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

To determine who earned the most total credits in Science and Math among Zara, Bryan, Charlie, and Diana, we must analyze the information provided in both statements. While each statement has valuable information, neither one alone gives a complete picture; combined, they provide the necessary context to assess the total credits for each individual.

A) Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient. Statement (1) provides comparisons between Zara, Bryan, Charlie, and Diana, but it lacks specific numerical values to definitively determine who has the most credits. Therefore, while it contains useful information, it does not provide a complete answer on its own.

B) Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient. Statement (2) suggests that Diana has higher credits in Science than both Bryan's and Charlie's combined totals, but it doesn't specify how many credits each individual has. As such, this statement alone does not allow us to conclusively determine who has the most credits.

C) BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient. When combined, the information from both statements enables us to compare the credits of all four friends. Statement (1) establishes relative differences, while statement (2) provides crucial insights into Diana's performance relative to others, allowing for a complete assessment.

D) EACH statement ALONE is sufficient. Neither statement provides enough information independently to ascertain who has the most credits. Each lacks critical data that the other supplies.

Conclusion To conclude, both statements must be utilized together to evaluate the performance of Zara, Bryan, Charlie, and Diana effectively. Each statement offers distinct insights that, while incomplete in isolation, collectively enable us to ascertain who earned the most total credits in Science and Math. Hence, the answer lies in the combined analysis of both statements.

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

The information provided in both statements does not allow us to conclusively determine the original or new positions of Beth and Carol relative to Ann after their movement. Thus, we cannot ascertain whether the distance between Beth's and Carol's homes decreased by 90% based solely on the distances described.

A) Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient. Statement (1) only provides the total distance traveled before Beth and Carol moved, which does not give any information about their specific locations or how their movements affect the distance between them. Therefore, it cannot be sufficient to answer the question.

B) Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient. Statement (2 indicates a decrease in distance between Beth's and Carol's homes, but does not provide enough context about their original distances from Ann or the initial arrangement to conclude the impact of their movements. Thus, it also cannot be sufficient.

C) BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient. Combining both statements still does not yield enough information to determine the spatial relationship between Beth's and Carol's homes after their movements. The lack of specific distance values prevents a clear conclusion.

D) EACH statement ALONE is sufficient. Neither statement alone contains sufficient information to establish the necessary spatial relationships, making this option incorrect.

Conclusion Both statements fail to provide the necessary context regarding the relative positioning of Beth's and Carol's homes and the implications of their movements. Consequently, even when considered together, they do not lead to a sufficient conclusion about the changes in distance, confirming that the information offered is inadequate for solving the problem presented.

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 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.

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.

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.

11,800

To calculate the total cost for the store under Plan A in the first year, we need to consider the one-time purchase and installation cost of $10,000, along with the monthly maintenance cost of $250 for 12 months. Since Plan A does not include cash loading costs, they will not incur that expense. The total comes to $10,000 + ($250 × 12), which equals $11,800.

A) 1,800 This amount incorrectly suggests that the total costs are minimal and does not account for the significant one-time purchase and installation cost or the monthly maintenance fees. The $1,800 figure does not reflect the actual expenses related to purchasing the ATM and ongoing maintenance.

B) 10,000 While this option represents the one-time purchase and installation cost of the ATM, it neglects to include the ongoing maintenance costs incurred throughout the year. Consequently, this amount significantly underestimates the total expenditure for the store.

D) 14,800 This figure inaccurately combines the one-time installation cost with a miscalculation of the monthly expenses. It appears to assume an additional cost that is not accounted for in the provided information regarding maintenance, resulting in an inflated total.

E) 16,000 This amount overestimates the store's first-year expenses by incorrectly adding cash loading costs, which are not applicable under Plan A. It also fails to correctly sum up the maintenance costs and the purchase price, leading to an erroneous total.

Conclusion In summary, the total expenditure for the store under Plan A for the first year is accurately calculated at $11,800. This includes the $10,000 one-time purchase and installation cost and $3,000 for maintenance over the year. All other options either overlook key costs or miscalculate the expenses, making them incorrect.