Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.

The first statement provides the initial revenue for 2001, allowing us to calculate subsequent years' revenues based on a consistent 10% increase. In contrast, the second statement lacks the necessary initial revenue figure to determine the revenue for the years in question.

A) Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
Statement (1) indicates that the predicted revenue for 2001 is $11,000,000. From this, we can calculate the revenues for the following years, applying the 10% increase successively until we exceed $16,000,000. This calculation shows that by 2005, the predicted revenue surpasses $16,000,000, making statement (1) sufficient.

B) Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
Statement (2) claims that the predicted revenue for 2004 is $4,641,000 more than the revenue for 2000. However, without knowing the revenue for 2000, we cannot infer the actual revenue for 2004 or any subsequent years. Hence, statement (2) is insufficient on its own.

C) BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
While combining both statements might provide additional information, statement (1) alone is sufficient to determine the first year the revenue exceeds $16,000,000. Therefore, this option is incorrect, as statement (1) stands alone.

D) EACH statement ALONE is sufficient.
This option is false as statement (2) does not provide enough information to determine the revenue for the required years, while statement (1) does.

E) Statements (1) and (2) TOGETHER are NOT sufficient.
This option is incorrect because statement (1) alone is sufficient to find the answer, rendering the combination unnecessary.

Conclusion
In this scenario, statement (1) gives a clear starting point for revenue calculations, enabling us to determine the first year that revenue exceeds $16,000,000. Statement (2) lacks the essential initial revenue data, making it insufficient for solving the problem on its own. Thus, the analysis confirms that statement (1) is the key to resolving the question.

Sufficient information is provided for Products A and D.

For Products A and D, the subtotals in the table can be divided by the integer number of units purchased to determine the unit price. If the subtotal is less than €3 multiplied by the number of units, we can conclude that the unit price is less than €3.

A) Product A
The subtotal and integer quantity for Product A allow us to calculate the unit price. If the subtotal is less than €3 × number of units, we can confirm that the unit price is less than €3. Information is sufficient.

B) Product B
For Product B, we do not have enough information about the number of units purchased relative to the subtotal to determine if the unit price is less than €3. Information is insufficient.

C) Product C
Similarly, for Product C, the relationship between subtotal and units purchased is unclear. Without this, we cannot determine whether the unit price is less than €3. Information is insufficient.

D) Product D
The subtotal and integer quantity for Product D allow us to calculate the unit price. If the resulting unit price is less than €3, we can reach a definitive conclusion. Information is sufficient.

Conclusion
The unit price can be definitively determined to be less than €3 for Products A and D, given the subtotals and integer quantities. For Products B and C, there is not enough information to determine this, highlighting the importance of knowing both the subtotal and the number of units purchased.

Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.

Statement (1) provides a specific probability for selecting 2 adults, which allows for the calculation of the number of adults in relation to the total group size. However, statement (2) does not provide a precise number of adults, only indicating that they constitute more than 50% of the group, which is insufficient for a definitive calculation.

A) Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
This statement correctly identifies the sufficiency of statement (1). Given the probability of selecting 2 adults as 1/3, we can derive that if there are at least 2 adults and 2 children, the total number of adults can be determined mathematically, fulfilling the requirement to answer the question.

B) Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
This statement is incorrect because while statement (2) indicates that adults make up more than 50% of the group, it does not provide enough specific information to determine the exact number of adults. Therefore, this statement alone cannot suffice to answer the question.

C) BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
This option is also incorrect because statement (1) alone provides enough information to answer the question without needing to combine it with statement (2). Thus, both statements together are not necessary for sufficiency.

D) EACH statement ALONE is sufficient.
This option is false, as statement (2) alone does not provide enough information to determine the number of adults. Only statement (1) is sufficient on its own.

E) Statements (1) and (2) TOGETHER are NOT sufficient.
This choice is incorrect since statement (1) alone is indeed sufficient. The combination of both statements is unnecessary.

Conclusion
In this analysis, we find that statement (1) sufficiently provides the necessary probability to derive the number of adults in the group, whereas statement (2) lacks specificity for a conclusive answer. Thus, only statement (1) can stand alone as sufficient, making option A the correct choice.

Statements (1) and (2) TOGETHER are NOT sufficient.

The average age of all faculty members cannot be determined solely from the information provided in either statement or from their combination. While we know the average age of nontenured faculty members and the ratio of nontenured to tenured faculty, we lack specific age information for tenured faculty members to compute an overall average.

A) Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
Statement (1) indicates there are four × 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.

B) Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
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.

C) BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
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.

D) EACH statement ALONE is sufficient.
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.

Conclusion
Both statements fail to provide sufficient information to determine the average age of all faculty members in the Physics Department. Without specific age data for the tenured faculty, we cannot calculate an overall average, rendering the combination of both statements equally inadequate. Thus, the answer is that statements (1) and (2) together are not sufficient.

Cora's time slot can be determined independently from both statements.

Cora's time slot must begin with an even hour and cannot be immediately before George's slot, which runs from 9:00 a.m. to 10:00 a.m. Since the only even-numbered hour after George's is 10:00 a.m., her possible slot can only be the 11:00 a.m.-12:00 p.m. slot, making each statement alone sufficient to conclude Cora's time.

A) Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
Statement (1) indicates that Cora's time slot is not immediately before George's, but it does not provide information on the even-numbered requirement. Therefore, while it suggests a later time, it cannot assure Cora's time slot, making this statement insufficient on its own.

B) Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
Statement (2) reveals that Cora's time slot is later than George's, which does imply she works in the 10:00 a.m.-11:00 a.m. or 11:00 a.m.-12:00 p.m. slots. However, it does not confirm the even-numbered requirement for her time slot. Thus, this statement alone is also insufficient.

C) BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
Combining both statements does help establish Cora's time slot, as neither can independently provide the solution. The first rules out the slot before George, while the second confirms it must be later, making them jointly sufficient but not independently so.

D) EACH statement ALONE is sufficient.
This is correct because both statements independently clarify Cora's time slot. Statement (1) confirms she is not in the 10:00 a.m. slot, while statement (2) confirms she must be in the 11:00 a.m. slot, fulfilling both the even and time slot requirements alone.

Conclusion
Each statement can independently determine Cora's time slot as 11:00 a.m.-12:00 p.m. Statement (1) confirms she cannot be in George's time slot, while statement (2) establishes she works later in the day. Hence, both statements are sufficient on their own.