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Number properties

by vinay1983 » Tue Sep 24, 2013 11:39 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 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
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by theCodeToGMAT » Tue Sep 24, 2013 11:51 pm
Answer [spoiler] {C}[/spoiler]

8x + 2(1) = 42
x = 5

So, x+1 = 6
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by ganeshrkamath » Wed Sep 25, 2013 12:00 am
vinay1983 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 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
24a - 42 = 16(a-1) + 22
24a - 42 = 16a + 6
8a = 48
a = 6

Choose C

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by Brent@GMATPrepNow » Wed Sep 25, 2013 6:10 am
vinay1983 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 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
Here's a similar solution with some extra details.

A shelf that goes from holding 24 books to holding 16 books lost 8 books
2 shelves that go from holding 24 books to 16 books lost a total of 16 books
3 shelves that go from holding 24 books to 16 books lost a total of 24 books
4 such shelves lost a total of 32 books
5 such shelves lost a total of 40 books

A shelf that goes from holding 24 books to holding 22 books lost 2 books
So, if there 1 one of these shelves, then the book total = 40 + 2 = 42

This gives us a total of 6 shelves.

Answer: C

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