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Breaking Branches

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by DonPaw » Thu Nov 10, 2011 12:17 am
Kim finds a 1-meter tree branch and marks it off in thirds and fifths. She then breaks the branch along all the markings and removes one piece of every distinct length. What fraction of the original branch remains


Is there any fastest way to solve it in less than 2 mins
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by shankar.ashwin » Thu Nov 10, 2011 12:25 am
Let the branch be 15 m long, LCM of 3 and 5. It would be marked every 1/5th and every 1/3rd (or) at every multiples of 3 and 5. So the marking would be at

3
5
6
9
10
12
15


The possible distinct lengths are 3,2 and 1 (or) 6 metres will be removed and 9/15 = 3/5 will remain.

Since its only a fraction, 1 meter or 15 meters, the fraction is the same
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by DonPaw » Thu Nov 10, 2011 12:34 am
Thanks Ashwin,

Specially I liked the approach of making it 15 m long. However, the answer is not 3/5.

it picked out unique branches and left out common. We need to find the total leftovers.
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by shankar.ashwin » Thu Nov 10, 2011 12:45 am
But they ask for what fraction of original remains?

You remove '6', you have 15-6 = 9 parts left. Whats the answer BTW? 6/15?
DonPaw wrote:Thanks Ashwin,

Specially I liked the approach of making it 15 m long. However, the answer is not 3/5.

it picked out unique branches and left out common. We need to find the total leftovers.
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by DonPaw » Thu Nov 10, 2011 12:58 am
Sorry Ashwin,

your answer is right .. it is 3/5. I looked at the wrong answer. Apology.
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by GMATGuruNY » Thu Nov 10, 2011 1:08 am
DonPaw wrote:Kim finds a 1-meter tree branch and marks it off in thirds and fifths. She then breaks the branch along all the markings and removes one piece of every distinct length. What fraction of the original branch remains


Is there any fastest way to solve it in less than 2 mins
I posted a solution here:

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by shankar.ashwin » Thu Nov 10, 2011 1:22 am
Well of course!! Mitch taught me this method.. :) Hope I am not plagiarizing :)
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by gmatpup » Thu Nov 10, 2011 6:38 am
May I ask why 1, 2, and 3 are the only distinct lengths?


Thanks so much :)
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