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In a class of 30 students, 2 students did not borrow any [#permalink]
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30 Sep 2010, 11:17
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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
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Re: max books [#permalink]
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30 Sep 2010, 11:22
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 6032=28 books are left to distribute among 3024=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 2815=13 books. Answer: D. Hope it's clear.
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Re: max books [#permalink]
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30 Sep 2010, 11:28
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(D), 13
We know that 2 students borrowed 0 books, 12 borrowed 1 book, 10 borrowed 2 books, and 6 borrowed 3 or more books. The average of books per student is 2.
Let a, b, c, d, e, and f be the number of books borrowed by each of the 6 students who borrowed 3 or more.
So we have:
\(\frac{12 + 20 + a + b + c + d + e + f}{30} = 2\)
\(a + b + c + d + e + f = 28\)
Now, to maximize one of these, we need to minimize the other 5. So set them all equal to 3:
\(3 + 3 + 3 + 3 + 3 + f = 28\)
\(f = 28  15 = 13\)
So the maximum is 13.



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Re: max books [#permalink]
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30 Sep 2010, 11:55
Total book borrowed = 30*2 = 60 2 borrowed 0 books, 12 borrowed 1 book, 10 borrowed 2 books; So that accounts for 32 books, leaving 28 books for the 6 students And we know that each of these had atleast 3 books To maximize the highest number of books, give all but one student 3 books (the minimum they must have) and all the rest to the last student So 5 students get a total of 15 books; leaving 13 for the last student. Answer = (D)
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In a class of 30 students, 2 students did not borrow any [#permalink]
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25 Mar 2012, 11:30
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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



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Re: Word problems [#permalink]
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25 Mar 2012, 11:33
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 6032=28 books are left to distribute among 3024=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 2815=13 books. Answer: D. 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, 01:05
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, 05:27



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Re: In a class of 30 students, 2 students did not borrow any [#permalink]
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17 Feb 2014, 08:32
Option D. A total of 2(no book)+12(1 book)+10(2 books)=24 students borrowed 32 books. Total books borrowed=30*2=60 Books left=28 Rest of the students borrowed at least 3 books each=>6*3=18 Now to maximize books borrowed by any one individual we'll suppose,2818=10 have been borrowed by one person only. Max total becomes=3+10=13
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Re: In a class of 30 students, 2 students did not borrow any [#permalink]
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26 Jan 2015, 12:06
D  13.....Distribute 3 books to remaining 6....total will come 50....but our total should be 60......so 6050 = 10....add original 3....10+3 = 13



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Re: In a class of 30 students, 2 students did not borrow any [#permalink]
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02 Feb 2015, 22:51
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Average for 30 students = 2, so total books = 60 Unallocated books = 60  (1*12 + 2*10+3*6) = 60  50 = 10 Maximum books per individual possible = 10+3 = 13 Answer = D
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Re: In a class of 30 students, 2 students did not borrow any [#permalink]
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31 Oct 2016, 11:02
X/30 (total students) = 2 > x = 60 (# of books checked out)
We have 12+2(10)+6(at least 3), leaving us with 10 to account for, thus one of the students who borrowed at least 3, could add on an additional 10 books, walking out with a total of 13.



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Re: In a class of 30 students, 2 students did not borrow any [#permalink]
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31 Oct 2016, 12:09
here is the solution of this problem, Hope it is clear
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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, 17:07
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 6032 = 28 books Now the least books borrows by them => 3 So for the maximum number => 3,3,3,3,3,3,x => x= 2815 = 13
Hence D
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Re: In a class of 30 students, 2 students did not borrow any [#permalink]
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06 Jan 2018, 23:30
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