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Kaplan-train departure (tough)

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Kaplan-train departure (tough)

by singhsa » Sat Sep 25, 2010 11:32 pm
A woman is planning a trip that involves 3 connecting trains that depart from Stations X, Y, and Z, respectively. The first train leaves Station X every hour, beginning at 6 a.m., and arrives at Station Y hours later. The second train leaves Station Y every half hour, beginning at 9 a.m., and arrives at Station Z hours later. The third train leaves Station Z every 45 minutes, beginning at 8 a.m. What is the least total amount of time the woman must spend waiting between trains if all trains depart and arrive on schedule, and if she arrives at Station Z no later than 3:30 p.m.?

OA -25 mins
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by narik11 » Sun Sep 26, 2010 12:12 am
singhsa wrote:A woman is planning a trip that involves 3 connecting trains that depart from Stations X, Y, and Z, respectively. The first train leaves Station X every hour, beginning at 6 a.m., and arrives at Station Y hours later. The second train leaves Station Y every half hour, beginning at 9 a.m., and arrives at Station Z hours later. The third train leaves Station Z every 45 minutes, beginning at 8 a.m. What is the least total amount of time the woman must spend waiting between trains if all trains depart and arrive on schedule, and if she arrives at Station Z no later than 3:30 p.m.?

OA -25 mins
Is the ime taken from Station X to Station Y, and Station Y to Station Z : "A hour later"
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by euro » Sun Sep 26, 2010 4:31 am
singhsa wrote:A woman is planning a trip that involves 3 connecting trains that depart from Stations X, Y, and Z, respectively. The first train leaves Station X every hour, beginning at 6 a.m., and arrives at Station Y hours later. The second train leaves Station Y every half hour, beginning at 9 a.m., and arrives at Station Z hours later. The third train leaves Station Z every 45 minutes, beginning at 8 a.m. What is the least total amount of time the woman must spend waiting between trains if all trains depart and arrive on schedule, and if she arrives at Station Z no later than 3:30 p.m.?

OA -25 mins
The travel time between stations is not very clear from the problem so I will assume it 1-hour since it says "an hour later".

Train from X starting 9 a.m. -> reaching Y at 10 a.m.
Train from Y starting 10:30 a.m. -> reaching Z at 11:30 a.m. (At Y, waiting time 30 mins.)
Train from Z starting at 11:45 a.m. (At Z, waiting time 15 mins.)
Total waiting time 30+15 = 45 mins.

I can't figure out how the waiting time can be anything other than a multiple of 15 mins.
What is the source of this question?
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by singhsa » Sun Sep 26, 2010 5:03 am
euro wrote:
singhsa wrote:A woman is planning a trip that involves 3 connecting trains that depart from Stations X, Y, and Z, respectively. The first train leaves Station X every hour, beginning at 6 a.m., and arrives at Station Y hours later. The second train leaves Station Y every half hour, beginning at 9 a.m., and arrives at Station Z hours later. The third train leaves Station Z every 45 minutes, beginning at 8 a.m. What is the least total amount of time the woman must spend waiting between trains if all trains depart and arrive on schedule, and if she arrives at Station Z no later than 3:30 p.m.?

OA -25 mins
The travel time between stations is not very clear from the problem so I will assume it 1-hour since it says "an hour later".

Train from X starting 9 a.m. -> reaching Y at 10 a.m.
Train from Y starting 10:30 a.m. -> reaching Z at 11:30 a.m. (At Y, waiting time 30 mins.)
Train from Z starting at 11:45 a.m. (At Z, waiting time 15 mins.)
Total waiting time 30+15 = 45 mins.

I can't figure out how the waiting time can be anything other than a multiple of 15 mins.
What is the source of this question?
Kaplan test
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by diebeatsthegmat » Tue Sep 28, 2010 5:39 pm
singhsa wrote:A woman is planning a trip that involves 3 connecting trains that depart from Stations X, Y, and Z, respectively. The first train leaves Station X every hour, beginning at 6 a.m., and arrives at Station Y hours later. The second train leaves Station Y every half hour, beginning at 9 a.m., and arrives at Station Z hours later. The third train leaves Station Z every 45 minutes, beginning at 8 a.m. What is the least total amount of time the woman must spend waiting between trains if all trains depart and arrive on schedule, and if she arrives at Station Z no later than 3:30 p.m.?

OA -25 mins
can you recheck the PS
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by singhsa » Wed Sep 29, 2010 2:28 am
diebeatsthegmat wrote:
singhsa wrote:A woman is planning a trip that involves 3 connecting trains that depart from Stations X, Y, and Z, respectively. The first train leaves Station X every hour, beginning at 6 a.m., and arrives at Station Y hours later. The second train leaves Station Y every half hour, beginning at 9 a.m., and arrives at Station Z hours later. The third train leaves Station Z every 45 minutes, beginning at 8 a.m. What is the least total amount of time the woman must spend waiting between trains if all trains depart and arrive on schedule, and if she arrives at Station Z no later than 3:30 p.m.?

OA -25 mins
can you recheck the PS
I did....OA is 25 mins only.

Maybe experts might be able to help here.
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by francoimps » Thu Jul 31, 2014 4:55 pm
Departure Times (DT) & Time to Destination (TD)
DT: Station X: 6am, 7am, 8am, 9am...
TD: 1 hour and 45 min

DT: Station Y: 9am, 9:30am, 10:00am, 10:30am...
TD: after 2 hours and 20 min

DT:: 8am, 8:45am, 9:30am, 10:15am, 11:00am, 11:45am, 12:30nn, 1:15pm, 2:00pm, 2:45pm, 3:30

Option 1: take 7am departure from station x

Departure form X: 7am
Arrival at Y: 8:45am
Wait time: 15min.

Departure from Y: 9:00am
Arrival at Z: 11:20am
Wait time: 25min.

Departure from Z: 11:45am.

Total Wait Time = 15 +25 = 40

Option 2: take 8am departure from station x

Departure form X: 8am
Arrival at Y: 9:45am
Wait time: 15min.

Departure from Y: 10:00am
Arrival at Z: 12:20am
Wait time: 10min.

Departure from Z: 12:30am.

Total Wait Time = 15 +10 = 25

Answer: 25
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by [email protected] » Fri Aug 01, 2014 6:09 pm
Hi singhsa,

This question would have come with 5 answer choices that you could have "used against" the question. By not using those answer choices to your advantage, you have made this question harder to deal with (you're essentially limited to "brute forcing" the solution). Remember to take advantage of all the information that you have to work with when dealing with Quant questions.

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by GMATGuruNY » Sat Aug 02, 2014 2:44 am
The problem should read as follows:
A woman is planning a trip that involves 3 connecting trains that depart from Stations X, Y, and Z, respectively. The first train leaves Station X every hour, beginning at 6 a.m., and arrives at Station Y 1(3/4) hours later. The second train leaves Station Y every half hour, beginning at 9 a.m., and arrives at Station Z 2(1/3) hours later. The third train leaves Station Z every 45 minutes, beginning at 8 a.m. What is the least total amount of time the woman must spend waiting between trains if all trains depart and arrive on schedule, and if she arrives at Station Z no later than 3:30 p.m.?

15 minutes
25 minutes
1 hour 15 minutes
1 hour 40 minutes
4 hours 30 minutes
The woman must arrive at Station Z by 3:30pm.
Let DT = departure time and AT = arrival time.
Write out the schedule and WORK BACKWARDS from DT = 3:30pm for the third train.

Train 1:
AT: 06:45, 07:45, 08:45, 09:45, 10:45, 11:45, 12:45, 01:45, 02:45...

Train 2:
DT: 09:00, 09:30, 10:00, 10:30, 11:00, 11:30, 12:00, 12:30, 01:00.
AT: 11:20, 11:50, 12:20, 12:50, 01:20, 01:50, 02:20, 02:50, 03:20.

Train 3:
DT: 08:00, 08:45, 09:30, 10:15, 11:00, 11:45, 12:30, 01:15, 02:00, 02:45, 03:30.

The times in red yield a wait-time of 15 minutes between trains 1 and 2 (from 12:45 to 01:00) and a wait-time of 10 minutes between trains 2 and 3 (from 03:20 to 03:30), for a total wait-time of 25 minutes.

The correct answer is B.
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by Matt@VeritasPrep » Sat Aug 02, 2014 11:27 am
This question has a strong east coast (or European) bias, as few people in the rest of car-crazy America are used to dealing with transit tables!

That said, here's a pretty quick and easy way of approaching the problem.

The first train ALWAYS arrives at 45 minutes past the hour (7:45, 8:45, etc).

The second train ONLY leaves at 30 past or on the hour (9:30, 10:00, 10:30, etc.)

So there is a MANDATORY wait of AT LEAST 15 minutes between the first and second trains. (If we arrive at :45 and leave at :00.)

Now we'll move to the third train. The second train only arrives at 20 or 50 minutes past the hour (11:50, 12:20, 12:50, etc.)

Since the third train CANNOT leave at 20 or 50 minutes past the hour (it leaves at 8, 8:45, 9:30, 10:15, 11, etc., so either :00, :45, :30, :15), we have AT LEAST a 10 minute wait. (Either :20 to :30, or :50 to :00.)

That gives us a minimum of 15 minutes + 10 minutes, or 25 minutes.
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by francoimps » Sat Aug 02, 2014 4:27 pm
Matt@VeritasPrep wrote:This question has a strong east coast (or European) bias, as few people in the rest of car-crazy America are used to dealing with transit tables!

That said, here's a pretty quick and easy way of approaching the problem.

The first train ALWAYS arrives at 45 minutes past the hour (7:45, 8:45, etc).

The second train ONLY leaves at 30 past or on the hour (9:30, 10:00, 10:30, etc.)

So there is a MANDATORY wait of AT LEAST 15 minutes between the first and second trains. (If we arrive at :45 and leave at :00.)

Now we'll move to the third train. The second train only arrives at 20 or 50 minutes past the hour (11:50, 12:20, 12:50, etc.)

Since the third train CANNOT leave at 20 or 50 minutes past the hour (it leaves at 8, 8:45, 9:30, 10:15, 11, etc., so either :00, :45, :30, :15), we have AT LEAST a 10 minute wait. (Either :20 to :30, or :50 to :00.)

That gives us a minimum of 15 minutes + 10 minutes, or 25 minutes.
Finally a quick way to do it. Can all transit be problems be solved this way though?
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by Matt@VeritasPrep » Sat Aug 02, 2014 5:08 pm
francoimps wrote:Finally a quick way to do it. Can all transit be problems be solved this way though?
This is a rather unusual problem, so I wouldn't lose too much sleep over it! But yeah, I'd look for a clever solution on any such problem: there has to be a better way than compiling the whole timetable by hand.
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