Question number 27. Jane is traveling on a train in which each coach has the same number of compartments. She is sitting in the 7th coach, in the 50th compartment from the engine. How many compartments are there in each coach? Let's draw a picture to represent this train. I'll just simply use a timeline idea, where on one side I have the engine, and then between the engine and Jane there are 6 coaches, each with the same number of compartments, so each with some number, let's call it N, compartments. And then here is going to be coach 7, and somewhere in there, in number 50, in compartment 50 is Jane. Okay, so the smallest choice here we have for the number of compartments is 7. So say n is equal to 7, and there are 7 compartments in each coach. The end of the 6 coaches, therefore, here, is marked with a number 6 times 7, 42, and the number 43 is, in fact, in coach number 7. And with 7 compartments in each coach, we have numbers 43, 44, 45, 46, 47, 48, and 49 are the 7 compartments in that coach. Since Jane is sitting in compartment number 50, she is not quite in coach number 7. She would be coach number 8 in this case. So A is not the answer, and then we continue. The next calculation should give us the answer. We increase that number of compartments per coach to 8, then 6 times 8, or 48 compartments, all in the 6 first coaches, and coach number 7 begins with compartment number 49. So definitely, Jane is, in that case, sitting in coach number 7, just in the 2nd seat of that coach. So we have decided that there must be 8 compartments per coach, and the answer here, for 27, is B, 8.

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