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GMAT Diagnostic Test Question 25 Field: word problems (rate) Difficulty: 700

A train is traveling at a constant speed from city A to city B. Along this trip the train makes three one-hour stops and reaches city B. At city B the train is stopped again for 1 hour. After that the train makes the return trip from city B to city A at a constant speed which is twice the speed of the first trip. Along this return trip the train makes ten thirty minutes stops and reaches city A. If both trips took the same amount of time, how many hours was the round trip?

We know that each trip took the same amount of time and has the same distance.Then we can equal either distance or time. I chose distance, dzyubam chose time.

t = total time. This is important because t is the total time for each way of the round trip including stops Total time of stop first part of the trip = 1 hour * 3 = 3 hours Total time of stop second part of the trip = 0.5 hour *10 = 5 hours

d = s (t -3) First part of the trip d= 2s (t-5) Second part of the trip

Both distance are the same s (t – 3) = 2s (t – 5) (t – 3) = 2 (t – 5) t – 3 = 2t – 10 t = 7 (7 * 2) both ways + 1 hour stop when reached destination 14 + 1 = 15 hours Total Trip

First, we have to calculate the amount of time the train spent for the stops. \(3*1=3\) hours for the first trip and \(10*0.5=5\) for the return trip. Now, we can write an equation with \(S\) for one-way distance and \(V\) for train's speed:

\(\frac{S}{V} + 3 = \frac{S}{2V} + 5\)

\(\frac{S}{V} - \frac{S}{2V} = 2\)

\(\frac{2S-S}{2V} = 2\)

\(\frac{S}{2V} = 2\)

\(\frac{S}{V} = 4\)

So, the roundtrip lasted for \(7+7+1=15\) hours (we should count the 1 hour stop in the destination point as well).
_________________

aren't we missing a really simple explanation? trips both took the same time. so when the train went twice as fast it go away with 5 hrs stopped instead of 3. i.e. saved 2 hours. t+5 = 2t+3 t = 2 I guess I'm saying a similar solution but this is a simpler way for me to consider it.

First, we have to calculate the amount of time the train spent for the stops. \(3*1=3\) hours for the first trip and \(10*0.5=5\) for the return trip. Now, we can write an equation with \(S\) for one-way distance and \(V\) for train's speed:

\(\frac{S}{V} + 3 = \frac{S}{2V} + 5\)

\(\frac{S}{V} - \frac{S}{2V} = 2\)

\(\frac{2S-S}{2V} = 2\)

\(\frac{S}{2V} = 2\)

\(\frac{S}{V} = 4\)

So, the roundtrip lasted for \(7+7+1=15\) hours (we should count the 1 hour stop in the destination point as well).

First, we have to calculate the amount of time the train spent for the stops. \(3*1=3\) hours for the first trip and \(10*0.5=5\) for the return trip. Now, we can write an equation with \(S\) for one-way distance and \(V\) for train's speed:

\(\frac{S}{V} + 3 = \frac{S}{2V} + 5\)

\(\frac{S}{V} - \frac{S}{2V} = 2\)

\(\frac{2S-S}{2V} = 2\)

\(\frac{S}{2V} = 2\)

\(\frac{S}{V} = 4\)

So, the roundtrip lasted for \(7+7+1=15\) hours (we should count the 1 hour stop in the destination point as well).

Let the time for each trip be \(t\) hours, then the roundtrip took \(t+t+1=2t+1\) hours (each trip took the same amount of time plus 1 hour of waiting after the first half of the trip).

Next,, during the first trip the train was stopped for 3*1=3 hours and for the second trip it was stopped for 10*0.5=5 hours, so for the first trip it was moving at some constant rate, say \(r\), for \(t-3\) hours and for the second trip it was moving for the constant rate of \(2r\), for \(t-5\) hours.

Now, since the distance for the first and the second trip was the same then \(r*(t-3)=2r*(t-5)\) --> \(t=7\).

I didn't know where to write this comment, so here i go: the diagnostic problems in general are great. The difficulty level, and especially the explanations are absolutely fantastic. I'm learning a lot. Sometimes I feel like sitting in a lecture hall listening to a brilliant professor giving one of his best early morning lectures at an ivory tower. Except for one aggaravating problem. Wording. I mean, If the author(s) of this test paid just a little more attention to wording, the ambiguity wouldn't be so bad. I don't know whether the authors intended to make some problems appear somewhat ambiguous in order to make them a little tougher?!

Thank you for the kind words and welcome to GMAT Club! We're gradually improving the wording where necessary. You're welcome to suggest any changes to the questions you might find ambiguous. The questions were not worded poorly on purpose. Feel free to post in the threads of Diagnostic Test questions to comment on the wording. Thanks .

sirdookie wrote:

I didn't know where to write this comment, so here i go: the diagnostic problems in general are great. The difficulty level, and especially the explanations are absolutely fantastic. I'm learning a lot. Sometimes I feel like sitting in a lecture hall listening to a brilliant professor giving one of his best early morning lectures at an ivory tower. Except for one aggaravating problem. Wording. I mean, If the author(s) of this test paid just a little more attention to wording, the ambiguity wouldn't be so bad. I don't know whether the authors intended to make some problems appear somewhat ambiguous in order to make them a little tougher?!

thanks for welcoming me here. i think i've found this board just in time. i was looking for some challenging quant problems and this site provides those. hey i wouldn't have paid $79 to be a "premier" member if i wasn't imprssed by the test on the contrary....! Wording was good in most of the problems, but there were just a few that completely threw me off the track. over all what i've gathered from taking diagnostic test was pretty much what i expected; on 600-650 level problems i was 100% correct. on 700 level slightly over half right. on 750 level i was wrong more than half of the time . that just confirmed the scores i was getting on other practice tests, namely, GMAT Preps (scaled scores from 47-50 range).

Thank you for the kind words. We are glad you like the Tests. Hope your Quant score goes up after practicing with GMAT Club Test .

sirdookie wrote:

dyzybam,

thanks for welcoming me here. i think i've found this board just in time. i was looking for some challenging quant problems and this site provides those. hey i wouldn't have paid $79 to be a "premier" member if i wasn't imprssed by the test on the contrary....! Wording was good in most of the problems, but there were just a few that completely threw me off the track. over all what i've gathered from taking diagnostic test was pretty much what i expected; on 600-650 level problems i was 100% correct. on 700 level slightly over half right. on 750 level i was wrong more than half of the time . that just confirmed the scores i was getting on other practice tests, namely, GMAT Preps (scaled scores from 47-50 range).

this is very helpful - although troubling how much work i have yet to do. only 6 more weeks before the big day. I took one of the GMAC practice tests last night (saving the second one until test day nears) and scored a 630 (Q 38). I've pretty much given up all social life to prep for this thing and am really hoping to flirt with the magical 700. I hope i am not being unrealistic. That being said, this site one of the best resources i have found. Thanks to all that have contributed and i will try and be a gracious consumer of the knowledge and share anything i have that is helpful.

this is very helpful - although troubling how much work i have yet to do. only 6 more weeks before the big day. I took one of the GMAC practice tests last night (saving the second one until test day nears) and scored a 630 (Q 38). I've pretty much given up all social life to prep for this thing and am really hoping to flirt with the magical 700. I hope i am not being unrealistic. That being said, this site one of the best resources i have found. Thanks to all that have contributed and i will try and be a gracious consumer of the knowledge and share anything i have that is helpful.

This question could have been a bit better worded. It should make it more obvious the distance in both trips are the same. I was taught to never assume things in problems like this and unless it said something like "the train made a return trip the same way back" this question can not be solved.

Just saying "return trip" and assuming it means "return trip the same way" is a bit culturally biased (I hate going back the same way).

Course, once you state the distance is constant, this becomes an easy problem . Guess it shows how hard it is to write a good test!

A train is traveling at a constant speed and after making three one-hour stops reaches its destination.

i think though it is not totally wrong but for gmat which seeks more right things ....that three one-hour stops could easily understoood as stop after every one hour....5 dollar ride...may mean ride which cost 5 dollar... so as it is quantative question not SC i think making it clear will help ...even to understand and solve question with in 2 minutes

wow, this one left me scratching my nerves. The way i did was lets suppose initial speed is D/T MILES/HR. if D is total distance it would take train to travel one way T hours. + 3 hour rest makes it T+3 hours. 2ndly on return speed doubles hence it travels D MILES in T/2hrs. +5 hours rest makes it T/2+5=(T+10)/2. we know both times are equal hence T+3=(T+10)/2 then T=4. then each way becomes 7HRS+1 hr rest between 2 trips gives 15 total.