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The speed of a railway engine is 42 Km per hour

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The speed of a railway engine is 42 Km per hour [#permalink] New post 26 Feb 2014, 09:30
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The speed of a railway engine is 42 Km per hour when no compartment is attached, and the reduction in speed is directly proportional to the square root of the number of compartments attached. If the speed of the train carried by this engine is 24 Km per hour when 9 compartments are attached, the maximum number of compartments that can be carried by the engine is:

A. 49
B. 48
C. 46
D. 47
E. 44
[Reveal] Spoiler: OA

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Re: The speed of a railway engine is 42 Km per hour [#permalink] New post 26 Feb 2014, 12:56
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ankur1901 wrote:
The speed of a railway engine is 42 Km per hour when no compartment is attached, and the reduction in speed is directly proportional to the square root of the number of compartments attached. If the speed of the train carried by this engine is 24 Km per hour when 9 compartments are attached, the maximum number of compartments that can be carried by the engine is:

A. 49
B. 48
C. 46
D. 47
E. 44

Dear ankur1901,
I'm happy to give my two cents. :-)

The wording of this question is less than ideal. I found this question in a free source on Google Books. I don't know if you are familiar with the sarcastic saying, "Free, and worth it!" The quality of free material varies considerably, and much of it is not necessarily helpful in preparing for the GMAT.

This statement is problematic:
the reduction in speed is directly proportional to the square root of the number of compartments attached
Does "reduction" mean amount subtracted? or percentage decrease? There are at least two interpretations, and the wording does not provide a clear interpretation between them.

Evidently what the question intends is the subtraction interpretation. What is subtracted from the speed is directly proportional to the square root of the number of compartments attached.

In other words, if S = speed, and N = number of compartments, then

S = 42 - k*sqrt(N)

where k is a constant of the proportionality. In general, if A is directly proportional to B, we can write A = k*B and solve for k.

If N = 9, then S = 24

24 = 42 - k*sqrt(9) = 42 - 3k

3k = 18

k = 6

Now, we need to know: what value of N makes S go to zero?

0 = 42 - 6*sqrt(N)

6*sqrt(N) = 42

sqrt(N) = 7

n = 7^2 = 49

With 49 compartments, the train does not budge. Therefore, it would budge if there were one fewer cars. Thus, 48 is the maximum number of cars the engine can pull and still move.

Here's a high quality GMAT PS practice question:
http://gmat.magoosh.com/questions/2613
When you submit your answer, the following page will have a complete video explanation.

Does all this make sense?
Mike :-)
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Re: The speed of a railway engine is 42 Km per hour [#permalink] New post 26 Feb 2014, 17:53
ankur1901 wrote:
The speed of a railway engine is 42 Km per hour when no compartment is attached, and the reduction in speed is directly proportional to the square root of the number of compartments attached. If the speed of the train carried by this engine is 24 Km per hour when 9 compartments are attached, the maximum number of compartments that can be carried by the engine is:

A. 49
B. 48
C. 46
D. 47
E. 44


Reduction in speed is directly proportional to square root of no. of compartments

speed when no compartments= 42
speed with 9 compartments = 24
reduced speed = 18

18 = K*sqrt of 9
=> k = 6

Train doesnt move when there are more compartments... so assuming that the speed is reduced by 42

42=6*sqrt of n (n is no. of compartments)
=>n = 49

So for the train to atleast move there should be one compartment less than 49 => 48

Hope this clarifies.
Re: The speed of a railway engine is 42 Km per hour   [#permalink] 26 Feb 2014, 17:53
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