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# Two trains, X and Y, started simultaneously from opposite en

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Director
Joined: 17 Dec 2012
Posts: 637
Location: India
Re: Two trains, X and Y, started simultaneously from opposite en  [#permalink]

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30 May 2017, 17:17
Bunuel wrote:
The Official Guide For GMAT® Quantitative Review, 2ND Edition

Two trains, X and Y, started simultaneously from opposite ends of a 100-mile route and traveled toward each other on parallel tracks. Train X, traveling at a constant rate, completed the 100-mile trip in 5 hours; Train Y, traveling at a constant rate, completed the 100-mile trip in 3 hours. How many miles had Train X traveled when it met Train Y?

(A) 37.5
(B) 40.0
(C) 60.0
(D) 62.5
(E) 77.5

1. They would have met in 100/(100/5+100/3) hrs =15/8 hrs
2. In that time X would have traveled, Time *speed =15/8 *20=37.5
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Joined: 14 May 2017
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Schools: Anderson '20 (M)
GMAT 1: 740 Q48 V44
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Re: Two trains, X and Y, started simultaneously from opposite en  [#permalink]

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30 Jun 2017, 20:47
Another one that we can solve without putting pen to paper. We should always take our time when approaching questions to glance at the answers and use our intuition to solve quickly. This test is as much about being strategic as it is about being intelligent.

Here's the approach: Train Y travels at a speed of 100/3 which is about 33.33 miles per hour. In contrast, Train X travels at 100/5 = 20 miles per hour. Hence, after 2 hours, Train Y will have traveled 66.66 miles, and Train X will have traveled 40 miles, which means they would have passed each other at this point.

Therefore, we know Train X must have traveled less than 40 miles when it met with Train Y. Only Answer A is less than 40 miles.

We should always be on the lookout for "smart" approaches... Think like the test makers.

Happy GMAT Hunting...
CEO
Joined: 12 Sep 2015
Posts: 2705
Re: Two trains, X and Y, started simultaneously from opposite en  [#permalink]

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07 Dec 2017, 10:24
Top Contributor
Bunuel wrote:
The Official Guide For GMAT® Quantitative Review, 2ND Edition

Two trains, X and Y, started simultaneously from opposite ends of a 100-mile route and traveled toward each other on parallel tracks. Train X, traveling at a constant rate, completed the 100-mile trip in 5 hours; Train Y, traveling at a constant rate, completed the 100-mile trip in 3 hours. How many miles had Train X traveled when it met Train Y?

(A) 37.5
(B) 40.0
(C) 60.0
(D) 62.5
(E) 77.5

Train X completed the 100-mile trip in 5 hours
Speed = distance/time
= 100/5
= 20 mph

Train Y completed the 100-mile trip in 3 hours
Speed = distance/time
= 100/3
33 mph (This approximation is close enough. You'll see why shortly)

How many miles had Train X traveled when it met Train Y?

When the two trains meet, each train will have been traveling for the same amount of time
So, we can write: Train X's travel time = Train Y's travel time

time = distance/speed
We know each train's speed, but not the distance traveled (when they meet). So, let's assign some variables.

Let d = the distance train X travels
So, 100-d = the distance train Y travels (since their COMBINED travel distance must add to 100 miles)

We can now turn our word equation into an algebraic equation.
We get: d/20 = (100 - d)/33
Cross multiply to get: (33)(d) = (20)(100 - d)
Expand: 33d = 2000 - 20d
Add 20d to both sides: 53d = 2000
So, d = 2000/53

IMPORTANT: Before you start performing any long division, first notice that 2000/50 = 40
Since the denominator is greater than 50, we can conclude that 2000/53 is LESS THAN 40
Since only one answer choice is less than 40, the correct answer must be A

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Director
Joined: 09 Mar 2016
Posts: 758
Re: Two trains, X and Y, started simultaneously from opposite en  [#permalink]

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13 Mar 2018, 05:15
Bunuel wrote:
The Official Guide For GMAT® Quantitative Review, 2ND Edition

Two trains, X and Y, started simultaneously from opposite ends of a 100-mile route and traveled toward each other on parallel tracks. Train X, traveling at a constant rate, completed the 100-mile trip in 5 hours; Train Y, traveling at a constant rate, completed the 100-mile trip in 3 hours. How many miles had Train X traveled when it met Train Y?

(A) 37.5
(B) 40.0
(C) 60.0
(D) 62.5
(E) 77.5

Problem Solving
Question: 119
Category: Algebra Applied problems
Page: 77
Difficulty: 600

GMAT Club is introducing a new project: The Official Guide For GMAT® Quantitative Review, 2ND Edition - Quantitative Questions Project

Each week we'll be posting several questions from The Official Guide For GMAT® Quantitative Review, 2ND Edition and then after couple of days we'll provide Official Answer (OA) to them along with a slution.

We'll be glad if you participate in development of this project:
2. Please vote for the best solutions by pressing Kudos button;
3. Please vote for the questions themselves by pressing Kudos button;
4. Please share your views on difficulty level of the questions, so that we have most precise evaluation.

Thank you!

Greetings everyone
Can anyone share some useful formulas like relative speed etc ?

many thanks!
_________________

In English I speak with a dictionary, and with people I am shy.

Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 8188
Location: Pune, India
Re: Two trains, X and Y, started simultaneously from opposite en  [#permalink]

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13 Mar 2018, 11:39
1
dave13 wrote:
Bunuel wrote:
The Official Guide For GMAT® Quantitative Review, 2ND Edition

Two trains, X and Y, started simultaneously from opposite ends of a 100-mile route and traveled toward each other on parallel tracks. Train X, traveling at a constant rate, completed the 100-mile trip in 5 hours; Train Y, traveling at a constant rate, completed the 100-mile trip in 3 hours. How many miles had Train X traveled when it met Train Y?

(A) 37.5
(B) 40.0
(C) 60.0
(D) 62.5
(E) 77.5

Problem Solving
Question: 119
Category: Algebra Applied problems
Page: 77
Difficulty: 600

GMAT Club is introducing a new project: The Official Guide For GMAT® Quantitative Review, 2ND Edition - Quantitative Questions Project

Each week we'll be posting several questions from The Official Guide For GMAT® Quantitative Review, 2ND Edition and then after couple of days we'll provide Official Answer (OA) to them along with a slution.

We'll be glad if you participate in development of this project:
2. Please vote for the best solutions by pressing Kudos button;
3. Please vote for the questions themselves by pressing Kudos button;
4. Please share your views on difficulty level of the questions, so that we have most precise evaluation.

Thank you!

Greetings everyone
Can anyone share some useful formulas like relative speed etc ?

many thanks!

Check out these two posts:
https://www.veritasprep.com/blog/2012/0 ... elatively/
https://www.veritasprep.com/blog/2012/0 ... -concepts/

They discuss relative speed in detail.
_________________

Karishma
Veritas Prep GMAT Instructor

Save up to \$1,000 on GMAT prep through 8/20! Learn more here >

GMAT self-study has never been more personalized or more fun. Try ORION Free!

Senior Manager
Joined: 22 Feb 2018
Posts: 254
Re: Two trains, X and Y, started simultaneously from opposite en  [#permalink]

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13 Mar 2018, 12:25
1
VeritasPrepKarishma wrote:
dave13 wrote:
Bunuel wrote:
The Official Guide For GMAT® Quantitative Review, 2ND Edition

Two trains, X and Y, started simultaneously from opposite ends of a 100-mile route and traveled toward each other on parallel tracks. Train X, traveling at a constant rate, completed the 100-mile trip in 5 hours; Train Y, traveling at a constant rate, completed the 100-mile trip in 3 hours. How many miles had Train X traveled when it met Train Y?

(A) 37.5
(B) 40.0
(C) 60.0
(D) 62.5
(E) 77.5

Problem Solving
Question: 119
Category: Algebra Applied problems
Page: 77
Difficulty: 600

GMAT Club is introducing a new project: The Official Guide For GMAT® Quantitative Review, 2ND Edition - Quantitative Questions Project

Each week we'll be posting several questions from The Official Guide For GMAT® Quantitative Review, 2ND Edition and then after couple of days we'll provide Official Answer (OA) to them along with a slution.

We'll be glad if you participate in development of this project:
2. Please vote for the best solutions by pressing Kudos button;
3. Please vote for the questions themselves by pressing Kudos button;
4. Please share your views on difficulty level of the questions, so that we have most precise evaluation.

Thank you!

Greetings everyone
Can anyone share some useful formulas like relative speed etc ?

many thanks!

Check out these two posts:
https://www.veritasprep.com/blog/2012/0 ... elatively/
https://www.veritasprep.com/blog/2012/0 ... -concepts/

They discuss relative speed in detail.

Train X speed =100/5 Mile/hr
Train Y speed =100/3 Mile/hr
Relative Speed of X w.r.t Y =X speed - Y speed
but as direction of Y is opposite to X, -ve sign will be placed before Train Y's Speed.

Realtive speed of X w.r.t Y = 100/5 - (-100/3) = 100/5+100/3 = 800/15

Total distance travelled = 100 Mile

Time taken when train X meets train Y = 100 /Relative speed of X w.r.t Y
= 15/8 hrs.

Distance travelled by Train X when it meets Train Y = (100/5) * (15/8)
=75/2 Miles
_________________

Good, good Let the kudos flow through you

Director
Joined: 09 Mar 2016
Posts: 758
Two trains, X and Y, started simultaneously from opposite en  [#permalink]

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14 Mar 2018, 09:17
Princ What does "w.r.t " mean ?
_________________

In English I speak with a dictionary, and with people I am shy.

Director
Joined: 09 Mar 2016
Posts: 758
Two trains, X and Y, started simultaneously from opposite en  [#permalink]

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14 Mar 2018, 09:30
VeritasPrepKarishma wrote:
dave13 wrote:
Bunuel wrote:
The Official Guide For GMAT® Quantitative Review, 2ND Edition

Two trains, X and Y, started simultaneously from opposite ends of a 100-mile route and traveled toward each other on parallel tracks. Train X, traveling at a constant rate, completed the 100-mile trip in 5 hours; Train Y, traveling at a constant rate, completed the 100-mile trip in 3 hours. How many miles had Train X traveled when it met Train Y?

(A) 37.5
(B) 40.0
(C) 60.0
(D) 62.5
(E) 77.5

Problem Solving
Question: 119
Category: Algebra Applied problems
Page: 77
Difficulty: 600

GMAT Club is introducing a new project: The Official Guide For GMAT® Quantitative Review, 2ND Edition - Quantitative Questions Project

Each week we'll be posting several questions from The Official Guide For GMAT® Quantitative Review, 2ND Edition and then after couple of days we'll provide Official Answer (OA) to them along with a slution.

We'll be glad if you participate in development of this project:
2. Please vote for the best solutions by pressing Kudos button;
3. Please vote for the questions themselves by pressing Kudos button;
4. Please share your views on difficulty level of the questions, so that we have most precise evaluation.

Thank you!

Greetings everyone
Can anyone share some useful formulas like relative speed etc ?

many thanks!

Check out these two posts:
https://www.veritasprep.com/blog/2012/0 ... elatively/
https://www.veritasprep.com/blog/2012/0 ... -concepts/

They discuss relative speed in detail.

Hi VeritasPrepKarishma many thanks for the useful links. one question why have you guys chosen such font like century gothic with a bit grey font color for writing articles ? it would be better if you could use some standard font like calibri... a bit hard to read with concentration just saying you know
_________________

In English I speak with a dictionary, and with people I am shy.

Senior Manager
Joined: 22 Feb 2018
Posts: 254
Re: Two trains, X and Y, started simultaneously from opposite en  [#permalink]

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14 Mar 2018, 09:44
1
dave13 wrote:
Princ What does "w.r.t " mean ?

Hi Dave13

w.r.t means "with respect to"
For example: Speed of A with respect to B
_________________

Good, good Let the kudos flow through you

Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 8188
Location: Pune, India
Re: Two trains, X and Y, started simultaneously from opposite en  [#permalink]

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15 Mar 2018, 03:54
1
dave13 wrote:

Hi VeritasPrepKarishma many thanks for the useful links. one question why have you guys chosen such font like century gothic with a bit grey font color for writing articles ? it would be better if you could use some standard font like calibri... a bit hard to read with concentration just saying you know

Those are default settings with which we cannot mess, Dave!
But I will pass on your feedback to the concerned people. Thank You!
_________________

Karishma
Veritas Prep GMAT Instructor

Save up to \$1,000 on GMAT prep through 8/20! Learn more here >

GMAT self-study has never been more personalized or more fun. Try ORION Free!

Re: Two trains, X and Y, started simultaneously from opposite en &nbs [#permalink] 15 Mar 2018, 03:54

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