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100 points for $49 worth of Veritas practice GMATs FREE VERITAS PRACTICE GMAT EXAMS Earn 10 Points Per Post Earn 10 Points Per Thanks Earn 10 Points Per Upvote ## Is the average (arithmetic mean) of x, y, and z equal to the tagged by: Max@Math Revolution ##### This topic has 2 expert replies and 0 member replies ### GMAT/MBA Expert ## Is the average (arithmetic mean) of x, y, and z equal to the ## Timer 00:00 ## Your Answer A B C D E ## Global Stats Difficult [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 _________________ Math Revolution Finish GMAT Quant Section with 10 minutes to spare. The one-and-only Worldâ€™s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy. Only$149 for 3 month Online Course
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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.

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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.

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