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16 Sep 2014, 01:10
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C
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Difficulty:
35%
(medium)
Question Stats:
73% (01:37) correct
27%
(01:40)
wrong
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Trains depart from Station A to Station B every 15 minutes (one train per departure), starting from 8:00 am, and travel at the same constant speed. At 11:05 am, a train, traveling at a constant speed, departs from Station B to Station A. If the distance between the two stations is 80 kilometers, how many trains traveling from A to B will the train traveling from B to A encounter during its journey?
(1) Trains from Station A to Station B travel at a constant speed of 40 kilometers per hour.
(2) The train from Station B to Station A travels at a constant speed of 40 kilometers per hour.
(1) Trains from Station A to Station B travel at a constant speed of 40 kilometers per hour.
(2) The train from Station B to Station A travels at a constant speed of 40 kilometers per hour.
16 Sep 2014, 01:10
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Official Solution:
Trains depart from Station A to Station B every 15 minutes (one train per departure), starting from 8:00 am, and travel at the same constant speed. At 11:05 am, a train, traveling at a constant speed, departs from Station B to Station A. If the distance between the two stations is 80 kilometers, how many trains traveling from A to B will the train traveling from B to A encounter during its journey?
(1) Trains from Station A to Station B travel at a constant speed of 40 kilometers per hour.
The above implies that trains from Station A to Station B are on the track for 2 hours. Therefore, the train from Station B is guaranteed to meet the 8 trains from Station A that departed between 9:15 a.m. and 11:00 a.m. If the train from B to A can cover the 80-kilometer distance in just 1 minute, it will only meet these 8 trains since it will arrive at Station A before the next train at 11:15 a.m. departs from Station A. However, if the train from B to A is much slower, it will meet more than 8 trains from Station A. Therefore, statement (1) is not sufficient to answer the question.
(2) The train from Station B to Station A travels at a constant speed of 40 kilometers per hour.
Since the train from Station B to Station A is on the track for 2 hours, it will arrive at Station A at 1:05 p.m. If trains from Station A to Station B take more than 3 hours and 5 minutes to arrive at Station B, then the train from B to A will meet all 21 trains that depart from Station A to Station B between 8:00 a.m. and 1:05 p.m. However, if the train from A to B can cover 80 kilometers in 1 minute, then the train from B to A will meet only 8 trains that depart from Station A to Station B between 11:15 a.m. and 1:05 p.m. Therefore, statement (2) is not sufficient to answer the question.
(1)+(2) We have no unknowns left, and can solve the question. However, for those who are interested, we can proceed as follows. Both, trains from Station A to B and the train from Station B to A are on the track for 2 hours. Therefore, the train traveling from B to A, in 2 hours, between 11:05 a.m. and 1:05 p.m., will encounter all 16 trains from Station A that departed between 9:15 a.m. and 1:05 p.m. Sufficient.
Answer: C
Trains depart from Station A to Station B every 15 minutes (one train per departure), starting from 8:00 am, and travel at the same constant speed. At 11:05 am, a train, traveling at a constant speed, departs from Station B to Station A. If the distance between the two stations is 80 kilometers, how many trains traveling from A to B will the train traveling from B to A encounter during its journey?
(1) Trains from Station A to Station B travel at a constant speed of 40 kilometers per hour.
The above implies that trains from Station A to Station B are on the track for 2 hours. Therefore, the train from Station B is guaranteed to meet the 8 trains from Station A that departed between 9:15 a.m. and 11:00 a.m. If the train from B to A can cover the 80-kilometer distance in just 1 minute, it will only meet these 8 trains since it will arrive at Station A before the next train at 11:15 a.m. departs from Station A. However, if the train from B to A is much slower, it will meet more than 8 trains from Station A. Therefore, statement (1) is not sufficient to answer the question.
(2) The train from Station B to Station A travels at a constant speed of 40 kilometers per hour.
Since the train from Station B to Station A is on the track for 2 hours, it will arrive at Station A at 1:05 p.m. If trains from Station A to Station B take more than 3 hours and 5 minutes to arrive at Station B, then the train from B to A will meet all 21 trains that depart from Station A to Station B between 8:00 a.m. and 1:05 p.m. However, if the train from A to B can cover 80 kilometers in 1 minute, then the train from B to A will meet only 8 trains that depart from Station A to Station B between 11:15 a.m. and 1:05 p.m. Therefore, statement (2) is not sufficient to answer the question.
(1)+(2) We have no unknowns left, and can solve the question. However, for those who are interested, we can proceed as follows. Both, trains from Station A to B and the train from Station B to A are on the track for 2 hours. Therefore, the train traveling from B to A, in 2 hours, between 11:05 a.m. and 1:05 p.m., will encounter all 16 trains from Station A that departed between 9:15 a.m. and 1:05 p.m. Sufficient.
Answer: C
15 Mar 2023, 03:47
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I have edited the question and the solution by adding more details to enhance its clarity. I hope it is now easier to understand.
