Number properties

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vinay1983: Legendary Member; Posts: 643; Joined: Wed Aug 14, 2013 4:27 amFollowed by: 7 members; Thanked: 48 times

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

You can, for example never foretell what any one man will do, but you can say with precision what an average number will be up to!

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Source: Beat The GMAT — Problem Solving | Tue Sep 24, 2013 11:39 pm

theCodeToGMAT: Legendary Member; Posts: 1556; Joined: Tue Aug 14, 2012 11:18 pmFollowed by: 34 members; Thanked: 448 times; GMAT Score:650

by theCodeToGMAT » Tue Sep 24, 2013 11:51 pm

Answer [spoiler] {C}[/spoiler]

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

So, x+1 = 6

R A H U L

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ganeshrkamath: Master | Next Rank: 500 Posts; Posts: 283; Joined: Sun Jun 23, 2013 11:56 pmFollowed by: 26 members; Location: Bangalore, India; Thanked: 97 times; GMAT Score:750

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

Cheers

Every job is a self-portrait of the person who did it. Autograph your work with excellence.

Kelley School of Business (Class of 2016)
GMAT Score: 750 V40 Q51 AWA 5 IR 8
https://www.beatthegmat.com/first-attemp ... tml#688494

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Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members; Location: Vancouver, BC; Thanked: 5254 times; GMAT Score:770

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

Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com

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