airan wrote: ↑

Sat Jul 05, 2008 10:53 pm

(1) c-a = c + b;
2) c = 0;

Target question: Does the average (arithmetic mean) of a, b, and c equal c?
This is a good candidate for rephrasing the target question.
If the average of a, b, and c equals c, we can write: (a + b + c)/3 = c
Multiply both sides of the equation by 3 to get: a + b + c = 3c
Subtract c from both sides: a + b = 2c
So.....
REPHRASED target question: Does a + b = 2c?

Statement 1: c - a = c + b
Add a to both sides to get: c = a + b + c
Subtract c from both sides to get: 0 = a + b
Since we have no information about the value of c, we can’t answer the REPHRASED target question with certainty.
So, statement 1 is NOT SUFFICIENT

Statement 2: c = 0
Since we have no information about the values of a and b, we can’t answer the REPHRASED target question with certainty.
So, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined
Statement 1 tells us that a + b = 0
Statement 2 tells us that c = 0
If c = 0, then we also know that 2c = 0
So, we can take the equation a + b = 0 and substitute 2c for 0 to get: a + b = 2c, which means the answer to the REPHRASED target question is YES, a + b = 2c
So, the combined statements are SUFFICIENT

Answer: C