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Kim finds a 1-meter tree branch and marks it off in thirds [#permalink]
 04 Oct 2012, 00:49
Question Stats:
47% (02:19) correct
52% (01:46) wrong based on 2 sessions
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
Last edited by Bunuel on 04 Oct 2012, 03:17, 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]
04 Oct 2012, 03:31
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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, Answer: E. Similar question to practice: on-the-number-line-above-the-segment-from-0-to-1-has-been-104204.htmlHope it helps.
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Re: Kim finds a 1-meter tree branch and marks it off in thirds [#permalink]
04 Feb 2013, 03:47
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Re: Kim finds a 1-meter tree branch [#permalink]
04 Oct 2012, 02:39
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]
06 Oct 2012, 02:50
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, Answer: E. Similar question to practice: on-the-number-line-above-the-segment-from-0-to-1-has-been-104204.htmlHope 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]
06 Oct 2012, 03:48
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, Answer: E. Similar question to practice: on-the-number-line-above-the-segment-from-0-to-1-has-been-104204.htmlHope 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]
06 Oct 2012, 04:54
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]
04 Feb 2013, 03:41
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, Answer: E. Similar question to practice: on-the-number-line-above-the-segment-from-0-to-1-has-been-104204.htmlHope 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 [#permalink]
01 Mar 2013, 09:30
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
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Re: Kim finds a 1-meter tree branch and marks it off in thirds [#permalink]
01 Mar 2013, 09:38
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 So, answer will be E. Hope it helps!
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Re: Kim finds a 1-meter tree branch and marks it off in thirds [#permalink]
01 Mar 2013, 10:00
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Re: Kim finds a 1-meter tree branch and marks it off in thirds
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