A bookcase has s shelves with n books on each shelf, where n is a mult

Question

A bookcase has s shelves with n books on each shelf, where n is a multiple of both s and s-1. If all of the books on the highest shelf were removed and redistributed equally among the other shelves, which of the following represents the number of books that would be on each of the other shelves?

A. \(\frac{ns}{s - 1}\)

B. \(\frac{n(s+1)}{s}\)

C. \(\frac{(n+1)s}{s-1}\)

D. \(\frac{(n-1)s}{s-1}\)

E. \(\frac{(n+1)(s-1)}{s}\)

A.  \frac{ns}{s - 1}

B.  \frac{n(s+1)}{s}

C.  \frac{(n+1)s}{s-1}

D.  \frac{(n-1)s}{s-1}

E.  \frac{(n+1)(s-1)}{s}

EgmatQuantExpert · Answer

Solution

Given:  
• A bookcase has s shelves, with n books on each shelf
 o Given that n is a multiple of both s and s-1

To find:  
• Which one among the given option will represent the number of book on each shelves if all books on the highest shelf were removed and equally redistributed among other shelves

Approach and Working:   
• Total number of books =  n * s  = ns
• When the highest shelf is not considered, number of shelves become s-1
 o Here the total number of books remains constant 
• Therefore, now ns number of books are getting distributed among s-1 shelves
 o So, each shelf will have  \frac{ns}{(s-1)}  books

Hence, the correct answer is option A.

Answer: A

ScottTargetTestPrep · Answer

The total number of books on the shelves is ns. We are given that the books on the highest shelf were removed and redistributed equally among the other shelves. We see that the total number of books did not change; the number of shelves did. The number of shelves is now s - 1, and therefore, the number of books that would be on each of the s - 1 shelves is ns/(s - 1).

Answer: A

Heisenberg12 · Answer

Let n = 20.

s=5. That way, n will be multiple of both s and s-1. (20=4*5)

If 20 books are removed from top shelf AND equally divided among the remaining 4 shelves, then each shelf gets 5 extra books. Therefore, each shelf then has 25 books.

Putting n=20 and s=5 in the equations above,

we get the answer A.

nigina93 · Answer

For such wordy questions, I prefer to change unkjnown variables with numbers. Here we go:
Let the number of shelves be s=5, let the number of books on each shelf be n=20 (multiply of both s and s-1/ 5 and 4, respectively). We are taking all the books (20) from one shelf and removing them to the other 4 and each shelf gets 5 additional books 20/4. So overall, each shelf owns original 20+5replaced from top shelf. Hope it helps. Cheers

A bookcase has s shelves with n books on each shelf, where n is a mult

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A bookcase has s shelves with n books on each shelf, where n is a mult

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