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If the average (arithmetic mean) of set A is 100 and the av

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If the average (arithmetic mean) of set A is 100 and the av

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[GMAT math practice question]

If the average (arithmetic mean) of set A is 100 and the average (arithmetic mean) of set B is 100, what is the range of sets A and B combined?

1) The range of set A is 20.
2) The range of set B is 30.

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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.

There is no relationship between the average of a set and its range.
In addition, there is no way of determining the range of a set from the ranges of its subsets. Notice that “E” is in “no rElation”. Many questions about “relation” have the answer E.
Thus, E is likely to be the answer.

We can verify this by considering both conditions together:
If A = { 90, 110 } and B = { 85, 115 }, then the range of A∪B={85,90,110,115} is 30.
If A = { 90, 110 } and B = { 92, 93, 95, 98, 122 }, then the range of A∪B={ 90, 92, 93, 95, 98, 110, 122 } is 32.
Since the range of A∪B is not uniquely determined, both conditions together are not sufficient.

Therefore, the answer is E.
Answer: E

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