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A train always travels at one of two speeds: 160 km/hr in

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A train always travels at one of two speeds: 160 km/hr in [#permalink]  09 Dec 2007, 06:27
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A train always travels at one of two speeds: 160 km/hr in rural areas and 40 km/hr in urban areas. Was its average speed from A to B greater than 100 km/hr?

(1) More than 2/3 of the distance from A to B is through rural areas.
(2) The distance from A to B is more than 1000 km.
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Expert's post
A.

(1) V=(Lu+Lr)/(Lu/40+Lr/160), let k=Lr/Lu=(2/3)/(1/3)=2 ==>
V=(1+2)/(1/40+2/160)=3*160/(4+2)=80 km/h - suff

(2) The distance from A to B does not influence on average speed.- insuff
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Re: DS: Train [#permalink]  06 Jan 2008, 08:19
The more the train travels through rural a areas, the greater its average speed. Lets calculate the relationship between Lu and Lr so that the average speed is 100 km/h

v=[Lu+Lr]/[Lu/40 + Lr/160]=100 => Lr/Lu=4 which means that in order to reach an average speed of 100 km/h, the train must travel 1/5 of the distance through urban areas and 4/5 of the distance through rural areas. So in order to reach an average speed greater than 100 km/h, the train must travel less than 1/5 of the distance through urban areas and more than 4/5 of the distance through rural areas.

Therefore, we can not conclude anything from S1 nor S2

OA should be E
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Re: DS: Train [#permalink]  06 Jan 2008, 08:38
kevincan wrote:
A train always travels at one of two speeds: 160 km/hr in rural areas and 40 km/hr in urban areas. Was its average speed from A to B greater than 100 km/hr?

(1) More than 2/3 of the distance from A to B is through rural areas.
(2) The distance from A to B is more than 1000 km.

1. Since the distance doesn't matter, let's plug in 480km for the distance and say that exactly 2/3 of the distance from A to B is rural (since we don't know exactly how much it is)
320km = rural
160km = urban

320km/160 = 2 hours in rural
160km/40 = 4 hours in urban
480km/6 hours = 80km/h

INSUFFICIENT

2. distance doesn't matter. INSUFFICIENT

this is a great example of the test makers favorite trick with averages. It's the TIME spent at each speed that we need to get the average, NOT the distance.
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Re: DS: Train [#permalink]  06 Jan 2008, 09:04
automan wrote:
The more the train travels through rural a areas, the greater its average speed. Lets calculate the relationship between Lu and Lr so that the average speed is 100 km/h

v=[Lu+Lr]/[Lu/40 + Lr/160]=100 => Lr/Lu=4 which means that in order to reach an average speed of 100 km/h, the train must travel 1/5 of the distance through urban areas and 4/5 of the distance through rural areas. So in order to reach an average speed greater than 100 km/h, the train must travel less than 1/5 of the distance through urban areas and more than 4/5 of the distance through rural areas.

Therefore, we can not conclude anything from S1 nor S2

OA should be E

I'm not convinced the answer is E. It seems we can conclude something from A. In your analysis you said that in order to have an avg. speed greater than 100km/hr the train needs to travel 4/5 the distance at 160km/hr.

Well S1 tells us that it will travel exactly 2/3 of the distance at 160km/hr. So we can answer a definitive NO for s1. The train will not exceed 100km/hr. S2 is irrelevant.

Knowing the ratio here is enough.

1. Since the distance doesn't matter, let's plug in 480km for the distance and say that exactly 2/3 of the distance from A to B is rural (since we don't know exactly how much it is)
320km = rural
160km = urban

320km/160 = 2 hours in rural
160km/40 = 4 hours in urban
480km/6 hours = 80km/h

You found the answer here... 80km/hr... We know that the train will NEVER exceed 100km/hr b/c the ratio is 2/3.

I was w/ A and im still w/ A/
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Re: DS: Train [#permalink]  06 Jan 2008, 09:22
Expert's post
I think Eschn3am is right.

(1) More than 2/3 of the distance from A to B is through rural areas.

therefore, 80<Vavr<=160. insuff.

+1 Kudos
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Re: DS: Train [#permalink]  06 Jan 2008, 09:26
walker wrote:
I think Eschn3am is right.

(1) More than 2/3 of the distance from A to B is through rural areas.

therefore, 80<Vavr<=160. insuff.

+1 Kudos

Ah MAN.... lol I hate it when that happens. def. Kudos to Eschn3am.
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Re: DS: Train [#permalink]  06 Jan 2008, 09:36
GMATBLACKBELT wrote:
automan wrote:
The more the train travels through rural a areas, the greater its average speed. Lets calculate the relationship between Lu and Lr so that the average speed is 100 km/h

v=[Lu+Lr]/[Lu/40 + Lr/160]=100 => Lr/Lu=4 which means that in order to reach an average speed of 100 km/h, the train must travel 1/5 of the distance through urban areas and 4/5 of the distance through rural areas. So in order to reach an average speed greater than 100 km/h, the train must travel less than 1/5 of the distance through urban areas and more than 4/5 of the distance through rural areas.

Therefore, we can not conclude anything from S1 nor S2

OA should be E

I'm not convinced the answer is E. It seems we can conclude something from A. In your analysis you said that in order to have an avg. speed greater than 100km/hr the train needs to travel 4/5 the distance at 160km/hr.

Well S1 tells us that it will travel exactly 2/3 of the distance at 160km/hr. So we can answer a definitive NO for s1. The train will not exceed 100km/hr. S2 is irrelevant.

Knowing the ratio here is enough.

1. Since the distance doesn't matter, let's plug in 480km for the distance and say that exactly 2/3 of the distance from A to B is rural (since we don't know exactly how much it is)
320km = rural
160km = urban

320km/160 = 2 hours in rural
160km/40 = 4 hours in urban
480km/6 hours = 80km/h

You found the answer here... 80km/hr... We know that the train will NEVER exceed 100km/hr b/c the ratio is 2/3.

I was w/ A and im still w/ A/

You have calculated that if the train travels 2/3 of the distance through rural areas the average speed is 80 km/h . Now imagine that the train travels all the time through rural areas, making S1 true (the train travel 100% of the time through rural areas). In this case the average speed is 160 km/h. Therefore we can no conclude anything.

I hope this makes my reasoning more understable.
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Re: DS: Train [#permalink]  06 Jan 2008, 09:38
Expert's post
automan, +1 Kudos
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Re: DS: Train [#permalink]  06 Jan 2008, 09:42
walker wrote:
automan, +1 Kudos

Another one for you. You always try the most difficult questions!! I have a lot to learn from you
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Re: DS: Train [#permalink]  06 Jan 2008, 09:46
walker wrote:
I think Eschn3am is right.

(1) More than 2/3 of the distance from A to B is through rural areas.

therefore, 80<Vavr<=160. insuff.

+1 Kudos

why it is insufficient? I agree 80<Vavr but still you have information to solve problem,
am I missing some point?
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Re: DS: Train [#permalink]  06 Jan 2008, 09:48
kazakhb wrote:
walker wrote:
I think Eschn3am is right.

(1) More than 2/3 of the distance from A to B is through rural areas.

therefore, 80<Vavr<=160. insuff.

+1 Kudos

why it is insufficient? I agree 80<Vavr but still you have information to solve problem,
am I missing some point?

We want to know if the average speed is greater than 100km/h. Given the information from statement one we see that the average speed must be greater than 80km/h and less than or equal to 160km/h.

80 < average <= 160

this isn't enough to know if the average is greater than 100 because it could be 81 or 160.

and statement 2 doesn't help us at all because the averages will work out to be the same, regardless of distance.
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Re: DS: Train [#permalink]  06 Jan 2008, 09:50
Expert's post
kazakhb wrote:
walker wrote:
I think Eschn3am is right.

(1) More than 2/3 of the distance from A to B is through rural areas.

therefore, 80<Vavr<=160. insuff.

+1 Kudos

why it is insufficient? I agree 80<Vavr but still you have information to solve problem,
am I missing some point?

Q. Was its average speed from A to B greater than 100 km/hr?
1. 80<Vavr<=160, So, speed greater 100? maybe yes and maybe no
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Re: DS: Train [#permalink]  06 Jan 2008, 10:04
automan wrote:
GMATBLACKBELT wrote:
automan wrote:
The more the train travels through rural a areas, the greater its average speed. Lets calculate the relationship between Lu and Lr so that the average speed is 100 km/h

v=[Lu+Lr]/[Lu/40 + Lr/160]=100 => Lr/Lu=4 which means that in order to reach an average speed of 100 km/h, the train must travel 1/5 of the distance through urban areas and 4/5 of the distance through rural areas. So in order to reach an average speed greater than 100 km/h, the train must travel less than 1/5 of the distance through urban areas and more than 4/5 of the distance through rural areas.

Therefore, we can not conclude anything from S1 nor S2

OA should be E

I'm not convinced the answer is E. It seems we can conclude something from A. In your analysis you said that in order to have an avg. speed greater than 100km/hr the train needs to travel 4/5 the distance at 160km/hr.

Well S1 tells us that it will travel exactly 2/3 of the distance at 160km/hr. So we can answer a definitive NO for s1. The train will not exceed 100km/hr. S2 is irrelevant.

Knowing the ratio here is enough.

1. Since the distance doesn't matter, let's plug in 480km for the distance and say that exactly 2/3 of the distance from A to B is rural (since we don't know exactly how much it is)
320km = rural
160km = urban

320km/160 = 2 hours in rural
160km/40 = 4 hours in urban
480km/6 hours = 80km/h

You found the answer here... 80km/hr... We know that the train will NEVER exceed 100km/hr b/c the ratio is 2/3.

I was w/ A and im still w/ A/

You have calculated that if the train travels 2/3 of the distance through rural areas the average speed is 80 km/h . Now imagine that the train travels all the time through rural areas, making S1 true (the train travel 100% of the time through rural areas). In this case the average speed is 160 km/h. Therefore we can no conclude anything.

I hope this makes my reasoning more understable.

yes that reasoning seems far fetched, but one can't deny it.

Whats the OA kevin?
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Re: DS: Train [#permalink]  27 Nov 2008, 04:01
automan wrote:
The more the train travels through rural a areas, the greater its average speed. Lets calculate the relationship between Lu and Lr so that the average speed is 100 km/h

v=[Lu+Lr]/[Lu/40 + Lr/160]=100 => Lr/Lu=4 which means that in order to reach an average speed of 100 km/h, the train must travel 1/5 of the distance through urban areas and 4/5 of the distance through rural areas. So in order to reach an average speed greater than 100 km/h, the train must travel less than 1/5 of the distance through urban areas and more than 4/5 of the distance through rural areas.

Therefore, we can not conclude anything from S1 nor S2

OA should be E

can someone describe step by step how it can be simplified?
Re: DS: Train   [#permalink] 27 Nov 2008, 04:01
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