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# M01-34

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Math Expert
Joined: 02 Sep 2009
Posts: 50044

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16 Sep 2014, 00:16
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Difficulty:

15% (low)

Question Stats:

80% (00:39) correct 20% (01:11) wrong based on 162 sessions

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Train A leaves the Keleti station in Budapest at 5:00PM and travels to Moscow at the speed of 50 mph. If train B leaves Keleti for Moscow some time later on the same day, at what time will train B overtake train A? The distance between the cities is 970 miles.

(1) Train B leaves Keleti at 6:00PM.

(2) Train A travels at $$\frac{5}{6}$$ the speed of train B.

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Joined: 02 Sep 2009
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16 Sep 2014, 00:16
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Official Solution:

Statement (1) by itself is not sufficient. The speed is also needed to answer the question.

Statement (2) by itself is not sufficient. The departure time is also needed to answer the question.

Statements (1) and (2) combined are sufficient. Approach 1: From S1 we know that train A is already 50 miles ahead of train B. From S2 we can find the speed of train B. $$V_{train B} = \frac{V_{train A}}{\frac{5}{6}} = \frac{50}{\frac{5}{6}} = 60$$mph. Knowing the distance between the trains and the difference between the speed of trains we can find the time when train B overtakes train A. $$\frac{50}{60-50} = 5$$hours. 6PM + 5 hours = 11PM.

Another approach is to use the formula of physics (kinematic): $$x=vt+x_{0}$$ where $$x$$ is the location at time $$t$$ and $$x_{0}$$ is the initial location at time $$t = 0$$

Write the equations of both trains as follows:
$$x_{train A}= 50t + 50$$
$$x_{train B}= 60t$$

$$x_{train A}=x_{train B}$$, represents the time at which the two trains meet each other. Therefore, $$t=5$$ indicates the time difference between the two trains. Add that time to the start of train A to calculate the time at which train B will overtake train A.

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Joined: 10 May 2014
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11 Dec 2014, 14:14
Hey,

Two questions:

- Does this imply that they will meet at 300 miles from Keleti Station as well (since 60*5 = 300)? Maybe at some point before reaching Kiev, one might say...

- Is the portion "The distance between the two cities is 970 miles" completely irrelevant to answer this question?

Thanks,
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Math Expert
Joined: 02 Sep 2009
Posts: 50044

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12 Dec 2014, 06:59
minwoswoh wrote:
Hey,

Two questions:

- Does this imply that they will meet at 300 miles from Keleti Station as well (since 60*5 = 300)? Maybe at some point before reaching Kiev, one might say...

- Is the portion "The distance between the two cities is 970 miles" completely irrelevant to answer this question?

Thanks,

1. Yes.

2. Not entirely. We need to know that the distance is greater than 300 miles, because if it's not it would need that B won't overtake A while traveling to Moscow.
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Joined: 20 Jan 2015
Posts: 7
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25 Jan 2015, 18:38
I know the GMAT doesn't usually give "gotcha" questions, but I picked E for my answer because this question doesn't mention that the trains are headed in the same direction or on the same tracks. For instance, the train to Moscow could zig-zag east and west, but the Bangalore train could be a straight-shot. Did anyone else determine this question like me?
Intern
Joined: 09 Jan 2018
Posts: 3

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03 Aug 2018, 08:47
The question didnt mention the length of the trains . So i feel its ambigous
Re: M01-34 &nbs [#permalink] 03 Aug 2018, 08:47
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# M01-34

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