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35% (01:16) wrong based on 0 sessions
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 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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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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All shelves but one contained 16 booksi thought out of X shelves one shelve contain 16 and the last one 22. 
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D. n = no of shelves 24*n -42=16*n+22 n=8 Posted from my mobile device 
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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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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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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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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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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=144ans 8: 24(8) = 42+22+(16)(8) , 192 = 64+148 = 64+148=192!!!!!!
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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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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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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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24X- 42 = 16(x-1) +22 24x-16x = 48 8X = 48 X = 6 C
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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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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 Source: GMAT Club Tests - hardest GMAT questions Is there another way to solve this question ? like plug in or back solving etc. Thanks 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. Answer: C.
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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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