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If the average (arithmetic mean) of 3 integers x, y, z is 10

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by Max@Math Revolution » Tue Aug 14, 2018 4:32 pm

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[Math Revolution GMAT math practice question]

If the average (arithmetic mean) of 3 integers x, y, z is 10, what is the value of z?

1) x=1
2) x=5-y
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Source: — Data Sufficiency |
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by Max@Math Revolution » Wed Aug 15, 2018 6:32 am
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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.

The original condition gives ( x + y + z ) / 3 = 10 or x + y + z = 30. Rearranging yields z = 30 - ( x + y ). Condition 2) gives x + y = 5, so condition 2) is sufficient .


Condition 1) is not sufficient since it gives no information about the value of y.

Therefore, B is the answer.

Answer: B
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