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26 May 2017, 04:41
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If \(|a + 1| = |b - 1|\), what is the value of \(a - b\)?
(1) \(ab > 0\)
(2) \(\frac{a}{b} \ne -1\)
(1) \(ab > 0\)
(2) \(\frac{a}{b} \ne -1\)
26 May 2017, 04:41
Kudos
Bookmarks
Official Solution:
If you take the 1st step of the variable approach and modify the original condition and the question, this question becomes \(a + 1 = \pm (b - 1)\). From \(a + 1 = b - 1\) or \(a + 1 = -(b - 1) = -b + 1\), you get \(a - b = -2\) or \(a = -b\). There are 2 variables \((a, b)\) and 1 equation \((| a + 1| = |b - 1|)\), so in order to match the number of variables to the number of equations, you need 1 more equation. Therefore, the answer is D.
In the case of con 1), if \(ab > 0\), you get \(a + b \ne 0\) because the sign is the same.Then, you get \(a - b = -2\), hence it is unique and sufficient.
In the case of con 2), from \(\frac{a}{b} \ne -1\), \(a \ne -b\), you get \(a - b = -2\), hence it is unique and sufficient. Since con 1)= con2), the answer is D.
Answer: D
If you take the 1st step of the variable approach and modify the original condition and the question, this question becomes \(a + 1 = \pm (b - 1)\). From \(a + 1 = b - 1\) or \(a + 1 = -(b - 1) = -b + 1\), you get \(a - b = -2\) or \(a = -b\). There are 2 variables \((a, b)\) and 1 equation \((| a + 1| = |b - 1|)\), so in order to match the number of variables to the number of equations, you need 1 more equation. Therefore, the answer is D.
In the case of con 1), if \(ab > 0\), you get \(a + b \ne 0\) because the sign is the same.Then, you get \(a - b = -2\), hence it is unique and sufficient.
In the case of con 2), from \(\frac{a}{b} \ne -1\), \(a \ne -b\), you get \(a - b = -2\), hence it is unique and sufficient. Since con 1)= con2), the answer is D.
Answer: D
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