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Example Questions
Example Question #561 : Arithmetic
True or false: is the arithmetic mean of the set .
Statement 1:
Statement 2: is the arithmetic mean of and .
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.
BOTH STATEMENTS TOGETHER provide sufficient information to answer the question, but NEITHER STATEMENT ALONE provides sufficient information to answer the question.
BOTH STATEMENTS TOGETHER do NOT provide 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.
Assume both statements to be true, and examine two cases.
Case 1:
The arithmetic mean of and is
The conditions of both statements are satisfied.
The mean of the five numbers is their sum divided by 5:
Case 2:
The arithmetic mean of and is
The conditions of both statements are satisfied.
But the mean of the five numbers is
Therefore, the mean may or may not be equal to .