## Does the average (arithmetic mean) of a, b and c equals c ?

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### Does the average (arithmetic mean) of a, b and c equals c ?

by airan » Sat Jul 05, 2008 10:53 pm
(1) c-a = c + b;
2) c = 0;
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by ksutthi » Sun Jul 06, 2008 7:14 am
Let me try.

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

From (1) -a = b

That means (a+b+c)/3 = (a-a+c)/3 = c/3
c = 0, average = 0 which is equal to c
c = 1, average = 1/3 which is not equal to c

INSUFFICIENT

From (2) It tells nothing - INSUFFICIENT

(1) + (2), This is exactly as in (1) when c = 0 - SUFFICIENT

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### Re: Does the average (arithmetic mean) of a, b and c equals c ?

by [email protected] » Sat Nov 20, 2021 6:51 am
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