we need to find (x+y+z)/3

(1) 2x + y + 4z = 23
Not sufficient
(2) 3x + 4y + z = 22
Not sufficient

Adding 1 and 2 , we get
5x+5y+5z = 45
=> x+y+z = 9
Average (x+y+z)/3 = 3

Answer C
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Target question: What is the average of x, y, and z?

NOTE: the average of x, y and z = (x + y + z)/3

Statement 1: 2x + y + 4z = 23
This statement doesn't FEEL sufficient, so I'll TEST some values.
There are several values of x, y and z that satisfy statement 1. Here are two:
Case a: x = 0, y = 23 and z = 0. In this case, the average of x, y and z = (0 + 23 + 0)/3 = 23/3
Case b: x = 11, y = 1 and z = 0. In this case, the average of x, y and z = (11 + 1 + 0)/3 = 12/3 = 4
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Aside: For more on this idea of plugging in values when a statement doesn't feel sufficient, read my article: http://www.gmatprepnow.com/articles/dat ... lug-values

Statement 2: 3x + 4y + z = 22
There are several values of x, y and z that satisfy statement 1. Here are two:
Case a: x = 0, y = 0 and z = 22. In this case, the average of x, y and z = (0 + 0 + 22)/3 = 22/3
Case b: x = 0, y = 5 and z = 2. In this case, the average of x, y and z = (0 + 5 + 2)/3 = 7/3
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined
Statement 1 tells us that 2x + y + 4z = 23
Statement 2 tells us that 3x + 4y + z = 22
ADD the two equations to get: 5x + 5y + 5z = 45
Divide both sides by 5 to get: x + y + z = 9
Since the average of x, y and z = (x + y + z)/3, we can see that the average of x, y and z = 9/3 = 3
So, the average = 3
Since we can answer the target question with certainty, the combined statements are SUFFICIENT

Answer: C
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