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Kim finds a 1-meter tree branch and marks it off in thirds and fifths. 24 Jun 2011, 12:22
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56% (02:27) correct 44% (02:36) wrong based on 1648 sessions

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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
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E
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Kim finds a 1-meter tree branch and marks it off in thirds and fifths. 04 Oct 2012, 03:31
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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
Show more

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,

Answer: E.

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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Kim finds a 1-meter tree branch and marks it off in thirds and fifths. 14 Jul 2011, 03:40
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smodak
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.
Show more

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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Kim finds a 1-meter tree branch and marks it off in thirds and fifths. 14 Jul 2011, 05:23
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hey karishma thanks for the reply
have u found the distinct sizes by finding out the difference between them?
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Kim finds a 1-meter tree branch and marks it off in thirds and fifths. 18 Jul 2011, 22:35
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sushantarora
hey karishma thanks for the reply
have u found the distinct sizes by finding out the difference between them?
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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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Kim finds a 1-meter tree branch and marks it off in thirds and fifths. 08 Nov 2011, 04:50
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Responding to a pm:

enigma123
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

Any idea how can this be solved? I tried repeatedly and failed. :cry:
Show more

This is what you are doing: You are marking off at 1/3, 2/3 and 3/3
and at 1/5, 2/5, 3/5 etc

Or we can say that we are marking at 5/15, 10/15 and 15/15
and at 3/15, 6/15, 9/15 etc so that we can easily compare.

Attachment:
Ques4.jpg
Ques4.jpg [ 3.68 KiB | Viewed 25519 times ]
Now the first piece you get is 3/15 in length, next one is 2/15 and the next one is 1/15. Now think, will you get pieces of length 4/15, 5/15 etc? No because you mark off at every 3/15 (you mark at 3/15, 6/15, 9/15, 12/15 and 15/15). So it is not possible to get any piece which is greater than 3/15.

The length of distinct pieces combined = 1/15 + 2/15 + 3/15 = 6/15
The fraction of original branch that remains = 1 - 6/15 = 9/15 = 3/5
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Kim finds a 1-meter tree branch and marks it off in thirds and fifths. 06 Oct 2012, 02:50
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Bunuel
Archit143
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,

Answer: E.

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

Hope it helps.
Show more
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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Kim finds a 1-meter tree branch and marks it off in thirds and fifths. 06 Oct 2012, 03:48
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Bunuel
Archit143
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,

Answer: E.

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?
Show more

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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Kim finds a 1-meter tree branch and marks it off in thirds and fifths. 04 Feb 2013, 03:41
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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,

Answer: E.

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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Kim finds a 1-meter tree branch and marks it off in thirds and fifths. 04 Feb 2013, 03:47
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rajathpanta
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,

Answer: E.

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??
Show more

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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Kim finds a 1-meter tree branch and marks it off in thirds and fifths. 01 Mar 2013, 09:38
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mun23
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
Show more

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
So, answer will be E.

Hope it helps!
Attachments

File comment: image attached
image.JPG
image.JPG [ 17.49 KiB | Viewed 35521 times ]

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Kim finds a 1-meter tree branch and marks it off in thirds and fifths. 23 Aug 2013, 02:38
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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
Answer = E = 3/5
Attachments

line.JPG
line.JPG [ 15.26 KiB | Viewed 34841 times ]

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Kim finds a 1-meter tree branch and marks it off in thirds and fifths. 13 Jan 2014, 13:33
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Bunuel
Archit143
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,

Answer: E.

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

Hope it helps.
Show more

Hi Bunuel

Please help me regarding this question

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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Kim finds a 1-meter tree branch and marks it off in thirds and fifths. 14 Jan 2014, 01:24
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Bunuel
Archit143
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,

Answer: E.

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

Hope it helps.

Hi Bunuel

Please help me regarding this question

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
Show more

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

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

Hope it's clear.
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Kim finds a 1-meter tree branch and marks it off in thirds and fifths. 28 Sep 2014, 04:51
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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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Kim finds a 1-meter tree branch and marks it off in thirds and fifths. 28 Sep 2014, 08:32
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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?
Show more

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:
https://gmatclub.com/forum/on-the-number ... 04204.html
https://gmatclub.com/forum/a-straight-pi ... 45031.html
https://gmatclub.com/forum/a-100-meter-s ... 50349.html
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Kim finds a 1-meter tree branch and marks it off in thirds and fifths. 07 Feb 2016, 14:30
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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
Show more

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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Kim finds a 1-meter tree branch and marks it off in thirds and fifths. 07 Feb 2016, 21:27
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redfield

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.
Show more

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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Kim finds a 1-meter tree branch and marks it off in thirds and fifths. 15 Nov 2018, 10:49
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Hi fskilnik,

I got yet another doubt for the day:)

In the above question ,my approach was

LCM OF 3 and 5 is 15, so assumed the line to be 15 m long
Then marked it 1/3rds and 1/5ths => markings i get are 3,5,6,9,10,12,15 . On breaking them at every markings, only the portion between 12 and 15 remains => (15-12)/15 = 3/15 =1/5 is what I got. Please help me as figure where Im going wrong.

Thankyou again :)
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fskilnik
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Kim finds a 1-meter tree branch and marks it off in thirds and fifths. 15 Nov 2018, 11:02
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yashna36
Hi fskilnik,

I got yet another doubt for the day:)

In the above question ,my approach was

LCM OF 3 and 5 is 15, so assumed the line to be 15 m long
Then marked it 1/3rds and 1/5ths => markings i get are 3,5,6,9,10,12,15 . On breaking them at every markings, only the portion between 12 and 15 remains => (15-12)/15 = 3/15 =1/5 is what I got. Please help me as figure where Im going wrong.

Thankyou again :)
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Hi, yashna36!

Ok!

Nice idea! Please note there are three different lengths "between markings" available: 3 (3-0, for instance) , 2 (5-3, for instance) and 1 (6-5, for instance).

According to the question stem, you must take out ONE of each, hence you take out 3+2+1 = 6.

The answer is what is left = 15-6 = 9 and going back to the original unit, we have 9/15 = 3/5 as the correct answer.

I hope you got it!

Regards and success in your studies!
Fabio.
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