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Director  Status: Impossible is not a fact. It's an opinion. It's a dare. Impossible is nothing.
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In a class of 30 students, 2 students did not borrow any  [#permalink]

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Difficulty:   45% (medium)

Question Stats: 67% (02:22) correct 33% (02:48) wrong based on 485 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
Math Expert V
Joined: 02 Sep 2009
Posts: 58409
Re: Word problems  [#permalink]

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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: max books  [#permalink]

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5
2
(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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Math Expert V
Joined: 02 Sep 2009
Posts: 58409
Re: max books  [#permalink]

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3
6
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: max books  [#permalink]

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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.

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

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2
1
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
Intern  Joined: 30 Nov 2011
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Re: In a class of 30 students, 2 students did not borrow any  [#permalink]

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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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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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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,28-18=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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D - 13.....Distribute 3 books to remaining 6....total will come 50....but our total should be 60......so 60-50 = 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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1
Average for 30 students = 2, so total books = 60

Un-allocated books =

60 - (1*12 + 2*10+3*6) = 60 - 50 = 10

Maximum books per individual possible = 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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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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here is the solution of this problem,

Hope it is clear
Attachments IMAG0321.jpg [ 774.63 KiB | Viewed 5145 times ]

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GRE 1: Q169 V154 Re: In a class of 30 students, 2 students did not borrow any  [#permalink]

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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]

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nusmavrik 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

Since the average number of books per student was 2, the total number of books borrowed was 2 x 30 = 60 books.

The number of books borrowed by the students who borrowed two or fewer books is 2 x 0 + 12 x 1 + 10 x 2 = 32.

These 32 books were borrowed by 2 + 12 + 10 = 24 students.

So we have 60 - 32 = 28 books left for the remaining 6 students. Since we want to maximize the number of books borrowed by a single student, we must minimize the number of books borrowed by the other 5 students. We see that if 5 of these students borrowed 3 books each, then we have 28 - 15 = 13 books for the last student.

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

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_________________ Re: In a class of 30 students, 2 students did not borrow any   [#permalink] 15 Oct 2019, 08:51
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