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# A 100-meter sprinting track is marked off in sixths and in e

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A 100-meter sprinting track is marked off in sixths and in e [#permalink]  03 Apr 2013, 09:54
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A 100-meter sprinting track is marked off in sixths and in eighths. What is the shortest approximate distance, in meters, between any two of the marks that do not overlap?

A. 3.87
B. 4.16
C. 6.25
D. 8.06
E. 12.50
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Re: A 100-meter sprinting track is marked off in sixths and in e [#permalink]  03 Apr 2013, 09:57
This problem looks similar to one solved in following links, but was not able to solve it using the method described in those links.

on-the-number-line-above-the-segment-from-0-to-1-has-been-104204.html
kim-finds-a-1-meter-tree-branch-and-marks-it-off-in-thirds-140038.html
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Re: A 100-meter sprinting track is marked off in sixths and in e [#permalink]  03 Apr 2013, 11:15
A good strategy might be to find the points on a 100 m long track where these divisions will be marked.
1. One sixth division
100/6=16.67
200/6=33.34
300/6=50.01
200/6=66.68
200/6=83.35
600/6=100

2. One eighth division
100/8=12.5
200/8=25
300/8=37.5
400/8=50
500/8=62.5
600/8=75
700/8=87.5
800/8=100

Now let us find the divisions from each column that is closest to each other. Looking at the options, we can tell that c,d and e are out of question as there are clearly options of lesser lengths.
Let us choose between a and b. Check for differences between closest points. The distance will be greater than 4. So, b is the closest right answer.

Hope this helps.

kuttingchai wrote:
This problem looks similar to one solved in following links, but was not able to solve it using the method described in those links.

on-the-number-line-above-the-segment-from-0-to-1-has-been-104204.html
kim-finds-a-1-meter-tree-branch-and-marks-it-off-in-thirds-140038.html

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Re: A 100-meter sprinting track is marked off in sixths and in e [#permalink]  03 Apr 2013, 11:59
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kuttingchai wrote:
A 100-meter sprinting track is marked off in sixths and in eighths. What is the shortest approximate distance, in meters, between any two of the marks that do not overlap?

A 3.87
B 4.16
C 6.25
D 8.06
E 12.50

Convert the fraction to those which have a Common demoninator: $$1/6$$ , $$1/8$$ => $$1/24$$

List marks in terms of 24ths:

$$\frac{1}{6}$$ths:

$$\frac{4}{24} , \frac{8}{24} , \frac{12}{24} , \frac{16}{24} , \frac{20}{24} , \frac{24}{24}$$

$$\frac{1}{8}$$ths:

$$\frac{3}{24} , \frac{6}{24} , \frac{9}{24} , \frac{12}{24} , \frac{15}{24} , \frac{18}{24} , \frac{21}{24} , \frac{24}{24}$$

Without overlapping, the closest possible would be $$\frac{1}{24}$$, we see this occur four times when comparing the two groups: 4-3, 8-9, 16-15, 20-21

The track is 100 meters, so multiply $$\frac{1}{24}$$ by 100 --> $$\frac{1}{24}*100=\frac{100}{24}=4.166666$$
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Re: A 100-meter sprinting track is marked off in sixths and in e [#permalink]  03 Apr 2013, 22:54
Expert's post
kuttingchai wrote:
A 100-meter sprinting track is marked off in sixths and in eighths. What is the shortest approximate distance, in meters, between any two of the marks that do not overlap?

A 3.87
B 4.16
C 6.25
D 8.06
E 12.50

One can always scale the given length(in this case 100 mts) to a more convenient number like 240/2400 etc. Thus, for 240, the sixths markings are at 40,80,120,160,200,240.
For eights, it will be at 30,60,90,120,150,180,210,240. Thus, the minimum distance between non-overlapping marks is 10. Thus, for 240 it is 10, for 100 it will be 100/24 = 4.16

B.
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Re: A 100-meter sprinting track is marked off in sixths and in e [#permalink]  07 Apr 2013, 18:09
1/3 0.33, gives 1/6 0.165
1/4 0.25, gives 1/8 0.125
Which gives 0.4 (since the last distance is that difference)
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Last edited by tulsa on 24 Jul 2013, 03:36, edited 1 time in total.
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Re: A 100-meter sprinting track is marked off in sixths and in e [#permalink]  24 Jul 2013, 03:34
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Thank you for the replies - Understood where i went wrong.

 LCM of 6 and 8 is 24
 Therefore 24/6=4 so the marks are {4,8,12,16,20}
 Therefore 24/8=3 so the marks are {3,6,9,12,15,18,21}
Least possible distance is 1/24
Therefore least possible distance in meters = (1/24)*100 = 4.16
B
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Re: A 100-meter sprinting track is marked off in sixths and in e [#permalink]  28 Oct 2013, 23:59
Shortest Distance = Reciprocal of LCM of 6 & 8 = 1/24
1/24 x 100 = 4.16 (Answer = B)

For Example; had the problem been of marking 1/5 th & 1/7th,
then shortest distance = Reciprocal of LCM of 5 & 7 = 1/35

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Last edited by PareshGmat on 06 Mar 2014, 18:14, edited 1 time in total.
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Re: A 100-meter sprinting track is marked off in sixths and in e [#permalink]  29 Oct 2013, 05:56
Hello,

isn't it just 100/6= 16.66 and 100/8=12.5

16.66-12.5=4.16 or miss i something here?
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Re: A 100-meter sprinting track is marked off in sixths and in e [#permalink]  29 Oct 2013, 06:02
Expert's post
gmatbas wrote:
Hello,

isn't it just 100/6= 16.66 and 100/8=12.5

16.66-12.5=4.16 or miss i something here?

It won't always be this way.

Check similar problems:
on-the-number-line-above-the-segment-from-0-to-1-has-been-104204.html
kim-finds-a-1-meter-tree-branch-and-marks-it-off-in-thirds-140038.html
if-the-successive-tick-marks-shown-on-the-number-line-above-144053.html
a-straight-pipe-1-yard-in-length-was-marked-off-in-fourths-145031.html

Hope this helps.
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Re: A 100-meter sprinting track is marked off in sixths and in e [#permalink]  24 Nov 2014, 07:18
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Re: A 100-meter sprinting track is marked off in sixths and in e   [#permalink] 24 Nov 2014, 07:18
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