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.

Statement (1) indicates there are four times as many nontenured faculty members as tenured faculty members, but it does not provide any information about the age of the tenured faculty. Thus, it is insufficient to determine the overall average age.

Statement (2) tells us that there are 7 tenured faculty members, but it does not provide any age information about these faculty members. Therefore, this statement alone is also insufficient for calculating the average age of all faculty members.

While combining both statements provides a ratio and the number of tenured faculty, it still fails to supply any information about their ages. Hence, even together, these statements do not allow us to calculate the overall average age.

As previously explained, neither statement provides the necessary information about the ages of tenured faculty members. Therefore, this option is incorrect since each statement alone is insufficient.