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

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Re: Two trains, X and Y, started simultaneously from opposite en [#permalink]

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New post 30 May 2017, 16:17
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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Re: Two trains, X and Y, started simultaneously from opposite en [#permalink]

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New post 25 Jun 2017, 14:31

I like to sketch out the problem and many times it is a fast method.



As you can see train A meets train B somewhere between the 20 and 40th mile. Looking at the answer choices, it is pretty obvious that A is the answer.
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Re: Two trains, X and Y, started simultaneously from opposite en [#permalink]

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New post 30 Jun 2017, 19:47
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...

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Re: Two trains, X and Y, started simultaneously from opposite en [#permalink]

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New post 07 Dec 2017, 09:24
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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?
Let's start with a word equation.

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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Re: Two trains, X and Y, started simultaneously from opposite en   [#permalink] 07 Dec 2017, 09:24

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