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# m25#28

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26 Sep 2010, 15:53
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Each shelf of a bookcase contains 24 books. If the librarian took out 42 books and rearranged the remaining books so that all shelves but one contained 16 books and the last shelf contained 22 books, how many shelves does the bookcase have?

(A) 4
(B) 5
(C) 6
(D) 8
(E) 9

[Reveal] Spoiler: OA
C

Source: GMAT Club Tests - hardest GMAT questions

Is there another way to solve this question ? like plug in or back solving etc.
Thanks
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26 Sep 2010, 15:59
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The question says that initially each shelf has 24 books

Then after 42 are removed, one shelf is left with 22 and all the others with 16
So if there are x shelves, x-1 are left with 16 and the xth one with 22

Hence the equation :

24 x = 42 + 16 (x-1) + 22
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30 Nov 2010, 05:18
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I solved it this way..

each shelf contained 24 and after it contained 16 - so 8 books were taken out of each shelf

but for the last shelf only 22 books remained, so only 2 books were taken out..

so out of n-1 shelves a total 42-2 = 40 books were taken out
which means 8* (n-1) = 40 which gives n=6
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30 Oct 2012, 03:38
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Expert's post
shrive555 wrote:
Each shelf of a bookcase contains 24 books. If the librarian took out 42 books and rearranged the remaining books so that all shelves but one contained 16 books and the last shelf contained 22 books, how many shelves does the bookcase have?

(A) 4
(B) 5
(C) 6
(D) 8
(E) 9

[Reveal] Spoiler: OA
C

Source: GMAT Club Tests - hardest GMAT questions

Is there another way to solve this question ? like plug in or back solving etc.
Thanks

Each shelf of a bookcase contains 24 books. If the librarian took out 42 books and rearranged the remaining books so that all shelves but the last one contained 16 books and the last shelf contained 22 books, how many shelves does the bookcase have?

A. 4
B. 5
C. 6
D. 8
E. 9

Denoting $$x$$ the number of the shelves, we can build an equation: $$24x=16(x-1)+22+42$$. Solving the equation, we get $$x=6$$.

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26 Sep 2010, 17:21
All shelves but one contained 16 books

i thought out of X shelves one shelve contain 16 and the last one 22.
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30 Nov 2010, 03:57
D.

n = no of shelves
24*n -42=16*n+22
n=8

Posted from my mobile device
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30 Nov 2010, 04:06
Obviously I am wrong. Solving mentally and using the mobile sceen is obviously not the right way to solve such problems.
So the new equation is
24*n-42=16*(n-1)+ 22
n=6 hence c

the best way to solve this is by creating an equation.
Even for plugging numbers you need to get the equation right.

Posted from my mobile device
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30 Nov 2010, 05:23
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before taking the 42 books out , we have total no. of books = 24x where x can be taken as no. of selves/...
now after taking 42 books, there there are 16 books present in (x-1) selves and 22 books present in last self.. so we have no. of books = 42+16(x-1)+22

Equating we get

24x = 42+16(x-1)+22
24x = 42+16x-16+22
8x = 48
x=6
therefore total no. of selves = 6
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30 Nov 2010, 08:11
sleekmover wrote:
D.

n = no of shelves
24*n -42=16*n+22
n=8

Posted from my mobile device

i think you have made a mistake.

the equation will be:
24*n-42=16(n-1)+22

hence,
n =6.
final ans is 6.
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30 Nov 2010, 12:02
sonnco wrote:
sleekmover wrote:
Obviously I am wrong. Solving mentally and using the mobile sceen is obviously not the right way to solve such problems.
So the new equation is
24*n-42=16*(n-1)+ 22
n=6 hence c

the best way to solve this is by creating an equation.
Even for plugging numbers you need to get the equation right.

Posted from my mobile device

I made the same mistake the first time.

+1 made the same mistake but not sure if C is the right answer......

backsolving works for both

ans 6: $$24(6) = (6-1)*16 +22+42 , 144 = 5*16 +64= 80+64=144$$
ans 8: $$24(8) = 42+22+(16)(8) , 192 = 64+148 = 64+148=192$$

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30 Nov 2010, 13:47
No need to adjust for n-1, this is the equation i got:

16n + 6 = 24n -42

Left: The last shelf contains 6 more than the rest
Right: The number of books before any are removed.
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02 Dec 2011, 06:56
Two ways to solve this.

1) using the equation which I suggest because it is the quickest.

24x - 42= 16x +6
48= 8x
x= 6

2) if you're not good with forming equations plug in the answers and always start with the median of the choices. C happened to be the right choice so it would be quick. But if it wasn't C the number you got would indicate whether you choice needed to be higher or lower.
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04 Dec 2011, 00:40
x- number of shelves.

(24x-42) = 16(x-1)+ 22
as per the data given in the question.

Solving further, x=6.
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04 Dec 2011, 23:53
24X- 42 = 16(x-1) +22
24x-16x = 48
8X = 48
X = 6
C
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04 Feb 2012, 21:06
the wording of this question was confusing.... When it said all shelves but one had 16 books and the last one had 22... It sounded as if one shelf was left with no books then others had 16 books then the last one had 22 books.

16(x-2) + 22. Confusing...
However i understand the X-1 as well.
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04 Dec 2012, 11:33
24 books in each shelf
post taking out 42 books -16 in each shelf and 22 in last
all shelf will have 8 booksless ((24-16) and one shelf will have 2 books less(24-22)
so, 8books *5shelves + 2book * 1 shelf = 42, which is the exact no of books taken out from the shelf of 24
hence the answer is 5+1=6 shelves

a better way to solve such problems would be to create an equation with 1 variable as the process above can get complicated if the no. of shelves are more or books are more or both

24n-42= 16(n-1)+22 (n=no. of shelves)
8n= 48
n=6
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22 Jun 2013, 14:38
There is some logic that I'm missing. If 42 books are removed and yet replaced, it should have a net zero effect, in theory..
Why must (+/-) 42 books be in the equation?

Thanks for your help with this
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28 Nov 2013, 21:00
mejia401 wrote:
There is some logic that I'm missing. If 42 books are removed and yet replaced, it should have a net zero effect, in theory..
Why must (+/-) 42 books be in the equation?

Thanks for your help with this

Hi mejia 401,

The quiz says that the librarian took 42 books and then rearranged the remaining books. It means that she/he rearranged the (x-42) books. (x: total book). The quiz does not says that she/he replace the missed books.
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01 Dec 2013, 09:46
IMO C.

I solved this question in the following way...
Let the no. of shelfs be x.

So, 24x - 42 = 16 (x-1) + 22(1)
x = 6.
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03 Dec 2013, 09:44
My approach:

total of books= 24*(X), where X is number of shelves
total of books= 42+16*(X-1)+22
Resolving for X=6
Re: m25#28   [#permalink] 03 Dec 2013, 09:44
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# m25#28

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