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A train always travels at one of two speeds: 160 km/hr in [#permalink]

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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.

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

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

Answer E

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.

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.

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.

(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.

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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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=4which 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?