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GMATprep2: On the number line

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by nhai2003 » Sun Jul 12, 2009 10:29 pm
0---:-|---:--|-:--:-|--:---|-:----1

On the number line above, the segment from 0 to 1 has been divided into fifths, as indicated by the large tick marks, and also into sevenths, as indicated by the small tick marks. What is the LEAST possible distance between any two of the tick marks?
(A)1/70
(B)1/35
(C)2/35
(D)1/12
(E)1/7

I have no idea where to start. Guys please help!
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by rah_pandey » Mon Jul 13, 2009 2:44 am
take lcm and solve

the nos are 1/5,2/5,3/5,4/5,5/5
1/7,2/7,3/7....7/7

take LCM and have a common denominator so that it is easy to compare

7/35,14/35,21/35....
5/35,10/35,15/35...

min is 1/35...I hope it is clear.
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by ketkoag » Mon Jul 13, 2009 3:17 am
yes 1/35 is min.. same approach..
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by jnbimmer » Mon Dec 21, 2009 3:47 pm
the distance would be 7/35 - 5 /35 ?

Thanks
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by avaluxe » Tue May 25, 2010 9:40 am
@jnbimmer - No, the answer is 1/35. If you calculate out all the fractions of fifths and sevenths with an LCM of 35, you'll find that 3/7=15/35 and 2/5=14/35. The difference between these is is 1/35.

I'll admit that I got this wrong on my practice test last night and found this thread while looking for an explanation. I was on the right track but didn't calculate all of them and compare them all together.
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by Patrick_GMATFix » Tue May 25, 2010 9:59 am
As others have mentioned, rewriting fractions with a common denominator is key. Put everything into thirty-fifths. In general if you have to compare or order fractions, it makes sense to put them over a common denominator so that you can focus on comparing the numerators

For this question, the detailed and video solutions can be seen at GMATPrep question 1194

Welcome avaluxe.

Best of luck,
-Patrick
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by kstv » Tue May 25, 2010 5:04 pm
Though the Q is about dividing the segment 0 to 1, is fifths (1/5) and sevenths (1/7) it is same as dividing the the segment 0 to 35 (LCM of 7&5) in 5 and 7 parts.

Integers are easier to handle than fractions.

Then the five points are 0------- 7------- 14------- 21------- 28 -------35
and the seven points are 0----- 5-----10-----15-----20-----25-----30-----35

the least dist i.e 1 unit occcurs at two places between 20 - 21 and 14-15
This is similar to the explanation in the video mentioned above.
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