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# On the number line, the segment from 0 to 1 has been divided

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SVP
Joined: 04 May 2006
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Schools: CBS, Kellogg
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On the number line, the segment from 0 to 1 has been divided [#permalink]  01 Apr 2008, 19:47
On the number line, the segment from 0 to 1 has been divided into fifths and also into sevenths. What is the LEAST possiple distance between any two of the tick marks?

A. 1/70
B. 1/35
C. 2/35
D. 1/12
E. 1/7

Do you mind giving me a fast way of solving it? Thanks!
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Manager
Joined: 25 Mar 2008
Posts: 106
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Kudos [?]: 10 [0], given: 0

Re: A NUMBER LINE [#permalink]  03 Apr 2008, 05:40
can any one explain it wiht pic please ?
CEO
Joined: 17 Nov 2007
Posts: 3578
Concentration: Entrepreneurship, Other
Schools: Chicago (Booth) - Class of 2011
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Kudos [?]: 2123 [2] , given: 359

Re: A NUMBER LINE [#permalink]  03 Apr 2008, 05:53
2
KUDOS
Expert's post
B

Actually we have to find minimum of the expression:

$$f=|\frac{a}{5} - \frac{b}{7}|$$ where a e {0,1,2,3,4} and b e {1,2,3,4,5,6}

$$f=|\frac{7*a-5*b}{35}|$$

7*a: 7,14,21,28
5*b: 5,10,15,20,25,30

so, $$min(f)=\frac{1}{35}$$
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Current Student
Joined: 27 Mar 2008
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Schools: Kellogg Class of 2011
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Re: A NUMBER LINE [#permalink]  03 Apr 2008, 05:55

3/5 - 4/7 = 1/35
Manager
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Re: A NUMBER LINE [#permalink]  03 Apr 2008, 09:52
Where did you get 3/5 and 4/7?
SVP
Joined: 04 May 2006
Posts: 1936
Schools: CBS, Kellogg
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Kudos [?]: 430 [0], given: 1

Re: A NUMBER LINE [#permalink]  03 Apr 2008, 19:53
walker wrote:
B

Actually we have to find minimum of the expression:

$$f=|\frac{a}{5} - \frac{b}{7}|$$ where a e {0,1,2,3,4} and b e {1,2,3,4,5,6}

$$f=|\frac{7*a-5*b}{35}|$$

7*a: 7,14,21,28
5*b: 5,10,15,20,25,30

so, $$min(f)=\frac{1}{35}$$

Thank Walker, that is exactly what I want. I can generalize this problem for future!
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Schools: Chicago (Booth) - Class of 2011
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Kudos [?]: 2123 [0], given: 359

Re: A NUMBER LINE [#permalink]  03 Apr 2008, 20:12
Expert's post
It seems that the answer maybe generalized as $$\frac{1}{LCM(x,y)}$$
But honestly, I so tired after lulling my son at 3 am and my following 4th GMATPrep1 attempt that I am very lazy to prove (or disprove) this generalization...but maybe does somebody try?
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Senior Manager
Joined: 16 Aug 2004
Posts: 327
Location: India
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Re: A NUMBER LINE [#permalink]  03 Apr 2008, 21:14
I still have to reach the stage of generalization, you have a great method Mr Walker but my traditional method proves 1/35 answer B. It took a lot of time though.
Re: A NUMBER LINE   [#permalink] 03 Apr 2008, 21:14
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