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

Question

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.

BrentGMATPrepNow · Answer

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

Answer:  E

Cheers,
Brent

Sguha0305 · Answer

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

BrentGMATPrepNow · Answer

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

Cheers and thanks,
Brent

nikhilmathew1990 · Answer

I believe the catch in this is the decimal values.

fskilnik · Answer

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

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

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