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x, y and z are different integers. Is their average equal to

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by Max@Math Revolution » Mon Apr 08, 2019 11:06 pm

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[GMAT math practice question]

x, y and z are different integers. Is their average equal to their median?

1) Their range is 11.
2) Their median is 11.
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Source: — Data Sufficiency |
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by Max@Math Revolution » Wed Apr 10, 2019 11:57 pm
=>

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.

Suppose x, y and z are different integers with x < y < z.
For their average ( x + y + z ) / 3 to be equal to their median y,
we must have z - y = y - x, and so their range is z - x = z - y + y - x = 2(y-x).
This implies that z - x is an even integer.

Condition 1)
Since condition 1) gives an odd value for the range, the answer is 'no'. Thus, condition 1) is sufficient by CMT (Common Mistake Type) 1.

Condition 2)
If x = 10, y = 11 and z = 12, then the average and the median are the same, and the answer is 'yes'
If x = 10, y = 11 and z = 15, then the average 12 is different from the median 11, and the answer is 'no'.
Thus, condition 2) is not sufficient, since it does not yield a unique solution.

Therefore, A is the answer.
Answer: A
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