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Manager
Joined: 10 Sep 2012
Posts: 137
Followers: 2
Kudos [?]:
14
[0], given: 17
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The Z train leaves station A moving at a constant speed, and [#permalink]
 30 Oct 2012, 21:45
Question Stats:
78% (02:39) correct
21% (02:04) wrong based on 2 sessions
The Z train leaves station A moving at a constant speed, and passes by stations B and C, in this order. It takes the Z train 7 hours to reach station B, and 5 additional hours to reach station C. The distance between stations A and B is m kilometers longer than the distance between stations B and C. What is the distance between stations A and C in terms of m? A. 1.8m B. 6m C. 7m D. 9m E. 12m This question was difficult for me. I actually did the problem exactly the way the "alternative method" suggests but did not find an answer that worked. I picked m=7. my distance from b to c was 3. Therefore my distance from a to b was 10. So the total distance from a to c is 13. My goal is 13, with an m of 7. B does not fit this.... why does this not work? It seems like plugging in is failing me here. Correct.
According to this answer, the distance between A and C is 6m. If the distance between A and C is 6m, using our plug in of m=3 the distance is 18. Equate 2s+3 (the distance between A and C according to our table) with 18:
2s+3=6m=18
--> 2s=18-3=15 /:2
--> s=7.5
Use s=7.5 to calculate v, by applying the Distance = Speed×Time formula on the second row:
v∙5=7.5 \:5
---> v=1.5
check if v=1.5 fits the first row:
1.5∙7= 7.5+3= 10.5
7∙1.5 is indeed 10.5, so 6m makes for a velocity that fits both rows.
Therefore, this answer choice is correct.
Alternative method:
Plug in a number for the distance and find the resulting m, rather than the other way around.
For example, plug in a distance of 12 km A-C. Since the speed is constant, divide the distances of A-B and B-C as 7 km and 5 km, respectively, making m equal 7-5=2 additional kilometers in the first leg. The question asks for the value of the distance A-C, which we denoted as 12 km, and the m we plug in is m=2: only answer B will match your goal of 12 km. |
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Director
Status: Disappointed devil..
Joined: 15 Sep 2012
Posts: 592
Location: India
Concentration: Strategy, General Management
WE: Information Technology (Computer Software)
Followers: 20
Kudos [?]:
224
[3] , given: 23
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Re: The Z train leaves station A moving at a constant speed, and [#permalink]
30 Oct 2012, 21:57
3
This post received
KUDOS
anon1 wrote: The Z train leaves station A moving at a constant speed, and passes by stations B and C, in this order. It takes the Z train 7 hours to reach station B, and 5 additional hours to reach station C. The distance between stations A and B is m kilometers longer than the distance between stations B and C. What is the distance between stations A and C in terms of m? 1.8m 6m 7m 9m 12m This question was difficult for me. I actually did the problem exactly the way the "alternative method" suggests but did not find an answer that worked. I picked m=7. my distance from b to c was 3. Therefore my distance from a to b was 10. So the total distance from a to c is 13. My goal is 13, with an m of 7. B does not fit this.... why does this not work? It seems like plugging in is failing me here. Correct.
According to this answer, the distance between A and C is 6m. If the distance between A and C is 6m, using our plug in of m=3 the distance is 18. Equate 2s+3 (the distance between A and C according to our table) with 18:
2s+3=6m=18
--> 2s=18-3=15 /:2
--> s=7.5
Use s=7.5 to calculate v, by applying the Distance = Speed×Time formula on the second row:
v∙5=7.5 \:5
---> v=1.5
check if v=1.5 fits the first row:
1.5∙7= 7.5+3= 10.5
7∙1.5 is indeed 10.5, so 6m makes for a velocity that fits both rows.
Therefore, this answer choice is correct.
Alternative method:
Plug in a number for the distance and find the resulting m, rather than the other way around.
For example, plug in a distance of 12 km A-C. Since the speed is constant, divide the distances of A-B and B-C as 7 km and 5 km, respectively, making m equal 7-5=2 additional kilometers in the first leg. The question asks for the value of the distance A-C, which we denoted as 12 km, and the m we plug in is m=2: only answer B will match your goal of 12 km. The reason it is failing for you is that you chose incorrect numbers. If the question says it took 7 hrs to reach from A to B and 5 hrs to reach from B to C at a constant speed. It shows that distance AB and BC should be in ratio of 7/5. If you take such numbers you can solve problem. AB = 7, BC=5 Therefore AB-BC = 2 But from question, AB-BC =m => m=2 Now total distance = AB+BC= 12 Substitute 12 to get answer in terms of m Total distance =12 =6m Ans B So you get right answer not by plugging in numbers but by 'plugging in right numbers' Hope it helps and if does, kudos is right there << 
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Manager
Joined: 08 Dec 2012
Posts: 50
WE: Engineering (Consulting)
Followers: 0
Kudos [?]:
9
[1] , given: 31
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Re: The Z train leaves station A moving at a constant speed, and [#permalink]
23 Feb 2013, 08:03
1
This post received
KUDOS
Time taken from A to B = 7 hours
Time taken from B to C = 5 hours
Distance from A to B is m miles more than distance between B to C. Since the average speed is constant, time taken to travel m miles is 7-5 = 2 hours.
Total time taken for the entire trip (A to C) = 7 + 5 = 12hours
in 12 hours you can travel \frac{12}{2}*m miles = 6m miles.
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Intern
Status: Attacking Verbal!
Joined: 08 Jan 2013
Posts: 33
Location: United States (NC)
Concentration: Leadership, Strategy
GMAT Date: 06-20-2013
Followers: 0
Kudos [?]:
10
[1] , given: 18
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Re: The Z train leaves station A moving at a constant speed, and [#permalink]
29 Mar 2013, 01:43
1
This post received
KUDOS
The above methods are much faster, but I did it the long way.
From the question distance from A to B is "m" miles longer.
Distance from B to C = x
Distance from A to B = x + m
since speed is constant you have two equations equivalent to each other:
Speed = \frac{distance}{time}
So: \frac{x+m}{7} = \frac{x}{5}
7x = 5x + 5m
x = 2.5m
Add all the distance together = x + x + m = 2.5m + 2.5m + m = 6m, Answer B
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Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 3111
Location: Pune, India
Followers: 571
Kudos [?]:
2010
[1] , given: 92
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Re: The Z train leaves station A moving at a constant speed, and [#permalink]
29 Mar 2013, 03:33
1
This post received
KUDOS
anon1 wrote: The Z train leaves station A moving at a constant speed, and passes by stations B and C, in this order. It takes the Z train 7 hours to reach station B, and 5 additional hours to reach station C. The distance between stations A and B is m kilometers longer than the distance between stations B and C. What is the distance between stations A and C in terms of m? A. 1.8m B. 6m C. 7m D. 9m E. 12m This question was difficult for me. I actually did the problem exactly the way the "alternative method" suggests but did not find an answer that worked. I picked m=7. my distance from b to c was 3. Therefore my distance from a to b was 10. So the total distance from a to c is 13. My goal is 13, with an m of 7. B does not fit this.... why does this not work? It seems like plugging in is failing me here. Correct.
According to this answer, the distance between A and C is 6m. If the distance between A and C is 6m, using our plug in of m=3 the distance is 18. Equate 2s+3 (the distance between A and C according to our table) with 18:
2s+3=6m=18
--> 2s=18-3=15 /:2
--> s=7.5
Use s=7.5 to calculate v, by applying the Distance = Speed×Time formula on the second row:
v∙5=7.5 \:5
---> v=1.5
check if v=1.5 fits the first row:
1.5∙7= 7.5+3= 10.5
7∙1.5 is indeed 10.5, so 6m makes for a velocity that fits both rows.
Therefore, this answer choice is correct.
Alternative method:
Plug in a number for the distance and find the resulting m, rather than the other way around.
For example, plug in a distance of 12 km A-C. Since the speed is constant, divide the distances of A-B and B-C as 7 km and 5 km, respectively, making m equal 7-5=2 additional kilometers in the first leg. The question asks for the value of the distance A-C, which we denoted as 12 km, and the m we plug in is m=2: only answer B will match your goal of 12 km. Use a variable, plug in numbers or simply look at the big picture: Draw the diagram as you read the question. A.....................7 hrs......................B.................5 hrs............C A to B the distance is m km extra and the train takes 2 hrs extra to cover m kms. Then, what is the speed of the train? It is (m/2) kms/hr So the distance between A and C = Speed* Time = (m/2)*12 = 6m
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Re: The Z train leaves station A moving at a constant speed, and
[#permalink]
29 Mar 2013, 03:33
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