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

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On the number line, the segment from 0 to 1 has been divided [#permalink] New post 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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Re: A NUMBER LINE [#permalink] New post 03 Apr 2008, 05:40
can any one explain it wiht pic please ?
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Re: A NUMBER LINE [#permalink] New post 03 Apr 2008, 05:53
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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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Re: A NUMBER LINE [#permalink] New post 03 Apr 2008, 05:55
Answer is B - 1/35.

3/5 - 4/7 = 1/35
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Re: A NUMBER LINE [#permalink] New post 03 Apr 2008, 09:52
Where did you get 3/5 and 4/7?
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Re: A NUMBER LINE [#permalink] New post 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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Re: A NUMBER LINE [#permalink] New post 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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Re: A NUMBER LINE [#permalink] New post 03 Apr 2008, 21:14
I still have to reach the stage of generalization, you have a great method Mr Walker :idea: 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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On the number line, the segment from 0 to 1 has been divided

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