GMAT Math : Median
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Example Questions
Example Question #62 : Descriptive Statistics
Given five distinct positive integers - 
Statement 1:
Statement 1:
EITHER STATEMENT ALONE provides sufficient information to answer the question.
STATEMENT 1 ALONE provides sufficient information to answer the question, but STATEMENT 2 ALONE does NOT provide sufficient information to answer the question.
BOTH STATEMENTS TOGETHER do NOT provide sufficient information to answer the question.
BOTH STATEMENTS TOGETHER provide sufficient information to answer the question, but NEITHER STATEMENT ALONE provides sufficient information to answer the question.
STATEMENT 2 ALONE provides sufficient information to answer the question, but STATEMENT 1 ALONE does NOT provide sufficient information to answer the question.
EITHER STATEMENT ALONE provides sufficient information to answer the question.
Assume Statement 1 alone. By the Addition Property of Inequality, if
then 
By extension, the continued inequality in Statement 1 is equivalent to
A similar argument holds for Statement 2. By the Multiplication Property of Inequality, if
and 
By extension, the continued inequality in Statement 2 is also equivalent to
The median of five numbers (an odd number) is the number in the middle when they are arranged in ascending order. Therefore, it can be established from either statement alone that of the five, the median is 
Example Question #62 : Descriptive Statistics
Given five distinct positive integers -
Statement 1:
Statement 2:
BOTH STATEMENTS TOGETHER do NOT provide sufficient information to answer the question.
BOTH STATEMENTS TOGETHER provide sufficient information to answer the question, but NEITHER STATEMENT ALONE provides sufficient information to answer the question.
STATEMENT 1 ALONE provides sufficient information to answer the question, but STATEMENT 2 ALONE does NOT provide sufficient information to answer the question.
STATEMENT 2 ALONE provides sufficient information to answer the question, but STATEMENT 1 ALONE does NOT provide sufficient information to answer the question.
EITHER STATEMENT ALONE provides sufficient information to answer the question.
STATEMENT 1 ALONE provides sufficient information to answer the question, but STATEMENT 2 ALONE does NOT provide sufficient information to answer the question.
Assume Statement 1 alone. The median of five numbers (an odd number) is the number in the middle when they are arranged in ascending order. By Statement 1, this number is 
Statement 2 alone, however, gives that the mean is 
Case 1:
The mean is
making this consistent with Statement 2.
The median is the middle element, 
Case 2:
again, making this consistent with Statement 2.
The median is the middle element, 
Example Question #61 : Descriptive Statistics
What is the median of a data set comprising nineteen elements?
Statement 1: When arranged in ascending order, the ninth element is 72.
Statement 2: When arranged in descending order, the ninth element is 72.
BOTH statements TOGETHER are sufficient to answer the question, but NEITHER statement ALONE is sufficient to answer the question.
Statement 1 ALONE is sufficient to answer the question, but Statement 2 ALONE is not sufficient to answer the question.
EITHER statement ALONE is sufficient to answer the question.
BOTH statements TOGETHER are insufficient to answer the question.
Statement 2 ALONE is sufficient to answer the question, but Statement 1 ALONE is not sufficient to answer the question.
BOTH statements TOGETHER are sufficient to answer the question, but NEITHER statement ALONE is sufficient to answer the question.
In a data set of 19 elements, 19 being odd, the median is the element that occurs in the 
The answer is that both statements together are sufficient to answer the question, but neither statement alone is sufficient to answer the question.
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