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

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03 Apr 2013, 10:54

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A

B

C

D

E

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66% (02:44) correct
34% (02:06) wrong based on 110 sessions

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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?

Re: A 100-meter sprinting track is marked off in sixths and in e [#permalink]

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03 Apr 2013, 12:15

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

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.

Re: A 100-meter sprinting track is marked off in sixths and in e [#permalink]

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03 Apr 2013, 12:59

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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: \(1/6\) , \(1/8\) => \(1/24\)

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 --> \(\frac{1}{24}*100=\frac{100}{24}=4.166666\)

Re: A 100-meter sprinting track is marked off in sixths and in e [#permalink]

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03 Apr 2013, 23:54

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

Re: A 100-meter sprinting track is marked off in sixths and in e [#permalink]

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24 Jul 2013, 04:34

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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

Re: A 100-meter sprinting track is marked off in sixths and in e [#permalink]

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24 Nov 2014, 08:18

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