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# Trains puzzle

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Director
Joined: 23 Apr 2010
Posts: 581
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Kudos [?]: 86 [0], given: 7

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08 Feb 2011, 06:10
00:00

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Question Stats:

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Two stations connected by railroad. Trains start every hour from each station to the other, at the same time. A Train takes 5 hours to reach the other station. How many trains will a train meet during its journey?

I think the answer should be:
[Reveal] Spoiler:
5

But no OA is provided.
Director
Status: -=Given to Fly=-
Joined: 04 Jan 2011
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Location: India
Schools: Haas '18, Kelley '18
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WE: Education (Education)
Followers: 56

Kudos [?]: 222 [0], given: 78

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08 Feb 2011, 22:58
Assuming that all trains travel at the same speed,

So a train from Station A will meet a train from station B in 2.5 hrs

Within that span of time, two trains would have departed from station B.

Our train from station A would meet these two trains also.

So overall, the train meets 3 other trains
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Math Forum Moderator
Joined: 20 Dec 2010
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Kudos [?]: 1832 [0], given: 376

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08 Feb 2011, 23:35
Let's use 2400 hrs time notation.

A@n to symbolize a train's departure at "n*100" hrs from A. e.g. A@8 is train starting from A at 800 hrs
B@n to symbolize a train's departure at "n*100" hrs from B. e.g. B@10 is train starting from B at 1000 hrs

A@8 won't meet the train B@3 because B@3 already arrived at A when A@8 left the station. However, A@8 will meet every train after B@3 viz.
B@4,B@5,B@6,B@7,B@8,B@9,B@10,B@11,B@12. A total of 9 trains.

A@8 won't meet B@13 because it already reached station B at 1300 hrs, 5 hours after 800hrs.

Ans: 9
_________________
Director
Status: -=Given to Fly=-
Joined: 04 Jan 2011
Posts: 834
Location: India
Schools: Haas '18, Kelley '18
GMAT 1: 650 Q44 V37
GMAT 2: 710 Q48 V40
GMAT 3: 750 Q51 V40
GPA: 3.5
WE: Education (Education)
Followers: 56

Kudos [?]: 222 [0], given: 78

### Show Tags

08 Feb 2011, 23:37
@Fluke
Isn't the question about 'a' train?

So the answer can never be more than 4
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"Wherever you go, go with all your heart" - Confucius

1. How to Review and Analyze your Mistakes (Post by BB at GMAT Club)

2. 4 Steps to Get the Most out out of your CATs (Manhattan GMAT Blog)

My Experience With GMAT

1. From 650 to 710 to 750 - My Tryst With GMAT

2. Quest to do my Best - My GMAT Journey Log

Director
Joined: 23 Apr 2010
Posts: 581
Followers: 2

Kudos [?]: 86 [0], given: 7

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09 Feb 2011, 05:25
Fluke, you are right. Thanks. I got it.
Re: Trains puzzle   [#permalink] 09 Feb 2011, 05:25
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