Breaking Branches

This topic has expert replies
Junior | Next Rank: 30 Posts
Posts: 27
Joined: Sat May 01, 2010 7:57 pm

Breaking Branches

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

Legendary Member
Posts: 966
Joined: Sat Jan 02, 2010 8:06 am
Thanked: 230 times
Followed by:21 members

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

Junior | Next Rank: 30 Posts
Posts: 27
Joined: Sat May 01, 2010 7:57 pm

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.

Legendary Member
Posts: 966
Joined: Sat Jan 02, 2010 8:06 am
Thanked: 230 times
Followed by:21 members

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.

Junior | Next Rank: 30 Posts
Posts: 27
Joined: Sat May 01, 2010 7:57 pm

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.

User avatar
GMAT Instructor
Posts: 15539
Joined: Tue May 25, 2010 12:04 pm
Location: New York, NY
Thanked: 13060 times
Followed by:1906 members
GMAT Score:790

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:

https://www.beatthegmat.com/700-question-t87924.html
Private tutor exclusively for the GMAT and GRE, with over 20 years of experience.
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.

As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.

For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
Student Review #2
Student Review #3

Legendary Member
Posts: 966
Joined: Sat Jan 02, 2010 8:06 am
Thanked: 230 times
Followed by:21 members

by shankar.ashwin » Thu Nov 10, 2011 1:22 am
Well of course!! Mitch taught me this method.. :) Hope I am not plagiarizing :)

Senior | Next Rank: 100 Posts
Posts: 88
Joined: Sat Oct 15, 2011 6:38 pm
Thanked: 1 times
Followed by:1 members

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 :)