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26 May 2017, 04:43
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A certain apartment has only 1-room and 2-rooms. If the range of the total rental fees for 1-room and 2-rooms combined is \(1,000 and the range of the rental fees for 2-rooms is\)200, what is the range of the rental fees for 1-room?
(1) The smallest rental fee for 2-rooms is \(2,800.\\
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(2) The smallest rental fee for 2-room is\)200 more expensive than the greatest rental fee for 1-room.
(1) The smallest rental fee for 2-rooms is \(2,800.\\
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(2) The smallest rental fee for 2-room is\)200 more expensive than the greatest rental fee for 1-room.
26 May 2017, 04:45
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Official Solution:
You can the 1st step of the variable approach and modify the original condition and the question. From range=Max-min, range\((R_{1})=L_{1}-S_{1}\) of 1-room and range=\(200=L_{2}-S_{2}\) of 2-rooms, there are 5 variables \((R_{1}, L_{1}, L_{2}, S_{1}, S_{2})\) and 3 equations (the range of the total rental fees for 1-room and 2-rooms combined is \(1,000,\)R_{1}=L_{1}-S_{1}, 200=L_{2}-S_{2}\(). In order to match the number of variables to the number of equations, C is most likely to be the answer.\\
\\
By solving con 1) & con 2),\\
\\
\\
\\
you get what is shown in the diagram above. Then, you get\)R_{1}=L_{2}-S_{1}\(=\)2,600-\(2,000=\)600, hence it is unique and sufficient. Therefore, the answer is C.
However, this is also a statistics question, one of the key questions, so you can apply "CMT4 (A: if you get C too easily, consider A or B).
In the case of con 1), you cannot find the difference between \(L_{1}\) and \(S_{2}\), hence it is not sufficient.
In the case of con 2)
As shown in the diagram above, you get \(R_{1}=L_{2}-S_{1}\)=$600, hence it is unique and sufficient. Therefore, the answer is B. You should be aware of these types of integer and statistics questions related to CMT 4.
Answer: B
You can the 1st step of the variable approach and modify the original condition and the question. From range=Max-min, range\((R_{1})=L_{1}-S_{1}\) of 1-room and range=\(200=L_{2}-S_{2}\) of 2-rooms, there are 5 variables \((R_{1}, L_{1}, L_{2}, S_{1}, S_{2})\) and 3 equations (the range of the total rental fees for 1-room and 2-rooms combined is \(1,000,\)R_{1}=L_{1}-S_{1}, 200=L_{2}-S_{2}\(). In order to match the number of variables to the number of equations, C is most likely to be the answer.\\
\\
By solving con 1) & con 2),\\
\\
\\\\
you get what is shown in the diagram above. Then, you get\)R_{1}=L_{2}-S_{1}\(=\)2,600-\(2,000=\)600, hence it is unique and sufficient. Therefore, the answer is C.
However, this is also a statistics question, one of the key questions, so you can apply "CMT4 (A: if you get C too easily, consider A or B).
In the case of con 1), you cannot find the difference between \(L_{1}\) and \(S_{2}\), hence it is not sufficient.
In the case of con 2)
As shown in the diagram above, you get \(R_{1}=L_{2}-S_{1}\)=$600, hence it is unique and sufficient. Therefore, the answer is B. You should be aware of these types of integer and statistics questions related to CMT 4.
Answer: B
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