, 2 students did not borrow any  [#permalink]

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02 Oct 2006, 12:01

GMAT Instructor
Joined: 04 Jul 2006
Posts: 1251
Re: In a class of 30 students, 2 students did not borrow any  [#permalink]

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02 Oct 2006, 12:03
$uckafr33 wrote: In a class of 30 students, 2 students did not borrow any books from the library, 12 students 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 student could have borrowed? a) 3 b) 5 c) 8 d) 13 e) 15 Let's minimize the number of books that the 30 could borrow, according to the guidelines: 2(0)+12(1)+10(2)+6(3)=12+20+18=50. But we know that the sum is 30*2=60, so there are 10 books unaccounted for- give them to a GMAT student who has already borrowed 3 ==>3+10=13 SVP Joined: 01 May 2006 Posts: 1775 Re: In a class of 30 students, 2 students did not borrow any [#permalink] ### Show Tags 02 Oct 2006, 12:05 (D) for me..... and I think that there is typo problem As we look for the max x of books that a student can borrow, we can write av(students) = 2 = (2*0 + 12*1 + 10*2 + (30-(2+12+10+1))*3 + 1*x) / 30 <=> 60 = 12 + 20 + 15 + x <=> x = 13 Retired Moderator Joined: 05 Jul 2006 Posts: 1722 Re: In a class of 30 students, 2 students did not borrow any [#permalink] ### Show Tags 02 Oct 2006, 13:28 10 people each borrowed 12 books..........this is wrong i think it is a typo....please check Intern Joined: 21 Sep 2006 Posts: 42 Re: In a class of 30 students, 2 students did not borrow any [#permalink] ### Show Tags 02 Oct 2006, 13:33 yezz wrote: 10 people each borrowed 12 books..........this is wrong i think it is a typo....please check My apologies...there is a typo. 10 students each borrowed 2 books. But thanks understand how to solve this now. Senior Manager Joined: 13 Sep 2006 Posts: 254 Location: New York Re: In a class of 30 students, 2 students did not borrow any [#permalink] ### Show Tags 03 Oct 2006, 12:21 1 One more for 13... 2 students borrowed 0 books (TOTAL 0 books) 12 students borrowed 1 book each (TOTAL 12 Books) 10 students borrowed 2 books each (TOTAL 20 Books) 32 books so far for 24 students hence 6 students left unaccounted for. Here is where I picked numbers. Say one student picks 13 then total number of books borroed is 45 and 5 students remain borrowing at lease 3 a piece (3*15 = 15). 15 +45 = 60 and 60 divided by 30 equals the mean of 2. Retired Moderator Joined: 20 Dec 2010 Posts: 1809 Re: In a class of 30 students, 2 students did not borrow any [#permalink] ### Show Tags 03 Jul 2011, 09:02 5 1$uckafr33 wrote:
In a class of 30 students, 2 students did not borrow any books from the library, 12 students 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 student could have borrowed?

a) 3 b) 5 c) 8 d) 13 e) 15

Total-> 30 students
0 book-> 2 students
1 book-> 12 students
2 books-> 10 students

Remaining 6 students:
To maximize the number of books taken by any 1 student, let's give the rest of the students exactly the minimum possible i.e. 3 AND give the rest "x" to the one student who is going to take the maximum.

$$\frac{2*0+1*12+2*10+3*5+x*1}{30}=2$$

$$\frac{47+x}{30}=2$$

$$x=60-47=13$$

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

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04 Jul 2011, 09:59
kevincan wrote:

Let's minimize the number of books that the 30 could borrow, according to the guidelines: 2(0)+12(1)+10(2)+6(3)=12+20+18=50. But we know that the sum is 30*2=60, so there are 10 books unaccounted for- give them to a GMAT student who has already borrowed 3 ==>3+10=13

Even i will go with the same approach and hence the same answer....
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Manager
Status: ==GMAT Ninja==
Joined: 08 Jan 2011
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Schools: ISB, IIMA ,SP Jain , XLRI
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Re: In a class of 30 students, 2 students did not borrow any  [#permalink]

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04 Jul 2011, 10:00
fluke wrote:

Total-> 30 students
0 book-> 2 students
1 book-> 12 students
2 books-> 10 students

Remaining 6 students:
To maximize the number of books taken by any 1 student, let's give the rest of the students exactly the minimum possible i.e. 3 AND give the rest "x" to the one student who is going to take the maximum.

$$\frac{2*0+1*12+2*10+3*5+x*1}{30}=2$$

$$\frac{47+x}{30}=2$$

$$x=60-47=13$$

Ans: "D"

That was quite smart fluke
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WarLocK
_____________________________________________________________________________
The War is oNNNNNNNNNNNNN for 720+
see my Test exp here http://gmatclub.com/forum/my-test-experience-111610.html
do not hesitate me giving kudos if you like my post.

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Joined: 03 Mar 2011
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Re: In a class of 30 students, 2 students did not borrow any  [#permalink]

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08 Jul 2011, 18:29
Thanks Fluke for the explanation. one more kudo
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Joined: 02 Sep 2009
Posts: 52285
Re: In a class of 30 students, 2 students did not borrow any  [#permalink]

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22 Jan 2015, 03:35
\$uckafr33 wrote:
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

"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.

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

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08 Jan 2019, 00:17
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Re: In a class of 30 students, 2 students did not borrow any &nbs [#permalink] 08 Jan 2019, 00:17
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