What is the Median of Data Set A? GMAT Data Sufficiency

Question: What is the median of data set A?

1. No number in data set A is less than the average (arithmetic mean) of the set
2. The average (arithmetic mean) of the data set A is equal to the range of the set

1. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
2. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
3. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
4. EACH statement ALONE is sufficient.
5. Statements (1) and (2) TOGETHER are NOT sufficient.

Correct Answer: C
Solution with Explanation:
Approach Solution (1):

1. No number in the data set A is less than the average (arithmetic mean) of the set

Since no number is less than the average, then no number is more than the average, which implies that the list contains identical elements: A = {x, x, x, …}. From this it follows that (the average) = (the median). But we don’t know the value of x, thus this statement is not sufficient

2. The average (arithmetic mean) of data set A is equal to the range of the set

Not sufficient: if A = {0, 0, 0, 0}, then (the median) = 0, but if A = {1, 2, 2, 3}, then (the median) = 2
(1) + (2) From (1) we have that the list contains identical elements. The range of all such sets is 0. Therefore, from (2) we have that (the average) = (the range) = 0 and since from (1) we also know that (the average) = (the median), then (the median) = 0
Sufficient

Correct Option: C

Approach Solution (2):

{2,2} or {3,3,3} does not satisfy statement 2

In the above mentioned set Average is not equal to range

For, {2,2} Average = 2, Range = 0

{3,3,3} Average = 3, Range = 0

Only set A = {x, x, x, x, …} where x = 0 satisfies both the statement

Correct Option: C

Approach Solution (3):

This is question is solved:

1) The set can be a one element set either {0} or {1} so median = 0 or 1.
Hence insufficient

2) For this the sets can be {1,1} or {0,0}.
Hence this statement too is insufficient
Combining 1 + 2, we get:
The set can only be a set with zeroes, as for {1} the range is zero which does not satisfy statement 2
Hence, the median will always be zero.
Sufficient

Correct Option: C

“What is the median of data set A?”- is a topic of the GMAT Quantitative reasoning section of GMAT. This question has been taken from the book "GMAT Quantitative Review". GMAT Quant section consists of a total of 31 questions. GMAT Data Sufficiency questions consist of a problem statement followed by two factual statements. GMAT data sufficiency comprises 15 questions which are two-fifths of the total 31 GMAT quant questions.

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