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GMAT Instructor
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A train always travels at one of two speeds: 160 km/hr in [#permalink]
 09 Dec 2007, 07:27
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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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CEO
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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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Director
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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=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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Director
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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 Answer Ethis 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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CEO
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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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CEO
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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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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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Director
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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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automan, +1 Kudos
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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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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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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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CEO
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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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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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Manager
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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?
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