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On a given week, the classical literature section in a certain library

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On a given week, the classical literature section in a certain library  [#permalink]

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New post 27 Sep 2016, 08:13
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A
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C
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  45% (medium)

Question Stats:

65% (02:02) correct 35% (02:24) wrong based on 106 sessions

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On a given week, the classical literature section in a certain library had 40 different books, all of which were in stock on the shelf on Monday morning. If 50 percent of the books that were borrowed during the week were returned to the library on or before Saturday morning of that same week, and if there were at least 22 books on the shelf that Saturday morning, what is the greatest number of the books that could have been borrowed during the week?

A. 40
B. 38
C. 36
D. 34
E. 32
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Re: On a given week, the classical literature section in a certain library  [#permalink]

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New post 27 Sep 2016, 10:28
2
1
N = Total number of books = 40
B = Number of borrowed books = ?

Number of books available >= 22
(B/2) + (N - B) >= 22
B + 2N - 2B >= 44
2N - B >= 44
B <= 2(40) - 44
B <= 36
Max possible number of borrowed books = 36

Answer: C
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Re: On a given week, the classical literature section in a certain library  [#permalink]

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New post 27 Sep 2016, 11:58
2
A) Not possible 40 books borrowed 20 would have been returned but we had 22 on Saturday
B) 38 would mean 21 books
C) 4+ 18 =22 books Correct 36 borrowed 4 left half (18) returned.

Ans c
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Re: On a given week, the classical literature section in a certain library  [#permalink]

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New post 21 Apr 2017, 17:06
can we please ask the experts to provide additional ways of solving this problem? i'm not 100% entirely with either approach presented. thank you!
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Re: On a given week, the classical literature section in a certain library  [#permalink]

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New post 02 May 2017, 07:13
On a given week, the classical literature section in a certain library had 40 different books, all of which were in stock on the shelf on Monday morning. If 50 percent of the books that were borrowed during the week were returned to the library on or before Saturday morning of that same week, and if there were at least 22 books on the shelf that Saturday morning, what is the greatest number of the books that could have been borrowed during the week?

A. 40
B. 38
C. 36
D. 34
E. 32


This is how I solved:


(1) set up equations:

b+n=40

\(\frac{b}{2}\)+n=22


(2) simplify:

\(\frac{b}{2}\)+n=22 --> b+2n=44


(3) combine:

(b+n-40) - (b+2n=44) = -n=-4 --> n=4.


(4) re-plug into expression:

b+2n=44 --> b+2(4)=44 --> b+8=44 --> b=36. (C).

Kudos please if helpful :)
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Re: On a given week, the classical literature section in a certain library  [#permalink]

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New post 03 May 2017, 15:06
book borrowed=x
(40-x)+0.5x=22
x=36
answer:C
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Re: On a given week, the classical literature section in a certain library  [#permalink]

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New post 04 May 2017, 00:12
Nevernevergiveup wrote:
On a given week, the classical literature section in a certain library had 40 different books, all of which were in stock on the shelf on Monday morning. If 50 percent of the books that were borrowed during the week were returned to the library on or before Saturday morning of that same week, and if there were at least 22 books on the shelf that Saturday morning, what is the greatest number of the books that could have been borrowed during the week?

A. 40
B. 38
C. 36
D. 34
E. 32



22+(b/2) 40
b = 36

regards
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Re: On a given week, the classical literature section in a certain library  [#permalink]

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New post 10 May 2017, 22:48
Total no. of books at the starting of Week(Munday) = 40.
Total no. of books at the end of the week (Sunday) = 22.

Difference = 40 - 22 = 18.

18 books are not returned. 18 = 50% of total books borrowed.

Hence, 18 * 2 = 36 total books borrowed.

Ans: Option C
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On a given week, the classical literature section in a certain library  [#permalink]

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New post 21 Sep 2018, 07:42
Nevernevergiveup wrote:
On a given week, the classical literature section in a certain library had 40 different books, all of which were in stock on the shelf on Monday morning. If 50 percent of the books that were borrowed during the week were returned to the library on or before Saturday morning of that same week, and if there were at least 22 books on the shelf that Saturday morning, what is the greatest number of the books that could have been borrowed during the week?

A. 40
B. 38
C. 36
D. 34
E. 32



hi pushpitkc is my solution correct ? :)

\(40 - 0.5x = 22\)
\(40-22 = 0.5x\)
\(18 = 0.5x\)
\(x = 36\)
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Re: On a given week, the classical literature section in a certain library  [#permalink]

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New post 21 Sep 2018, 12:09
dave13 wrote:
Nevernevergiveup wrote:
On a given week, the classical literature section in a certain library had 40 different books, all of which were in stock on the shelf on Monday morning. If 50 percent of the books that were borrowed during the week were returned to the library on or before Saturday morning of that same week, and if there were at least 22 books on the shelf that Saturday morning, what is the greatest number of the books that could have been borrowed during the week?

A. 40
B. 38
C. 36
D. 34
E. 32



hi pushpitkc is my solution correct ? :)

\(40 - 0.5x = 22\)
\(40-22 = 0.5x\)
\(18 = 0.5x\)
\(x = 36\)


dave13 - Since we require the greatest number of books, it is okay to equate. And yes, your solution is correct :)
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Re: On a given week, the classical literature section in a certain library &nbs [#permalink] 21 Sep 2018, 12:09
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