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# Stations X and Y are connected by two separate, straight,

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Manager
Joined: 08 Nov 2008
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Stations X and Y are connected by two separate, straight,  [#permalink]

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29 Mar 2009, 19:09
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Stations X and Y are connected by two separate, straight, parallel rail lines that are 250 miles long. Train P and train Q simultaneously left Station X and Station Y, respectively, and each train traveled to the other’s point of departure. The two trains passed each other after traveling for 2 hours. When the two trains passed, which train was nearer to its destination?

(1) At the time when the two trains passed, train P had averaged a speed of 70 miles per hour.
(2) Train Q averaged a speed of 55 miles per hour for the entire trip.

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Math Expert
Joined: 02 Sep 2009
Posts: 53066
Re: DS -Relative Speed - Set 14  [#permalink]

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26 Sep 2010, 03:24
10
1
7
Stations X and Y are connected by two separate, straight, parallel rail lines that are 250 miles long. Train P and train Q simultaneously left Station X and Station Y, respectively, and each train traveled to the other’s point of departure. The two trains passed each other after traveling for 2 hours. When the two trains passed, which train was nearer to its destination?
(1) At the time when the two trains passed, train P had averaged a speed of 70 miles per hour.
(2) Train Q averaged a speed of 55 miles per hour for the entire trip.

(1) As P averaged 70 miles per hour at the time when the two trains passed, hence when they passed each other P traveled 2*70=140 miles, so for P it was 110 miles left to cover and for Q 140. P was closer to its destination. Sufficient.

(2) Knowing average speed for entire trip won't help us to determine the distance either of train coverd at the time they passed each other (as the average speed at the time the met could have been different). Not sufficient.

Answer: A.
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Director
Joined: 14 Aug 2007
Posts: 670
Re: DS -Relative Speed - Set 14  [#permalink]

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29 Mar 2009, 19:55
1
tenaman10 wrote:
(1) At the time when the two trains passed, train P had averaged a speed of 70 miles per hour.
(2) Train Q averaged a speed of 55 miles per hour for the entire trip.

1)
When trains passed, train P had travelled 140 miles (while Q traveled 110 miles), so P was closer. suff.
2) We don't know whether Q's speed was "constant" over the entire journey.

A for me.
Manager
Joined: 19 May 2008
Posts: 146
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Re: DS -Relative Speed - Set 14  [#permalink]

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29 Mar 2009, 20:16
Statement 1 is sufficient. We know that when the trains passed, P had reached a distance of 140 miles (based on 70 m/hr avg speed). Hence P was just 110 miles from destination - which means Q was farther away from its destination.

Statement 2 - we know that after 2 hrs, train Q reached a distance of 110 miles - based on its avg speed throughout the journey - and also it took 4.5 hrs to reach destination. So as per the question, the 2 trains passed each other after 2 hrs, by which time Q had reached 110 miles, based on avg speed - so Q was farther from its destination.

Answer is D - both statements are sufficient on its own. What is the OA?
Manager
Joined: 19 May 2008
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Re: DS -Relative Speed - Set 14  [#permalink]

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29 Mar 2009, 20:18
Actually it should be A - since we don't know that the avg speed of the train after 2 hrs was 55 - we just know that Q avged 55 over the whole journey.
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Re: DS -Relative Speed - Set 14  [#permalink]

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17 Apr 2009, 09:27
2
gmat911 wrote:
why would you say it's A? A does not say anything about the other train. i think it's E since B does not tell you the speed when it was at 2 hours.... am i missing something?

Q asks that which train is closer to its destination when they met. As per sta 1, A has already travelled 140KM. SO the remaining distance of 250 km is 110 KM which the train 2 must have travelled. Therefore, we need not required the speed of B to know is it is closer to its destination than A. Hope it expalins
Manager
Joined: 19 Aug 2006
Posts: 211
Re: DS -Relative Speed - Set 14  [#permalink]

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03 May 2009, 10:47
stmnt1
nsf, because we can't get anything from it other than time of 2 hours - it says 70mi/h at the time they passed, but who knows what was the speed of P before then; cannot get the distance traveled by P either for the same reason.

stmnt2
S(q)=55mi/h
D(q)=250 miles
t(q)=4.5h
nsf - nothing about train P

Let's combine.

We can get the distance traveled by P by the time they met:
t(p)=2h
D(p)=250-D(q)=140 miles

From here, it's easy to see that P was closer to its destination at the time the trains met.

So, C is the answer.
Director
Joined: 23 May 2008
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Re: DS -Relative Speed - Set 14  [#permalink]

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03 May 2009, 11:59
bandit wrote:
gmat911 wrote:
why would you say it's A? A does not say anything about the other train. i think it's E since B does not tell you the speed when it was at 2 hours.... am i missing something?

Q asks that which train is closer to its destination when they met. As per sta 1, A has already travelled 140KM. SO the remaining distance of 250 km is 110 KM which the train 2 must have travelled. Therefore, we need not required the speed of B to know is it is closer to its destination than A. Hope it expalins

statement 1 says that train A was going 70mph "at the time the two trains passed" what about before and after the trains passed. We need a constant or average speed to tell the distance travelled. insuff

statement 2 gives us a constant speed for train Q so distance travelled was 110 miles. This is where they met so 250-110=140, the distance P travelled, so P is closer to destination

ans B IMO
Manager
Joined: 13 Jan 2009
Posts: 157
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Re: DS -Relative Speed - Set 14  [#permalink]

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19 Aug 2009, 23:02
1
It is not C, in my opinion. I go with E.

St 1. train P's speed 70mph at the time of trains pass each other, we can't determine it's speed before and after. Insuff.
St 2. train Q's speed average of 55mph, we can't determine train B's speed at the time of two trains pass each other.

Combined, we also don't get anything, Hence E is the answer!
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Re: DS -Relative Speed - Set 14  [#permalink]

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21 Aug 2009, 21:18
I believe that (1) is sufficient, because it notes that:

(1) At the time when the two trains passed, train P had averaged a speed of 70 miles per hour

Therefore after two hours with this average, the distance travelled would be 140. Def A.
Manager
Joined: 12 Aug 2009
Posts: 79
Re: DS -Relative Speed - Set 14  [#permalink]

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22 Aug 2009, 06:35
IMO - A . Becuase it says "had averaged" ....

It is tricky though. I hope GMAT does not test this kind of questions, where you need to pay so much attention.
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Re: DS -Relative Speed - Set 14  [#permalink]

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20 Sep 2009, 05:06
IMO two statements are similar. what is the difference?
think D. do not understand why is it C. what is the source? is OA right?

the formula states: avg sp = total distance/total time.

stmt1:

train A in two hours made 140 miles, thus it is closer than B to the destination. suff

stmt2:

train B in two hours did 110 miles. thus train A is closer. suff

can anyone post a clear explanation to this?
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Re: DS -Relative Speed - Set 14  [#permalink]

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22 Sep 2009, 07:09
Hi,

I think this:

(1) It said that the train P had averaged a speed of 70 miles per hour, at the time the two trains passed. BUT, we don't know nothing about TRAIN Q. ( INSUFF.)

(2) Train Q, had averaged a speed 55 M/h for the ENTIRE TRIP. In that way,We know that Train Q, travelled 110 Miles in 2 hours (55 M/h * 2 hours). BUT, we dont know about the Train P. (INSUFF)

Well, (1) + (2) :

FOR (2): We know Train Q had traveled 110 miles and has to travel 140 miles, MORE!. FOR (1), At the same time, Train P, had speed average 70 Miles per hour BUT HAD ALREADY TRAVELLED 140 miles when passed Train Q and so, Train P only has 110 miles to travel. In that way, TRAIN P was nearer than Q.

ANSWER = C.

What to do you think guys?

Cheers!
Intern
Joined: 19 Aug 2009
Posts: 14
Re: DS -Relative Speed - Set 14  [#permalink]

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23 Sep 2009, 11:08
gmatpill wrote:
Quote:
Stations X and Y are connected by two separate, straight, parallel rail lines that are 250 miles long. Train P and train Q simultaneously left Station X and Station Y, respectively, and each train traveled to the other’s point of departure. The two trains passed each other
after traveling for 2 hours. When the two trains passed, which train was nearer to its destination?
(1) At the time when the two trains passed, train P had averaged a speed of 70 miles per hour.
(2) Train Q averaged a speed of 55 miles per hour for the entire trip.

So many different answers. I'm going to stick my head out and say the answer is (D). Here's why:

(1) At the 2 hour mark, train P averaged 70 mph. After the 2 hr mark,
the train could have sped up or slowed down, but at that 2 hour mark,
train P averaged 70 mph for the previous 2 hours.

That means it must have traveled 2*70 = 140 miles during that
2 hr period.
Given that the entire trail is 250 miles, the midpoint is
125 miles. Clearly, train P passed the midpoint at the 140 mile mark.
That means the remaining 110 must be the distance that the other
train travelled.

All we need to know is that train P passed the midpoint, that means
it must be nearer to its destination--which means we have enough info
to answer the quesiton!

(2) Train Q averaging 55 mph for 2 hrs means it traveled 110
miles. 110 mile mark is less than the midpoint of the 250 mile trail
(125 miles). This means the OTHER train (P), must have traveled
further
and is therefore closer to its destination.

So in this case, either (1) or (2) provides sufficient info to tell us which train was closer to its destination.

Remember, the question TELLS you that you have a constant DISTANCE (250 miles) and a constant TIME (2 hrs) for you to do your analysis.

Remember the Rates Framework: There 3 components: Distance = Rate * Time. You have info on distance and time. All you need is some good info on rates. It turns out either statement (1) or (2) gives you good info on rates, so the answer is (D).

I think you misread statement B - The train does not average 55 mph for 2 hours; it averaged 55 mph for the entire trip. This could mean that in the first two hours it may have traveled at any speed faster or slower than 55 mph, which would make the statement NSF.

I strongly believe that the only suitable answer is A. Is there an explanation for the OA of C? Where did this question come from?
Intern
Joined: 25 Mar 2009
Posts: 48
Re: DS -Relative Speed - Set 14  [#permalink]

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24 Sep 2009, 08:43
gmatpill wrote:
Quote:
Stations X and Y are connected by two separate, straight, parallel rail lines that are 250 miles long. Train P and train Q simultaneously left Station X and Station Y, respectively, and each train traveled to the other’s point of departure. The two trains passed each other
after traveling for 2 hours. When the two trains passed, which train was nearer to its destination?
(1) At the time when the two trains passed, train P had averaged a speed of 70 miles per hour.
(2) Train Q averaged a speed of 55 miles per hour for the entire trip.

So many different answers. I'm going to stick my head out and say the answer is (D). Here's why:

(1) At the 2 hour mark, train P averaged 70 mph. After the 2 hr mark,
the train could have sped up or slowed down, but at that 2 hour mark,
train P averaged 70 mph for the previous 2 hours.

That means it must have traveled 2*70 = 140 miles during that
2 hr period.
Given that the entire trail is 250 miles, the midpoint is
125 miles. Clearly, train P passed the midpoint at the 140 mile mark.
That means the remaining 110 must be the distance that the other
train travelled.

All we need to know is that train P passed the midpoint, that means
it must be nearer to its destination--which means we have enough info
to answer the quesiton!

(2) Train Q averaging 55 mph for 2 hrs means it traveled 110
miles. 110 mile mark is less than the midpoint of the 250 mile trail
(125 miles). This means the OTHER train (P), must have traveled
further
and is therefore closer to its destination.

So in this case, either (1) or (2) provides sufficient info to tell us which train was closer to its destination.

Remember, the question TELLS you that you have a constant DISTANCE (250 miles) and a constant TIME (2 hrs) for you to do your analysis.

Remember the Rates Framework: There 3 components: Distance = Rate * Time. You have info on distance and time. All you need is some good info on rates. It turns out either statement (1) or (2) gives you good info on rates, so the answer is (D).

I don't think it's D, if D, it will be like this:
Stations X and Y are connected by two separate, straight, parallel rail lines that are 250 miles long. Train P and train Q simultaneously left Station X and Station Y, respectively, and each train traveled to the other’s point of departure. The two trains passed each other
after traveling for 2 hours. When the two trains passed, which train was nearer to its destination?
(1) At the time when the two trains passed, train P had averaged a speed of 70 miles per hour.
(2) At the time when the two trains passed, Train Q averaged a speed of 55 miles per hour for the entire trip.

It's easy to calculate but the point is the different of 1) with At the time when the two trains passed and 2)without phrase At the time when the two trains passed
IT's subtle, anyone pls help explain the meaning.
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Joined: 19 Oct 2009
Posts: 43
Re: DS -Relative Speed - Set 14  [#permalink]

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17 Nov 2009, 11:25
1
IMO A..

B is not sufficient because we don't know when the two trains meet. After 2 hrs means they can meet after 3, 4, 5 hrs etc...so if they meet exactly after 2 hrs, we know the answer but if they met after 4 hrs (which indeed can be the case : since 4 hrs are ofcourse after 2 hrs ), then we would get just opposite answer to what we get in case of 2 hrs.
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Re: DS -Relative Speed - Set 14  [#permalink]

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Updated on: 17 Nov 2009, 14:23
(1) At the time when the two trains passed, train P had averaged a speed of 70 miles per hour.

if S1 (1) At the time when the two trains passed, train P had averaged a speed of 70 miles per hour.
said instead (1) till the time when the two trains passed, train P had averaged a speed of 70 miles per hour.

then we can take train P's speed as 70 for first 2 hours, otherwise, we cannot assume that.

what is the source of the question ?

Edited
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Originally posted by srini123 on 17 Nov 2009, 11:50.
Last edited by srini123 on 17 Nov 2009, 14:23, edited 2 times in total.
Intern
Joined: 19 Oct 2009
Posts: 43
Re: DS -Relative Speed - Set 14  [#permalink]

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17 Nov 2009, 13:17
1
answer is A....gmat sets contain lots of wrong answer.... check this out

http://www.manhattangmat.com/forums/ds- ... -t679.html
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Joined: 25 Jan 2010
Posts: 4
Re: DS -Relative Speed - Set 14  [#permalink]

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29 Jan 2010, 05:30
From A we can deduce that passing time First train already passed 2*70km=140km And it mast pssed only 110km, But second train passed 110km.
So Answer is A,
From B we can deduce noting
Intern
Joined: 26 Aug 2010
Posts: 20
Re: DS -Relative Speed - Set 14  [#permalink]

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26 Sep 2010, 03:02
1
Consider the 2nd condition the following way:
You are given the average of a set = 50.
{40,50,60}, {10,50,90} are among many others that have the average of 50, including {50,50,50}.
It means that the speed of the train could seriously differ during his travel and, therefore, we can't define the speed of train Q in a moment of time the trains have met.
Re: DS -Relative Speed - Set 14   [#permalink] 26 Sep 2010, 03:02

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# Stations X and Y are connected by two separate, straight,

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