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

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

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07 Nov 2011, 14:21
5
00:00

Difficulty:

85% (hard)

Question Stats:

44% (02:28) correct 56% (02:10) wrong based on 75 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) 7/15
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 and fifths.  [#permalink]

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07 Nov 2011, 14:52
the problem asks you to divide the 1m price of wood in 5 and 3 parts. So think of a baseball bat and you are marking, using a pen, the fifths and thirds. So you would have 1/5, 2/5,3/5, 4/5 marks as well as 1/3 and 2/3 marks.

for comparison reasons you would multiply by fifths by 3 and the thirds by 5. This would give us in order 3/15, 5/15, 6/15, 9/15, 10/15, 12/15.

You can now see that there is 3 3/15 pieces, 2 2/15 pieces and 2 1/15 pieces. In the question, she takes out one piece of each: 1-( 3/15 + 2/15 +1/15 )=1-( 6/15 )= 9/15= 3/5

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

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07 Nov 2011, 15:17
Thanks loser. I understood most of it apart from:

You can now see that there is 3 3/15 pieces, 2 2/15 pieces and 2 1/15 pieces.

How did you get this ?
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MGMAT 1 --> 530
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Re: Kim finds a 1-meter tree branch and marks it off in thirds and fifths.  [#permalink]

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07 Nov 2011, 17:57
After the marks on the 1m object. You should have it marked as:3/15, 5/15, 6/15, 9/15, 10/15, 12/15.
So the first piece is 3/15-0= 3/15
Second is 5/15- 3/15 = 2/15
Third is 6/15-5/15= 1/15...
Last one should be 1-12/15= 3/15
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Re: Kim finds a 1-meter tree branch and marks it off in thirds and fifths.  [#permalink]

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08 Nov 2011, 04:50
2
Responding to a pm:

enigma123 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

Any idea how can this be solved? I tried repeatedly and failed.

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 [ 3.68 KiB | Viewed 2341 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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Re: Kim finds a 1-meter tree branch and marks it off in thirds and fifths.  [#permalink]

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12 Nov 2011, 09:33
100 cm long branch will be marked as:
20. 33.33. 40. 60. 66.66. 80 [i. e. you have marking at these points]
1st break: 20 cm, 2nd: 33.33 cm , 3rd: 40 cm and so on

Pieces we will have: 20 cm, 13.33 cm, 6.66 cm, 20 cm, 6.66 cm, 13.33 cm, and 20 cm. Total 100 cm.
Length of distinct pieces= 20+13:33+6.66=40 cm
Remaining= 100-40= 60.
==>60/100= 3/5
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Re: Kim finds a 1-meter tree branch and marks it off in thirds and fifths.  [#permalink]

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15 Nov 2018, 10:49
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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Kim finds a 1-meter tree branch and marks it off in thirds and fifths.  [#permalink]

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15 Nov 2018, 11:02
yashna36 wrote:
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

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

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15 Nov 2018, 18:31
What fraction of the original branch remains?

Isn't it ambiguous question stem?
It could give clear picture if author has mentioned the fraction of length remains after removing one piece of each distinct length.

I understood it as fraction of number of branch remains.
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Re: Kim finds a 1-meter tree branch and marks it off in thirds and fifths.  [#permalink]

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16 Nov 2018, 05:44
enigma123 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

gvij2017 wrote:
What fraction of the original branch remains?

Isn't it ambiguous question stem?
It could give clear picture if author has mentioned the fraction of length remains after removing one piece of each distinct length.

I understood it as fraction of number of branch remains.

The author has mentioned EXACTLY what you have asked him/her to do.

Regards,
Fabio.
_________________
Fabio Skilnik :: GMATH method creator (Math for the GMAT)
Our high-level "quant" preparation starts here: https://gmath.net
Re: Kim finds a 1-meter tree branch and marks it off in thirds and fifths.   [#permalink] 16 Nov 2018, 05:44
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