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Kim finds a 1-meter tree branch and marks it off in thirds a

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Kim finds a 1-meter tree branch and marks it off in thirds a [#permalink] New post 24 Jun 2011, 11:22
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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?

A. 2/5
B. 7/5
C. 1/2
D. 8/15
E. 3/5

OPEN DISCUSSION OF THIS QUESTION IS HERE: kim-finds-a-1-meter-tree-branch-and-marks-it-off-in-thirds-140038.html
[Reveal] Spoiler: OA
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Re: Tree Branches [#permalink] New post 24 Jun 2011, 12:28
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its option E

The rough diagram will be like following
Attachment:
1.jpg
1.jpg [ 18.85 KiB | Viewed 4108 times ]

In the diagram a tree branch of 1 meter is divided into 1/3 s and 1/5s
a b and c will be the distinct lengths

Now in the diagram there after removing one part of the distinct length the remaining will be 2 a's and 1 b and 1 c

a= 1/5 ...since it is a complete fifth part of the branch
also from the diagram we can make out that b+c = a = 1/5

hence the remaining branch will be 2*1/5 +1/5 = 3/5

hence E

You can conform the diagram by taking length of the branch 1m=100cm and 1/5=20cm amd 1/3= 33.33cm
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Re: Tree Branches [#permalink] New post 24 Jun 2011, 12:39
smodak 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?

A) 2/5
B) 7/15
C) 1/2
D) 8/15
E) 3/5
Please explain your answer.


Attachment:
3rd_5th_fraction.PNG
3rd_5th_fraction.PNG [ 6.92 KiB | Viewed 4104 times ]


Distinct fractions: \frac{3}{15}, \frac{1}{15}, \frac{2}{15}
Sum= \frac{6}{15}
Remaining,
\frac{9}{15}=\frac{3}{5}

Ans: "E"
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Re: Tree Branches [#permalink] New post 24 Jun 2011, 15:34
3 possible distinct lengths are 3/15,2/15,1/15

according to the question one of each kind are removed => removed thread length = 6/15

=>remaining thread length = 9/15 = 3/5

so the remaining is 3/5 of the original .

Answer is E.
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Re: Tree Branches [#permalink] New post 13 Jul 2011, 10:28
why is the 1m - 100 cm is not even considered.
How do u come to the conclusion of avoiding the length.

Kindly explain.
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Re: Tree Branches [#permalink] New post 14 Jul 2011, 02:25
hey if u ppl dont mind can you please explain it properly ,especially this diagram.
my mind is blocked thinking about it...
please asap..
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Re: Tree Branches [#permalink] New post 14 Jul 2011, 02:40
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smodak 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?

A) 2/5
B) 7/15
C) 1/2
D) 8/15
E) 3/5

Please explain your answer.


Markings are made on 1/5, 2/5, 3/5, 4/5 and 5/5
They are also made on 1/3, 2/3 and 3/3.
Its hard to compare these. So let's take their LCM.
Markings are made on 3/15, 6/15, 9/15, 12/15 and 15/15
They are also made on 5/15, 10/15 and 15/15.

So markings are on 3/15, 5/15, 6/15, 9/15, 10/15, 12/15 and 15/15.

Distinct sizes are: 2/15, 1/15, 3/15
Sum = 6/15

Leftover stick = 1 - 6/15 = 9/15 = 3/5
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Re: Tree Branches [#permalink] New post 14 Jul 2011, 04:23
hey karishma thanks for the reply
have u found the distinct sizes by finding out the difference between them?
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Re: Tree Branches [#permalink] New post 18 Jul 2011, 21:35
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sushantarora wrote:
hey karishma thanks for the reply
have u found the distinct sizes by finding out the difference between them?

Yes I have. Difference between 3/15 and 5/15 is 2/15.
Between 5/15 and 6/15 is 1/15.
Between 6/15 and 9/15 is 3/15.
and then they repeat...
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Re: Tree Branches [#permalink] New post 18 Jul 2011, 22:40
thanks again Karishma!!
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Re: Tree Branches [#permalink] New post 19 Jul 2011, 04:34
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Answer is E. I took time to undertand the question!! :(
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Re: Tree Branches [#permalink] New post 11 May 2013, 08:45
Can somebody tell me, what is wrong with my understanding? I solved it this way..
http://campl.us/iYfTEVGNqOO

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Re: Tree Branches [#permalink] New post 11 May 2013, 09:11
nikhil007 wrote:
Can somebody tell me, what is wrong with my understanding? I solved it this way..
http://campl.us/iYfTEVGNqOO

Posted from my mobile device Image



Hi, I have seen this snapshot.....But I advise you to just follow the steps given by Karishma.... above ... once you look at them carefully. I 'm sure you will be able to find your flaw,,,,,,,,,,,,,,,,

Hope ot Helps !!
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Re: Tree Branches [#permalink] New post 12 May 2013, 01:29
Expert's post
nikhil007 wrote:
Can somebody tell me, what is wrong with my understanding? I solved it this way..
http://campl.us/iYfTEVGNqOO

Posted from my mobile device Image


Check here: kim-finds-a-1-meter-tree-branch-and-marks-it-off-in-thirds-140038.html In case of any questions please post in that thread.

Similar question to practice: on-the-number-line-above-the-segment-from-0-to-1-has-been-104204.html

Hope it helps.
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Re: Kim finds a 1-meter tree branch and marks it off in thirds a [#permalink] New post 12 May 2013, 10:32
Tip - Since it is a question asking for a fraction.. You can always substitute the length by a more easier number to ease up calculations and draw an easier diagram.
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Re: Kim finds a 1-meter tree branch and marks it off in thirds a   [#permalink] 12 May 2013, 10:32
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