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:
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)
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.
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Does all this make sense?
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