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

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GMAT Instructor
Joined: 04 Jul 2006
Posts: 1262
A train always travels at one of two speeds: 160 km/hr in [#permalink]

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08 Oct 2007, 11:55
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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.

Kevin Armstrong
Manhattan Review
CEO
Joined: 29 Mar 2007
Posts: 2559

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08 Oct 2007, 12:17
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.

Kevin Armstrong
Manhattan Review

Ans is A.

We can plug in #'s or solve algebraically.

I chose to plug in w/ this choice.

Avg R: tot Distance/tot Time

Say Distance is 120km.
Rural || Urban
R 160 || 40
T 1/2hr || 1hr
D 80 || 40

Rural distance is 80 b/c 2/3*120=80. (same reasoning for Urban)

So we have 120/(1/2hr+1hr) --> 120/3/2Hrs ---> 120*2/3 ->80kph

So NO the train did not exceed an average speed of 100kmph

Just looking at B it says the distance exceeds 1000km. If you don't feel comfortable w/ the above. Just try 1200km. You will see the answer is still 80kmph
Director
Joined: 08 Jun 2007
Posts: 573

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08 Oct 2007, 12:38
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.

Kevin Armstrong
Manhattan Review

Stmtn 1 -
if total is assumed as 1 , we can find the average speed .
Comes to 80 miles/hr.

Stmtn2 - redundant information . need to know the break up of time or distance.

A
Director
Joined: 03 May 2007
Posts: 872
Schools: University of Chicago, Wharton School

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08 Oct 2007, 12:42
Hi Kevin,
Have you recently join Manhattan Review?
Congrats/goodluck..

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.

Kevin Armstrong
Manhattan Review

A. (160 x 2/3) + (40 x 1/3) = 360/3 = 120

so the average speed is al least 120 km/h
Manager
Joined: 03 Oct 2007
Posts: 60

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08 Oct 2007, 12:47
Ans is A.

Logic of the question suggests that we need only know what fraction of the entire trip was rural vs not, in order to find the actual time.

1st premise provides us exactly this information.

2nd premise is a dud.

By the way, this is a great candidate for time saving by avoiding unnecessary math. If you can visualize this problem, you need not write any math down to solve it -- give yourself more time for the other calc intensive problems down the road.

Another GMAC favorite in this genre is "did the train ever exceed speed X during such and such trip?". Well, maybe for a split second the train gassed it up and went super duper fast, while noone was looking... the answer to this question is usually E, because you usually cannot know if there was a split second surge in speed while the rest of the trip was normal.
Director
Joined: 18 Jul 2006
Posts: 524

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08 Oct 2007, 13:57
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.

Kevin Armstrong
Manhattan Review

A. If travel was 2/3 in rural, then average speed would be 80 km/h. BUT, travel is more than 2/3 in rural, so average speed is > 80 km/h
INSUFF

B. Total distance doesn't matter...INSUFF

Combining A & B doesn't help as we don't know how long train travelled in rural/urban area.

Ans E.
VP
Joined: 09 Jul 2007
Posts: 1100
Location: London

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08 Oct 2007, 14:48
from basics, what i know is that in order to find the average speed we need to find the distance and time only.
we do not have the time it took the train to travel with different rates of speed so. we can find the time using both of the statements.
i think it is C. speed is >40 mp/hour
will post the explanation if it is the correct answer.
Director
Joined: 03 May 2007
Posts: 872
Schools: University of Chicago, Wharton School

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08 Oct 2007, 14:53
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.

Kevin Armstrong
Manhattan Review

hmmm.........
the question doesnot seem that much difficult but i can guess a qusestion from him is not too simple as well.
VP
Joined: 09 Jul 2007
Posts: 1100
Location: London

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08 Oct 2007, 14:54
Fistail wrote:
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.

Kevin Armstrong
Manhattan Review

hmmm.........
the question doesnot seem that much difficult but i can guess a qusestion from him is not too simple as well.

kevin doesnt post simple questions?!
Current Student
Joined: 08 Oct 2007
Posts: 169
Location: Berkeley, CA
Schools: Berkeley-Haas MBA
WE 1: Investment Management (fund of funds)

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09 Oct 2007, 09:43
[quote="kevincan"]Perhaps the nicest way is to see what the average speed would be if fraction f of the trip were through rural areas.[/quote]

ooops! sorry guys ... My brain short circuited!
Director
Joined: 03 May 2007
Posts: 872
Schools: University of Chicago, Wharton School

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09 Oct 2007, 10:44
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

I guess i got it. Suppose the distance is 1200km.
rural area = 80% of 1200km = 960km
no of hours = 6 hours
urban area = 20% of 1200km = 240km
no of hours = 6 hours
so the average speed = (960+240)/12 = 100 km/h

Suppose: the rural area = 90% of 1200km = 1080 km
no of hours = 1080/160 hours
urban area = 10% of 1200 km = 120 km
no of hours = 3 hours

so the average speed = (1080 + 120)/(1080/160 + 12) => 100 km/h

so E.
Director
Joined: 22 Aug 2007
Posts: 566

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31 Oct 2007, 04:47
get clear E for this question,

Average speed= total distance/ total time=D/T
D=dr+du
T=total time=time in rural area+time in urban area
T=dr/40+du/160

A=D/(dr/40+du/160)

A=D*160*40/ (dr*40+du*160)=D*160*40/(dr+4*du)*40

thus

A=D*160/(dr+4*du)

(1) INSUFF

(2/3)D<dr, then (1/3)D>du, for convenience lets assume dr=(2/3)D and du=(1/3)D

A=D*160/((2/3)D+(1/3)*4*D)
A=160/(2/3+4*1/3) --------------------> whatever the total distance is THIS will be the equation for average speed

160/(2/3+4*1/3) =~27, to cancel previous assumption, lets calculate
160/(0,70+0,3*4)=~84

thus Average speed>27------------> average speed could be more than 100, could be less.

(2) INSUFF

obviously insuff

both) INSUFF

A=160/(2/3+4*1/3) --------------------> whatever the total distance is THIS will be the equation for average speed, thus yeilds the same result as A

calculations is a must for tough DS...
GMAT Instructor
Joined: 04 Jul 2006
Posts: 1262

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31 Oct 2007, 10:14
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.

Kevin Armstrong
Manhattan Review

Suppose f is the fraction of the total distance d that was through rural areas. Total time is fd/160 + (1-f)d/40 = (fd+4(1-f)d)/160

Average speed = 160 /(f+4(1-f))= 160/(4 -3f)
For this to be greater than 100, (4-3f)/8 > 1/5

4-3f > 8/5
3f > 12/5
f > 4/5
Re: DS: Train   [#permalink] 31 Oct 2007, 10:14
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