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

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.

gmatophobia · Answer

Statements 1 and 2 are individually not sufficient as each statement just provides the range of one of the two sets. Hence, we can eliminate A, B, and D.

Combined

The statements combined don't help either as we can formulate different combinations keeping the average at 100. The average value of a set is that value at which the elements of the set are 'balanced', i.e. that value at which the positive difference and negative difference of each member with respect to the average cancels out. Hence, merely knowing the average of a set (100 in this case), we can create multiple sets with an average value of 100. To understand this better let's consider the following examples -

Ex:

Case 1

A = {90, 100, 110}
B = {85, 100, 115}

Combined = {85, 90, 100 100, 110, 115}

Range = 30

Case 2

A = {90, 100, 110}
B = {95, 95,.... , 125}

Combined = {90, 95, ... , 125}

Range = 35

As we have multiple possible answers to the target question, the statements combined are not sufficient.

Option E

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

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GMAT Data Sufficiency (DS) Questions

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

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