12x-21=(x-1)*8+11goyalsau wrote:Not able to understand the language
12x-21=8x-8+11
4x=24
x=6
Number of bookshelves =6
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Source: Beat The GMAT — Problem Solving |
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sgmuthukumar
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12x-21=8x-8+11
4x=24
x=6
Number of bookshelves =6
Solution:
Let the number of shelves be n.
Since each shelf contains 12 books, total number of books in all n shelves is 12n.
When 21 books are removed, the remaining number of books is 12n - 21.
Now these 12n - 21 books are rearranged so that (n-1) shelves have 8 books and 1 shelf has 11 books.
So (n-1) shelves now have 8(n-1) books and all n shelves have 8(n-1) + 11 books.
Or 12n - 21 = 8(n-1) + 11.
Or 4n = 24.
Or n = 6.
Or the bookcase has 6 shelves.
Let the number of shelves be n.
Since each shelf contains 12 books, total number of books in all n shelves is 12n.
When 21 books are removed, the remaining number of books is 12n - 21.
Now these 12n - 21 books are rearranged so that (n-1) shelves have 8 books and 1 shelf has 11 books.
So (n-1) shelves now have 8(n-1) books and all n shelves have 8(n-1) + 11 books.
Or 12n - 21 = 8(n-1) + 11.
Or 4n = 24.
Or n = 6.
Or the bookcase has 6 shelves.
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Might be easiest just to plug in the answers, which represent the number of shelves.goyalsau wrote:Not able to understand the language
Answer choice C:
6 shelves, 12 books per shelf, means 6*12 = 72 books.
Removing 21 books leaves 72-21 = 51 books.
8 books on all but 1 shelf = 8*5 = 40 books.
51-40 = 11 books for the last shelf. Success!
The correct answer is C.
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pradeepkaushal9518
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great method of solving
actually question is each self can have 12. so suppose there are x selfs then total books will be 12x
but when 21 books are taken out and rearrange then the arranging changed
self contains 8 books and only one contains 11
so 12x-21=(x-1)8+11
solving x=6
actually question is each self can have 12. so suppose there are x selfs then total books will be 12x
but when 21 books are taken out and rearrange then the arranging changed
self contains 8 books and only one contains 11
so 12x-21=(x-1)8+11
solving x=6
A SMALL TOWN GUY
Thanks for your work Guys,
But i had the problem in understanding the language of the problem it says
So that all shelves but one contained 8 books and the last shelf contained 11 books.
You guys are absolutely right in your approach but can you please explain the above statement.
I know this may be part of CR section but still I would request guys to help me understand the sentence.
Means where to actually separate those two things all but one.
But i had the problem in understanding the language of the problem it says
So that all shelves but one contained 8 books and the last shelf contained 11 books.
You guys are absolutely right in your approach but can you please explain the above statement.
I know this may be part of CR section but still I would request guys to help me understand the sentence.
Means where to actually separate those two things all but one.
