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# PS-wire length segments

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19 Dec 2004, 23:22
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Could you tell me how you would go about solving this problem?

A wire is cut into three equal parts. The resulting segments are then cut into 4, 6, and 8 equal parts respectively. If each of the resulting segments has an integer length, what is the miniumum length of the wire?
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20 Dec 2004, 06:39
I would take the LCM of 4,6,8. It is 24. So each of the three pieces is 24 units, so actual length will be 24*3 = 72 units.
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20 Dec 2004, 08:21
The easiest way is to subsitute the values. We know that the segments have integer values. (1, 2, 3, 4....)

segments : 4---6---8

Let us take 1 as the integer of the first segment (4 parts). Hence one part is 0.25. But this will not give an integer value for the second segment (6 parts). Hence integer 1 is out.

Take interger 2 for the 1st segment.

Then we have the lengths are 2---3---4. Making the total lenght of the wire as 9.

This is the easiest way to solve. I hope this helped.

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Manager
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20 Dec 2004, 09:31
carsen,

The OA is not 9.
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20 Dec 2004, 12:43
let lenght of wire be x.

divided into three equal parts gives x/3

each of them is further divided into equal parts as follows

x/12 , x/18 , x/24. for all these to be intergers, we need the LCM which is 144.
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20 Dec 2004, 19:40
If the wire is cut in 3 equal parts , then the minimum length is some multiple of 3.
Then each one of that length is cut into 4,6 and 8 equal parts. So we've to find the minimum common multiple of 4,6 and 8 which is 24.

So the minimum length would be 24 * 3 = 72.
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20 Dec 2004, 23:38
IGNORE my last solution. I misread the question.

Let 'L' be the total lenght of the wire. Upon segmenting as per the requirement, each segment has

1st wire peice - L/12
2nd wire peice - L/18
3rd wire piece - L/24

The LCM for these values is 72. This is the minimum value.

To go about solving these... draw a line lenght "L". cut in to 3 peices, each of L/3. And we know these each L/3 shud be cut in to 4, 6, and 8 parts. Hence..

L/3 x 4= L/12
L/3 x 6 = L/18
L/3 x 8 = L/24.

Calculate the LCM. In this case, 72. Hence 72 is the answer. Pardon me for misunderstanding the question, earlier.

Regards
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20 Dec 2004, 23:47
Thanks for the help! The OA is 72.
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25 Dec 2009, 21:41
Can someone please explain to me why we need to take the LCM in this case?
And why is it important to find multiple of 3 if the wire was further cut into pieces?

I thought with pieces cut into 4,6,8 I can simply add them and since it has to be integer length, 4 + 6 + 8 = 18 would be the minimum length.

Thanks
Re: PS-wire length segments   [#permalink] 25 Dec 2009, 21:41
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