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

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by BTGmoderatorDC » Sun Oct 28, 2018 3:41 pm

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Answers

A

B

C

D

E

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Difficulty—

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.

OA E

Source: Magoosh
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Source: — Data Sufficiency |

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

by Brent@GMATPrepNow » Sun Oct 28, 2018 3:46 pm
BTGmoderatorDC 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.

OA E

Source: Magoosh
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
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by Jay@ManhattanReview » Sun Oct 28, 2018 9:58 pm
BTGmoderatorDC 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.

OA E

Source: Magoosh
Say the lengths of the three cut ropes are a, b, and c such that a > b > c.

From (1), we have a + b = 6 and from (2), we have b + c = 3.

We cannot find out the unique values of a, b or c.

However, we can derive the following information about their lengths.

1. Since b + c = 3, we have 0 < c <1.5 and 3 > b > 1.5

2. Since a + b = 6, we have b < 3 and a > 3

3. From (1) and (2), we have 4.5 > a > 3, 3 > b > 1.5 and 0 < c < 1.5

The correct answer: E

Hope this helps!

-Jay
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by fskilnik@GMATH » Mon Oct 29, 2018 2:49 am
BTGmoderatorDC 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.
Source: Magoosh
All lengths are presented in feet.

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

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.
Fabio Skilnik :: GMATH method creator ( Math for the GMAT)
English-speakers :: https://www.gmath.net
Portuguese-speakers :: https://www.gmath.com.br
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