Data Sufficiency

Vincen wrote: ↑

Sat Jan 23, 2021 6:28 am

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.

Answer: 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