2. The average[arithmetic mean] age of the nontenured faculty members in the Physics Department at University M is 40 years. What is the average age, in years, of all faculty members in the Physics Department? (1) There are 4 × as many nontenured faculty members as tenured faculty members. (2) There are 7 tenured faculty members.
Answer: E
The average age of all faculty members cannot be determined from the given statements.
Neither statement alone provides enough information to calculate the average age of all faculty members in the Physics Department, and even when combined, they do not yield a definitive answer.
A) Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
Statement (1) indicates that there are four times as many nontenured faculty members as tenured faculty members, but without knowing the actual number of tenured faculty members or their ages, we cannot compute the overall average age. Therefore, this statement alone is insufficient.
B) Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
Statement (2) provides the number of tenured faculty members but does not give any information about their ages. Without this information, we cannot determine the overall average age. Hence, this statement alone is also insufficient.
C) BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
Combining both statements does not resolve the issue of missing information regarding the ages of the tenured faculty. While we know there are tenured faculty members, we still lack their age details to determine the overall average. Thus, this option is incorrect.
D) EACH statement ALONE is sufficient.
As analyzed, neither statement provides the necessary information to calculate the average age of all faculty members. Therefore, this option is incorrect.
E) Statements (1) and (2) TOGETHER are NOT sufficient.
This is the correct answer, as combining the two statements does not allow for the calculation of the average age of all faculty members in the Physics Department. The necessary information about the ages of tenured faculty is missing.
Conclusion
In conclusion, the average age of all faculty members cannot be determined based on the provided statements. Both statements fail to provide critical information about the ages of the tenured faculty, and therefore, the correct answer is that the statements together are not sufficient to calculate the overall average age.