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# If each of the following fractions were written as a

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Manager
Joined: 02 Mar 2008
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Concentration: Finance, Strategy
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If each of the following fractions were written as a [#permalink]  05 Apr 2008, 00:55
00:00

Difficulty:

5% (low)

Question Stats:

100% (01:13) correct 0% (00:00) wrong based on 3 sessions
If each of the following fractions were written as a repeating decimal, which would have the longest sequence of different digits?
2/11
1/3
41/99
2/3
23/37
I am marching thru the OG, this is simple, but just wonder anyone got better trick for repeating decimal (hmm obviously if we play division game for A, B, D we can find; but i try to optimize calculation time )
SVP
Joined: 04 May 2006
Posts: 1943
Schools: CBS, Kellogg
Followers: 14

Kudos [?]: 208 [0], given: 1

Re: PS - repeating decimal [#permalink]  05 Apr 2008, 01:25
AlbertNTN wrote:
If each of the following fractions were written as a repeating decimal, which would have the longest sequence of different digits?
2/11
1/3
41/99
2/3
23/37
I am marching thru the OG, this is simple, but just wonder anyone got better trick for repeating decimal (hmm obviously if we play division game for A, B, D we can find; but i try to optimize calculation time )

I remember in one post Walker had some nice explaination about the terminating and repeating fraction.

He said that "1/17 has how many repeating numbers? (p-1) = 16 numbers". So I think E is my choice because E will have 37-1 =36 repeating digits?

Correct me if I wrong you and Walker
CEO
Joined: 17 Nov 2007
Posts: 3599
Concentration: Entrepreneurship, Other
Schools: Chicago (Booth) - Class of 2011
GMAT 1: 750 Q50 V40
Followers: 326

Kudos [?]: 1574 [0], given: 354

Re: PS - repeating decimal [#permalink]  05 Apr 2008, 01:25
Expert's post
E

1. reduce fraction if it is possible. Here we have all proper fractions.
2. because numerator does not influence on period of sequence, set all numerators to 1: 1/11, 1/3, 1/99, 1/3, 1/37
3. transform all fraction to the denominator such as 9, 99, 999 .....: 9/99, 3/9, 1/99, 3/9, 1/37
4. 1/37 we cannot write out as a fraction with denominator of 9 or 99. (actually we can with 999 but this is not necessary here) So, E is a winner.
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CEO
Joined: 17 Nov 2007
Posts: 3599
Concentration: Entrepreneurship, Other
Schools: Chicago (Booth) - Class of 2011
GMAT 1: 750 Q50 V40
Followers: 326

Kudos [?]: 1574 [0], given: 354

Re: PS - repeating decimal [#permalink]  05 Apr 2008, 01:28
Expert's post
sondenso wrote:
I remember in one post Walker had some nice explaination about the terminating and repeating fraction.

He said that "1/17 has how many repeating numbers? (p-1) = 16 numbers". So I think E is my choice because E will have 37-1 =36 repeating digits?

Correct me if I wrong you and Walker

I remember that I even proved rule with 99....999 by means of geometrical progression.... But it say that we should count 9 in 99...999 denominator.
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Manager
Joined: 02 Mar 2008
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Concentration: Finance, Strategy
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Kudos [?]: 36 [0], given: 1

Re: PS - repeating decimal [#permalink]  05 Apr 2008, 04:27
nice to see the 9 rule, is it some fundamental property of arithmetic? thanks
sodenso i don't think the rule works with 1/37 (only 3 repeated numbers) ...
CEO
Joined: 17 Nov 2007
Posts: 3599
Concentration: Entrepreneurship, Other
Schools: Chicago (Booth) - Class of 2011
GMAT 1: 750 Q50 V40
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Kudos [?]: 1574 [1] , given: 354

Re: PS - repeating decimal [#permalink]  05 Apr 2008, 07:03
1
KUDOS
Expert's post
I found that:

7-t59213

7-t57168
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Manager
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Posts: 213
Concentration: Finance, Strategy
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Kudos [?]: 36 [0], given: 1

Re: PS - repeating decimal [#permalink]  05 Apr 2008, 14:14
kool thank u. It seems that end of this month we can't reach u huh haha. jk, enjoy ur Harvard trip
CEO
Joined: 17 Nov 2007
Posts: 3599
Concentration: Entrepreneurship, Other
Schools: Chicago (Booth) - Class of 2011
GMAT 1: 750 Q50 V40
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Kudos [?]: 1574 [0], given: 354

Re: PS - repeating decimal [#permalink]  05 Apr 2008, 16:20
Expert's post
AlbertNTN wrote:
kool thank u. It seems that end of this month we can't reach u huh haha. jk, enjoy ur Harvard trip

Thanks
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SVP
Joined: 04 May 2006
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Re: PS - repeating decimal [#permalink]  05 Apr 2008, 20:24
AlbertNTN wrote:
nice to see the 9 rule, is it some fundamental property of arithmetic? thanks
sodenso i don't think the rule works with 1/37 (only 3 repeated numbers) ...

Thank you, I got it!

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Re: PS - repeating decimal [#permalink]  01 May 2008, 03:47
Quote:
I remember in one post Walker had some nice explaination about the terminating and repeating fraction.

He said that "1/17 has how many repeating numbers? (p-1) = 16 numbers". So I think E is my choice because E will have 37-1 =36 repeating digits?

Correct me if I wrong you and Walker

would you please point me to Walker post.
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Re: PS - repeating decimal [#permalink]  01 May 2008, 04:32
AlbertNTN wrote:
If each of the following fractions were written as a repeating decimal, which would have the longest sequence of different digits?
2/11
1/3
41/99
2/3
23/37
I am marching thru the OG, this is simple, but just wonder anyone got better trick for repeating decimal (hmm obviously if we play division game for A, B, D we can find; but i try to optimize calculation time )

I did this in my head in bout 2 min. its not really that bad. B,D elim right off the bat.

A. just solve out, you get .1818
C again just solve out you get .4141

No need to test for E.
Re: PS - repeating decimal   [#permalink] 01 May 2008, 04:32
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