Last year, Beth's home was d km due north of Ann's home and Carol's home was d km due south of Ann's home. Before Beth and Carol moved, the total distance was 100 kilometers for a trip that began at Ann's home, proceeded in a straight line to Beth's home, then to Carol's home, and then to Ann's home. (1) Before Beth and Carol moved, the total distance was 100 kilometers. (2) After Beth and Carol moved, the straight-line distance between Beth's home and Carol's home decreased by 90%.
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.
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.
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.
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.
Neither statement alone contains sufficient information to establish the necessary spatial relationships, making this option incorrect.
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.
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