8. 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%.
Answer: E
Statements (1) and (2) TOGETHER are NOT sufficient.
Both statements alone do not provide enough information to determine the specific distance between Beth's and Carol's homes after they moved, nor do they confirm the total distance traveled post-move.
A) Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
Statement (1) provides total distance information about the trip involving Ann, Beth, and Carol, but does not specify any details about the distances between Beth's and Carol's homes after they moved. Therefore, this option is incorrect.
B) Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
Statement (2) indicates that the straight-line distance between Beth's and Carol's homes decreased by 90%, but it lacks context about their original positions or how this affects the total distance traveled. Thus, this option is also incorrect.
C) BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
Even when combined, the two statements do not enable us to calculate or confirm the total distance traveled after Beth and Carol moved. The statements fail to provide a clear relationship or numerical values necessary for understanding the new distances. Hence, this option is incorrect.
D) EACH statement ALONE is sufficient.
Neither statement provides enough information individually to ascertain the total distance traveled after the moves. Therefore, this option is also incorrect.
E) Statements (1) and (2) TOGETHER are NOT sufficient.
This option correctly identifies that even when considering both statements, they do not provide adequate information to determine the distances involved after Beth and Carol's movements. The lack of specific numerical values or relationships means we cannot conclude anything definitive about the new distances.
Conclusion
The correct answer is E, as neither statement alone nor in combination provides sufficient information to determine the distances required. Both statements lack the necessary context and specifics to yield a definitive conclusion about the new distances between the homes after the moves.