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

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Kim finds a 1-meter tree branch and marks it off in thirds [#permalink]

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03 Oct 2012, 23:49
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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
[Reveal] Spoiler: OA

Last edited by Bunuel on 04 Oct 2012, 02:17, edited 1 time in total.
Renamed the topic and edited the question.
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Re: Kim finds a 1-meter tree branch and marks it off in thirds [#permalink]

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04 Oct 2012, 02:31
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Archit143 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. 7/5
C. 1/2
D. 8/15
E. 3/5

Since we want to find the fraction, we can assume some other length of the branch which will make calculation easier. Take the length of the branch to be 15-meter long (the least common multiple of 3 and 5).

In this case the branch would be cut at 3, 5, 6, 9, 10, and 12 meters (in red are given fifths of the length and in black thirds of the length).

Distinct lengths would be: 3, 5-3=2 and 10-9=1 meters long pieces, so she removes total of 3+2+1=6 meters, so 15-6=9 meters remains, which is 9/15=3/5 of the original branch,

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 [#permalink]

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07 Feb 2016, 20:27
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redfield wrote:
So distinct length actually referring to distinct differences between lengths once cut? Like the post above me I saw distinct as "unique" the way it is with factoring and this really threw me and I'm still struggling to fully comprehend the meaning of distinct in relation to this problem.

Distinct does mean unique, the same way as it is used with factors.

12 = 2*2*3
How many distinct prime factors does 12 have? It has 2 distinct prime factors: 2 and 3
There are two 2s but since we need just the distinct prime factors, we ignore the other 2.

Similarly, how many distinct lengths are there after you cut the branch into pieces? You get 3 distinct lengths: 3, 2 and 1. There are multiple pieces of the same length but since we need pieces of distinct length only, we leave the other pieces.
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Re: Kim finds a 1-meter tree branch and marks it off in thirds [#permalink]

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06 Oct 2012, 03:54
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EvaJager wrote:
10m is not a good choice in this case, because 10 is not divisible by 3. So the cuts cannot be at 3, 6, and 9, but should be at 3and1/3, 6and2/3. Also, the margins are 0 and 10, 1 is not a margin.
The best to take in this case is a length of 15m, it is both divisible by 3 and 5.

Eva - thanks for your response. I see it now!
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Re: Kim finds a 1-meter tree branch and marks it off in thirds [#permalink]

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04 Feb 2013, 02:47
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rajathpanta wrote:
Distinct lengths would be: 3, 5-3=2 and 10-9=1 meters long pieces, so she removes total of 3+2+1=6 meters, so 15-6=9 meters remains, which is 9/15=3/5 of the original branch,

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

Hope it helps.
Hi Bunuel,

See above highlighted. Shouldn't we first consider 6-5= 1 as the distinct lenghth. Is there any specific reason you jumped to 10-9??

The point is that 1-meter long piece is possible, so it does not matter whether you get that from 6-5 or 10-9.
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Re: Kim finds a 1-meter tree branch and marks it off in thirds [#permalink]

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01 Mar 2013, 08:38
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mun23 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

Image attached.

LCM of 3 and 5 is 15, so consider the rope as 15 units long.
Rope is divided into 3rd's and 5th's. (3rd's in blue and 5th in green)

The unique length pieces are marked in light green color in the image as 3 , 2 and 1
So, after 6units all the lengths are repeating.
So, part of the rope which will be left = (15-6)/15
= 9/15 = 3/5

Hope it helps!
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File comment: image attached

image.JPG [ 17.49 KiB | Viewed 6977 times ]

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Re: Kim finds a 1-meter tree branch and marks it off in thirds [#permalink]

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23 Aug 2013, 01:38
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Kindly refer attachment:
Equalise the denominator:
One thirds (marked in black) & one fifths (marked in blue)
7 pieces created & differences calculated
Removed the "distinct" lenghts & added the rest
3/15 + 1/15 + 2/15 + 3/15
= 9/15
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line.JPG [ 15.26 KiB | Viewed 6352 times ]

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Re: Kim finds a 1-meter tree branch and marks it off in thirds [#permalink]

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14 Jan 2014, 00:24
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Rock750 wrote:
Bunuel wrote:
Archit143 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. 7/5
C. 1/2
D. 8/15
E. 3/5

Since we want to find the fraction, we can assume some other length of the branch which will make calculation easier. Take the length of the branch to be 15-meter long (the least common multiple of 3 and 5).

In this case the branch would be cut at 3, 5, 6, 9, 10, and 12 meters (in red are given fifths of the length and in black thirds of the length).

Distinct lengths would be: 3, 5-3=2 and 10-9=1 meters long pieces, so she removes total of 3+2+1=6 meters, so 15-6=9 meters remains, which is 9/15=3/5 of the original branch,

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

Hope it helps.

Hi Bunuel

As per your explanation, the branch would be cut at 3, 5, 6, 9, 10, and 12 meters (in red are given fifths of the length and in black thirds of the length). So , distinct lengths should be: 3, 5-3 = 2 , 10-9 =1 AND 6 ??
So she removes total of 3+2+1+6 =12 meters, so 15-12=3 meters remains, which is 3/15=1/5 of the original branch ?

Thanks

Consider the diagram below:
---|--|-|---|-|--|---

Notice that we don't have a 6-meter long piece there.

Hope it's clear.
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Re: Kim finds a 1-meter tree branch [#permalink]

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04 Oct 2012, 01:39
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The best way to approach this kind of problem is by drawing a rough sketch (You will see a similar problem in OG12) and marking at the 3rd and 5th lengths..doing this we get logs of following distinct lengths..

3 pieces of 1/5 length and two piece each of 1/15 and 2/15 lengths. removing one piece each from pieces of each kind of lengths the all that will remain will be

2 pieces of 1/5 i.e 2/5, 1 piece of 1/15, and 1 piece of 2/15

Which gives us 2/5 + 1/15 + 2/15 -----> 3/5 Answer is E
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Re: Kim finds a 1-meter tree branch and marks it off in thirds [#permalink]

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06 Oct 2012, 01:50
Bunuel wrote:
Archit143 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. 7/5
C. 1/2
D. 8/15
E. 3/5

Since we want to find the fraction, we can assume some other length of the branch which will make calculation easier. Take the length of the branch to be 15-meter long (the least common multiple of 3 and 5).

In this case the branch would be cut at 3, 5, 6, 9, 10, and 12 meters (in red are given fifths of the length and in black thirds of the length).

Distinct lengths would be: 3, 5-3=2 and 10-9=1 meters long pieces, so she removes total of 3+2+1=6 meters, so 15-6=9 meters remains, which is 9/15=3/5 of the original branch,

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

Hope it helps.

Hi Bunuel- I took the total length to be 10 meter (length can be anything as question only asks for fraction) so the markings are 1,3,5,6,9,10 the unique lengths are 3,2,1 so 10-6 = 4 remains so fraction remaining is 4/10 = 2/5. Could you please correct me? Also the question says 1 piece of every unique length so the piece with the length 2 also can be take right?
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Re: Kim finds a 1-meter tree branch and marks it off in thirds [#permalink]

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06 Oct 2012, 02:48
Jp27 wrote:
Bunuel wrote:
Archit143 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. 7/5
C. 1/2
D. 8/15
E. 3/5

Since we want to find the fraction, we can assume some other length of the branch which will make calculation easier. Take the length of the branch to be 15-meter long (the least common multiple of 3 and 5).

In this case the branch would be cut at 3, 5, 6, 9, 10, and 12 meters (in red are given fifths of the length and in black thirds of the length).

Distinct lengths would be: 3, 5-3=2 and 10-9=1 meters long pieces, so she removes total of 3+2+1=6 meters, so 15-6=9 meters remains, which is 9/15=3/5 of the original branch,

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

Hope it helps.

Hi Bunuel- I took the total length to be 10 meter (length can be anything as question only asks for fraction) so the markings are 1,3,5,6,9,10 the unique lengths are 3,2,1 so 10-6 = 4 remains so fraction remaining is 4/10 = 2/5. Could you please correct me? Also the question says 1 piece of every unique length so the piece with the length 2 also can be take right?

10m is not a good choice in this case, because 10 is not divisible by 3. So the cuts cannot be at 3, 6, and 9, but should be at 3and1/3, 6and2/3. Also, the margins are 0 and 10, 1 is not a margin.
The best to take in this case is a length of 15m, it is both divisible by 3 and 5.
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Re: Kim finds a 1-meter tree branch and marks it off in thirds [#permalink]

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04 Feb 2013, 02:41
Distinct lengths would be: 3, 5-3=2 and 10-9=1 meters long pieces, so she removes total of 3+2+1=6 meters, so 15-6=9 meters remains, which is 9/15=3/5 of the original branch,

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

Hope it helps.[/quote]

Hi Bunuel,

See above highlighted. Shouldn't we first consider 6-5= 1 as the distinct lenghth. Is there any specific reason you jumped to 10-9??
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Re: Kim finds a 1-meter tree branch and marks it off in thirds [#permalink]

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13 Jan 2014, 12:33
Bunuel wrote:
Archit143 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. 7/5
C. 1/2
D. 8/15
E. 3/5

Since we want to find the fraction, we can assume some other length of the branch which will make calculation easier. Take the length of the branch to be 15-meter long (the least common multiple of 3 and 5).

In this case the branch would be cut at 3, 5, 6, 9, 10, and 12 meters (in red are given fifths of the length and in black thirds of the length).

Distinct lengths would be: 3, 5-3=2 and 10-9=1 meters long pieces, so she removes total of 3+2+1=6 meters, so 15-6=9 meters remains, which is 9/15=3/5 of the original branch,

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

Hope it helps.

Hi Bunuel

As per your explanation, the branch would be cut at 3, 5, 6, 9, 10, and 12 meters (in red are given fifths of the length and in black thirds of the length). So , distinct lengths should be: 3, 5-3 = 2 , 10-9 =1 AND 6 ??
So she removes total of 3+2+1+6 =12 meters, so 15-12=3 meters remains, which is 3/15=1/5 of the original branch ?

Thanks
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Re: Kim finds a 1-meter tree branch and marks it off in thirds [#permalink]

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28 Sep 2014, 03:51
Hi Bunuel, please excuse my ignorance, but even after going through all the explanations, I cannot make out what does the question mean exactly by distinct lengths?
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Re: Kim finds a 1-meter tree branch and marks it off in thirds [#permalink]

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28 Sep 2014, 07:32
nitin6305 wrote:
Hi Bunuel, please excuse my ignorance, but even after going through all the explanations, I cannot make out what does the question mean exactly by distinct lengths?

0---|--|-|---|-|--|---15

When you cut 15-meter piece at 3, 5, 6, 9, 10, and 12 meters you get 3 distinct lengths:
3 meters: from 0 to 3, from 6 to 9, and from 12 to 15;
2 meters: from 3 to 5 and from 10 to 12;
1 meter: from 5 to 6 and from 9 to 10.

Check similar questions to practice:
on-the-number-line-above-the-segment-from-0-to-1-has-been-104204.html
a-straight-pipe-1-yard-in-length-was-marked-off-in-fourths-145031.html
a-100-meter-sprinting-track-is-marked-off-in-sixths-and-in-e-150349.html
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Re: Kim finds a 1-meter tree branch and marks it off in thirds [#permalink]

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25 Oct 2014, 14:55
Grr!!! I had problems with this question, because I translated "distinct" as "unique". Once you cut the 1-meter branch along the markings, you will see that there will be 3-(3/15 pieces), 2-(2/15 pieces), and 2-(1/5 pieces). Remove of each length and 9/15=3/5 will be the answer.
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Re: Kim finds a 1-meter tree branch and marks it off in thirds [#permalink]

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07 Feb 2016, 13:30
Bunuel wrote:
nitin6305 wrote:
Hi Bunuel, please excuse my ignorance, but even after going through all the explanations, I cannot make out what does the question mean exactly by distinct lengths?

0---|--|-|---|-|--|---15

When you cut 15-meter piece at 3, 5, 6, 9, 10, and 12 meters you get 3 distinct lengths:
3 meters: from 0 to 3, from 6 to 9, and from 12 to 15;
2 meters: from 3 to 5 and from 10 to 12;
1 meter: from 5 to 6 and from 9 to 10.

Check similar questions to practice:
on-the-number-line-above-the-segment-from-0-to-1-has-been-104204.html
a-straight-pipe-1-yard-in-length-was-marked-off-in-fourths-145031.html
a-100-meter-sprinting-track-is-marked-off-in-sixths-and-in-e-150349.html

So distinct length actually referring to distinct differences between lengths once cut? Like the post above me I saw distinct as "unique" the way it is with factoring and this really threw me and I'm still struggling to fully comprehend the meaning of distinct in relation to this problem.
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Re: Kim finds a 1-meter tree branch and marks it off in thirds   [#permalink] 07 Feb 2016, 13:30
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