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GMAT Diagnostic Test Question 25

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GMAT Diagnostic Test Question 25 [#permalink] New post 06 Jun 2009, 22:06
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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?

A. 14
B. 15
C. 16
D. 17
E. 18

Solution: gmat-diagnostic-test-question-79355-20.html#p1071311
[Reveal] Spoiler: OA

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Last edited by Bunuel on 06 Oct 2013, 23:26, edited 3 times in total.
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Re: GMAT Diagnostic Test Question 26 [#permalink] New post 07 Nov 2009, 16:06
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Another way of solving this problem:

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
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Re: GMAT Diagnostic Test Question 26 [#permalink] New post 06 Jul 2009, 05:27
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Explanation:
Rating:

Official Answer: B

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).
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Re: GMAT Diagnostic Test Question 26 [#permalink] New post 05 Oct 2009, 01:40
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We can take another approach too..and kill the problem in a shorter time just coz the answer choices permit.

We have
1.Stoppage time for journey=3hrs.
2.Stoppage time for return journey-30min*10=300 min=5 hrs.
3.Additional stoppage time=1 hr.

Now Total stoppage =3+1+5=9 hrs.

Now as the speeds are in the ratio 1:2 and distance is constant, time take should be in ratio 2:1.

Time running should be a multiple of 2+1=3

So probable answer choice=9+3x hrs.

Options are 14,15,16,17,18

15 is the rite one as 15-9=6 divisible by 3 to give an answer as integer.

This method mite be incorrect for generic problems..but suits the most here as I previously said, the answer choices permit.

:)
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Re: GMAT Diagnostic Test Question 26 [#permalink] New post 26 Nov 2009, 22:23
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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.
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Re: GMAT Diagnostic Test Question 26 [#permalink] New post 23 Aug 2009, 08:36
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dzyubam wrote:
Explanation:
Rating:

Official Answer: B

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).


Damn, this one is tricky!
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Re: GMAT Diagnostic Test Question 26 [#permalink] New post 08 Nov 2010, 10:36
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I set a little bit different equation:

v-speed
T-time in either direction

v(T-3) - for the way there
2v(T-5) - on the way back

v(T-3)=2v(T-5)
vT-3v=2vT-10v
7v-vT=0
v(7-T)=0
T=7

The total time is (do not forget to add extra hour of waiting before return trip) 7+7+1=15
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Re: GMAT Diagnostic Test Question 26 [#permalink] New post 19 Oct 2009, 17:19
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. :shock: 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?!

cheers. All good babe!
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Re: GMAT Diagnostic Test Question 26 [#permalink] New post 20 Oct 2009, 01:30
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. :shock: 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?!

cheers. All good babe!

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Re: GMAT Diagnostic Test Question 26 [#permalink] New post 20 Oct 2009, 16:15
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. :roll: 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).

All good!!!
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Re: GMAT Diagnostic Test Question 26 [#permalink] New post 21 Oct 2009, 04:53
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 :wink: .
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. :roll: 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).

All good!!!

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Re: GMAT Diagnostic Test Question 26 [#permalink] New post 22 Oct 2009, 18:10
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.
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Re: GMAT Diagnostic Test Question 26 [#permalink] New post 22 Oct 2009, 23:18
Welcome to GMAT Club!
You will find a lot of useful info on our forums. Here's a couple of threads that might be helpful:
nink-s-guide-on-how-to-navigate-through-gmatclub-for-newbies-76938.html
everything-you-need-to-prepare-for-the-gmat-revised-77983.html
top-gmat-prep-books-guides-reviews-comments-77703.html

Have a good prep time and do nail that 700 :).
cmintz wrote:
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.

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Re: GMAT Diagnostic Test Question 26 [#permalink] New post 13 Nov 2009, 09:23
freakedgod wrote:
We can take another approach too..and kill the problem in a shorter time just coz the answer choices permit.

We have
1.Stoppage time for journey=3hrs.
2.Stoppage time for return journey-30min*10=300 min=5 hrs.
3.Additional stoppage time=1 hr.

Now Total stoppage =3+1+5=9 hrs.

Now as the speeds are in the ratio 1:2 and distance is constant, time take should be in ratio 2:1.

Time running should be a multiple of 2+1=3

So probable answer choice=9+3x hrs.

Options are 14,15,16,17,18

15 is the rite one as 15-9=6 divisible by 3 to give an answer as integer.

This method mite be incorrect for generic problems..but suits the most here as I previously said, the answer choices permit.

:)


what about 18? Also a multiple of 3. Doesn't help.
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Re: GMAT Diagnostic Test Question 26 [#permalink] New post 21 Nov 2009, 03:51
Crap, worked everything out right but forgot the last 1 hr stop at destination :evil:
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Re: GMAT Diagnostic Test Question 26 [#permalink] New post 23 Nov 2009, 05:23
That's the reason why we all have to practice and eliminate as many mistakes of this kind as possible :).
lonewolf wrote:
Crap, worked everything out right but forgot the last 1 hr stop at destination :evil:

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Re: GMAT Diagnostic Test Question 26 [#permalink] New post 08 Aug 2010, 11:51
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!
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Re: GMAT Diagnostic Test Question 26 [#permalink] New post 03 Sep 2010, 21:17
bb wrote:

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

just a suggestion

thanks
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Re: GMAT Diagnostic Test Question 26 [#permalink] New post 12 Sep 2010, 16:38
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.
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Re: GMAT Diagnostic Test Question 26 [#permalink] New post 04 Nov 2010, 06:56
dzyubam wrote:
Explanation:
Rating:

Official Answer: B

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).



How did you arrive at the value 7 from the ration S/V=4 ?

I did it till the last step but i got stuck at that step and forfeited this method .
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Conclusion : GMAT is long journey.

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Assumption : A long journey is a long trip.


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Re: GMAT Diagnostic Test Question 26   [#permalink] 04 Nov 2010, 06:56
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