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# NUMBER THEORY

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Manager
Joined: 04 Sep 2006
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NUMBER THEORY [#permalink]  03 Feb 2009, 10:11
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q : A certain shelf holds less than 50 books . what is the number of books in the shelf?

1. books in the shelf can be divided into some stacks of 3 books each , with 2 left over.

2. books in the shelf can be divided into some stacks of 7 books each , with 3 left over
SVP
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Re: NUMBER THEORY [#permalink]  03 Feb 2009, 11:30
vcbabu wrote:
q : A certain shelf holds less than 50 books . what is the number of books in the shelf?

1. books in the shelf can be divided into some stacks of 3 books each , with 2 left over.

2. books in the shelf can be divided into some stacks of 7 books each , with 3 left over

E. n could be 17 or 38.
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Joined: 28 Dec 2004
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Location: New York City
Schools: Wharton'11 HBS'12
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Re: NUMBER THEORY [#permalink]  03 Feb 2009, 21:05
i too get E but my way might be a bit different

1) say N=3K+2

2) says N=7U+3

3K+2=7U+3

or N=7U/3K +1

basically any multiple of 3&7 will work..
Manager
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Re: NUMBER THEORY [#permalink]  03 Feb 2009, 23:58
how E. n could be 17 or 38. are obtained

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Re: NUMBER THEORY [#permalink]  04 Feb 2009, 12:08
GMAT TIGER wrote:
vcbabu wrote:
q : A certain shelf holds less than 50 books . what is the number of books in the shelf?

1. books in the shelf can be divided into some stacks of 3 books each , with 2 left over.

2. books in the shelf can be divided into some stacks of 7 books each , with 3 left over

E. n could be 17 or 38.

I had to write out all the possibilities to figure it out...how did you do it?
SVP
Joined: 29 Aug 2007
Posts: 2497
Followers: 57

Kudos [?]: 555 [0], given: 19

Re: NUMBER THEORY [#permalink]  04 Feb 2009, 20:37
bigtreezl wrote:
GMAT TIGER wrote:
vcbabu wrote:
q : A certain shelf holds less than 50 books . what is the number of books in the shelf?

1. books in the shelf can be divided into some stacks of 3 books each , with 2 left over.
2. books in the shelf can be divided into some stacks of 7 books each , with 3 left over

E. n could be 17 or 38.

I had to write out all the possibilities to figure it out...how did you do it?

n = number of books

1. n = 3m + 2

2. n = 7k+3

reminder when divided by 7 is 3, which is 1 more than the reminder (2) when divided by 3. so look for all the possibilities that are multiples of 7 plus 1 i.e. 7k + 1. this must be a multiple of 3.

3m +2 = 7k+3
3m = 7k+1

solve for the above eq. when m = 5, k = 2. when m = 12, k = 5.

then find n in each cases...
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Re: NUMBER THEORY   [#permalink] 04 Feb 2009, 20:37
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