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# A length of rope is cut into three different lengths. What is the leng

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A length of rope is cut into three different lengths. What is the leng  [#permalink]

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24 Nov 2016, 09:41
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A length of rope is cut into three different lengths. What is the length of the shortest rope?

(1) The combined length of the longest two pieces is 6 feet.

(2) The combined length of the shortest two pieces is 3 feet.
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Joined: 12 Sep 2015
Posts: 4000
A length of rope is cut into three different lengths. What is the leng  [#permalink]

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Updated on: 20 May 2018, 10:31
Top Contributor
lalania1 wrote:
A length of rope is cut into three different lengths. What is the length of the shortest rope?

(1) The combined length of the longest two pieces is 6 feet.

(2) The combined length of the shortest two pieces is 3 feet.

Target question: What is the length of the shortest rope?
Let's assign some variables.
Let x = length of shortest rope
Let y = length of middle rope
Let z = length of longest rope

Statement 1: The combined length of the longest two pieces is 6 feet.
In other words, y + z = 6
Since we don't have any information about the TOTAL length of the rope before it was cut, there's no way to determine the value of x (the length of shortest rope)
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: The combined length of the shortest two pieces is 3 feet.
In other words, x + y = 6
Once gain, there's no way to determine the value of x (the length of shortest rope)
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined
Statement 1 tells us that y + z = 6
Statement 2 tells us that x + y = 3
Here we have 2 equations with 3 variables. In order to solve a system with 3 variables, we need 3 equations. As such, the combined statements are NOT SUFFICIENT

If you're not convinced, you might TEST SOME VALUES.
Case a: x = 1, y = 2 and z = 4. In this case, the length of the smallest piece is 1
Case b: x = 1.4, y = 1.6 and z = 4.4. In this case, the length of the smallest piece is 1.4
So, the combined statements are NOT SUFFICIENT

Cheers,
Brent
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Originally posted by GMATPrepNow on 24 Nov 2016, 09:53.
Last edited by GMATPrepNow on 20 May 2018, 10:31, edited 1 time in total.
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Joined: 10 Aug 2017
Posts: 2
Location: United States
Concentration: Finance, Technology
A length of rope is cut into three different lengths. What is the leng  [#permalink]

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20 May 2018, 10:01
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Quote:
If you're not convinced, you might TEST SOME VALUES.
Case a: x = 1, y = 2 and z = 4. In this case, the length of the smallest piece is 1
Case b: x = 2, y = 1 and z = 5. In this case, the length of the smallest piece is 2
So, the combined statements are NOT SUFFICIENT

So in a way you are saying that the smallest length is 1. Also in your assumption X is the smallest then the second case (Case b) is not even valid.
I am sure, I am missing something.
Will be great if you could explain the fallacy here.
TIA
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Joined: 12 Sep 2015
Posts: 4000
Re: A length of rope is cut into three different lengths. What is the leng  [#permalink]

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20 May 2018, 10:32
Top Contributor
Sguha0305 wrote:
Quote:
If you're not convinced, you might TEST SOME VALUES.
Case a: x = 1, y = 2 and z = 4. In this case, the length of the smallest piece is 1
Case b: x = 2, y = 1 and z = 5. In this case, the length of the smallest piece is 2
So, the combined statements are NOT SUFFICIENT

So in a way you are saying that the smallest length is 1. Also in your assumption X is the smallest then the second case (Case b) is not even valid.
I am sure, I am missing something.
Will be great if you could explain the fallacy here.
TIA

I forgot that I said x is the length of the shortest piece.
I've edited my response accordingly.

Cheers and thanks,
Brent
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Joined: 30 Jan 2018
Posts: 2
Location: India
GMAT 1: 680 Q47 V36
GPA: 4
Re: A length of rope is cut into three different lengths. What is the leng  [#permalink]

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20 May 2018, 10:44
Sguha0305 wrote:
Quote:
If you're not convinced, you might TEST SOME VALUES.
Case a: x = 1, y = 2 and z = 4. In this case, the length of the smallest piece is 1
Case b: x = 2, y = 1 and z = 5. In this case, the length of the smallest piece is 2
So, the combined statements are NOT SUFFICIENT

So in a way you are saying that the smallest length is 1. Also in your assumption X is the smallest then the second case (Case b) is not even valid.
I am sure, I am missing something.
Will be great if you could explain the fallacy here.
TIA

I believe the catch in this is the decimal values.
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Status: GMATH founder
Joined: 12 Oct 2010
Posts: 935
Re: A length of rope is cut into three different lengths. What is the leng  [#permalink]

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29 Oct 2018, 03:57
lalania1 wrote:
A length of rope is cut into three different lengths. What is the length of the shortest rope?

(1) The combined length of the longest two pieces is 6 feet.

(2) The combined length of the shortest two pieces is 3 feet.

All lengths are presented in feet.

$${\rm{rope}}\left( s \right):\,\,s < i < l\,\,\,\,\left\{ \matrix{ \,? = s\,\,\left( {{\rm{shortest}}} \right) \hfill \cr \,i\,\,\left( {{\rm{intermediate}}} \right) \hfill \cr \,l\,\,\left( {{\rm{longest}}} \right) \hfill \cr} \right.$$

Let go straight to (1+2). A BIFURCATION proves the correct answer is (E):

$$\left( {1 + 2} \right)\,\,\,\left\{ \matrix{ \,l + i = 6 \hfill \cr s + i = 3 \hfill \cr} \right.\,\,\,\,\,\left[ {{\rm{feet}}} \right]$$

$$\left\{ \matrix{ \,{\rm{Take}}\,\,\left( {l,i,s} \right){\rm{ = }}\left( {4,2,1} \right)\,\,\,\, \Rightarrow \,\,? = 1\,\,{\rm{viable}} \hfill \cr \,{\rm{Take}}\,\,\left( {l,i,s} \right){\rm{ = }}\left( {3.5,2.5,0.5} \right)\,\,\,\, \Rightarrow \,\,? = 0.5\,\,{\rm{viable}} \hfill \cr} \right.$$

This solution follows the notations and rationale taught in the GMATH method.

Regards,
Fabio.
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Fabio Skilnik :: GMATH method creator (Math for the GMAT)
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Re: A length of rope is cut into three different lengths. What is the leng   [#permalink] 29 Oct 2018, 03:57
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