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26 May 2017, 04:40
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Is \(| a - b + c | - a + b - c > 0\)?
(1) \(a + c < b\)
(2) \(a > 0\), \(b > 0\), and \(c > 0\)
(1) \(a + c < b\)
(2) \(a > 0\), \(b > 0\), and \(c > 0\)
26 May 2017, 04:40
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Official Solution:
In general, for absolute values, you must have \(AA\) to happen. Thus, if you can take the 1st step of the variable approach and modify the original condition and the question, you get from \(| a - b + c | - a + b - c > 0\), \(| a - b + c | > a - b + c\), to \(a - b + c < 0\)?, and then to \(a + c < b\).
Therefore, con 1) is yes and sufficient, and in the case of con 2), \((a, b, c) = (1, 3, 1)\) is yes, and \((a, b, c)=(1, 1, 1)\) is no, hence it is not sufficient. Therefore, the answer is A.
Answer: A
In general, for absolute values, you must have \(AA\) to happen. Thus, if you can take the 1st step of the variable approach and modify the original condition and the question, you get from \(| a - b + c | - a + b - c > 0\), \(| a - b + c | > a - b + c\), to \(a - b + c < 0\)?, and then to \(a + c < b\).
Therefore, con 1) is yes and sufficient, and in the case of con 2), \((a, b, c) = (1, 3, 1)\) is yes, and \((a, b, c)=(1, 1, 1)\) is no, hence it is not sufficient. Therefore, the answer is A.
Answer: A
08 Jun 2023, 23:55
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