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by 2010gmat » Tue Nov 24, 2009 9:00 pm
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?


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by papgust » Tue Nov 24, 2009 10:19 pm
IMO 6 shelves.

Given: 24 books in each shelf.

If the librarian takes 42 books, it will be 8 books from each shelf (i.e. 40) and 2 from 1 shelf (As the last shelf has 22 books)

8* (5 shelves) + 2 * (1 shelf) = 42.

Total no. of shelves = 5+1 = 6

I guess that GMAT will give this kind of a problem in a more complicated manner.
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by 2010gmat » Wed Nov 25, 2009 12:21 am
i cud nt understand ur approach...actually 4 and 8 will also satisfy this condition...
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by ershovici » Wed Nov 25, 2009 1:06 am
I solved it with backsolving
Look:
I started with 6 (Kaplan sugests taht we should start with the median number), so the result is 6*24=144(books), then 144-42=102(reamaining books). From this books (102-22)/16=5, so we have 5 shelves with 16 books each, and 1 with 22.
And 6 is the right answer
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by 2010gmat » Wed Nov 25, 2009 1:16 am
right..6 is the answer...so simple...i dont know wat i was trying to do :'(

8(n-1) + 2 = 42 ... n = 6...took just 20 sec to solve it....think am stressed out....need a break
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by beatthegmat2910 » Wed Nov 25, 2009 11:18 am
This is a very straightforward question with two conditions.

Now, let T be the total number of books. and x be the no. of shelves.
Before the books were rearranged, all shelves had 24 books each.
So, T=24x

Now, 42 books were removed, and all shelves except one had 16 books and the last shelf had 22 books.
So, T-42 = (x-1)16 + 22
T = 16x+48

Equating 1 and 2
24x = 16x+48
Solving for x --
x = 6
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by rahul.s » Sat Jan 23, 2010 1:33 am
yeah, i tried back solving as well. it makes the process simpler.
i always start with C, since the options on the GMAT are always in the ascending or descending order.

let's start with 6. so 24*6 = 144 .
the librarian removed 42 books. so 144 - 42 = 102
all shelves but one contain 16 books. the last shelf contains 22.
so 16*5 = 80, which leaves us with 22 for the last book shelf. so 5 + 1 = 6

C it is!
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by rahul.s » Sat Jan 23, 2010 1:38 am
papgust wrote:IMO 6 shelves.

Given: 24 books in each shelf.

If the librarian takes 42 books, it will be 8 books from each shelf (i.e. 40) and 2 from 1 shelf (As the last shelf has 22 books)

8* (5 shelves) + 2 * (1 shelf) = 42.

Total no. of shelves = 5+1 = 6

I guess that GMAT will give this kind of a problem in a more complicated manner.
this method is the best. but we need to think of it during the test, and we need to solve this within 100 seconds. so if we can't recollect this technique, back solving's a good backup :D
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by papgust » Sat Jan 23, 2010 6:28 am
Yup you are right. This can be solved using logic rather than equations. But it's doable within 100 seconds. If not, i agree that backsolving is the best for these kinds of problems.
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