Max@Math Revolution wrote:[GMAT math practice question]

Is the average (arithmetic mean) of x, y, and z equal to their median?

1) y is the average (arithmetic mean) of x, y, and z
2) z = 2y - x

Statement 1:
In other words, y is HALFWAY BETWEEN x and z, implying that x, y and z are EVENLY SPACED.
For any evenly spaced set, the average = the median.
Thus, the answer to the question stem is YES.
SUFFICIENT.

Statement 2:
x+z = 2y
(x+z)/2 = y
Implication:
y is the average of x and z -- the same information as that given in Statement 1.
Since Statement 1 is sufficient, so is Statement 2.
SUFFICIENT.

The correct answer is D.

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Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution.

The first step of the VA (Variable Approach) method is to modify the original condition and the question. We then recheck the question.

If data are symmetric, then the average and the median of the data are the same.

Condition 1):
If y is the mean of x, y and z, then x, y, z are symmetric. To see this note that ( x + y + z ) / 3 = y implies that y = ( x + z ) / 2. So, 2y = x + z and y - x = z - y, which means that x, y, z are symmetric.
Condition 1) is sufficient.

Condition 2):
z = 2y - x is equivalent to y - x = z - y, which is equivalent to condition 1).
Condition 2) is sufficient.

FYI, Tip 1) of the VA method states that D is most likely to be the answer if conditions 1) and 2) provide the same information.

Therefore, D is the answer.
Answer: D