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16 Sep 2014, 01:20
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D
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Difficulty:
55%
(hard)
Question Stats:
62% (02:02) correct
38%
(02:10)
wrong
based on 207
sessions
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For any numbers \(x\) and \(y\), \(x?y = xy - x - y\). If \(x?y = 1\), which of the following cannot be a value of \(y\) ?
A. -2
B. -1
C. 0
D. 1
E. 2
A. -2
B. -1
C. 0
D. 1
E. 2
16 Sep 2014, 01:20
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Bookmarks
Official Solution:
For any numbers \(x\) and \(y\), \(x?y = xy - x - y\). If \(x?y = 1\), which of the following cannot be a value of \(y\) ?
A. -2
B. -1
C. 0
D. 1
E. 2
We are given that a certain function, denoted as '?', is defined for all numbers \(x\) and \(y\) such that \(x?y = xy - x - y\).
Since also given that \(x?y = 1\), then \(xy - x - y = 1\).
Express \(x\) in terms of \(y\) to get \(x = \frac{y + 1}{y - 1}\).
If we substitute \(y = 1\) into this equation, the denominator becomes zero, leading to an undefined expression (as we cannot divide by zero). Therefore, \(y\) cannot be equal to 1.
Answer: D
For any numbers \(x\) and \(y\), \(x?y = xy - x - y\). If \(x?y = 1\), which of the following cannot be a value of \(y\) ?
A. -2
B. -1
C. 0
D. 1
E. 2
We are given that a certain function, denoted as '?', is defined for all numbers \(x\) and \(y\) such that \(x?y = xy - x - y\).
Since also given that \(x?y = 1\), then \(xy - x - y = 1\).
Express \(x\) in terms of \(y\) to get \(x = \frac{y + 1}{y - 1}\).
If we substitute \(y = 1\) into this equation, the denominator becomes zero, leading to an undefined expression (as we cannot divide by zero). Therefore, \(y\) cannot be equal to 1.
Answer: D
30 May 2023, 02:39
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I have edited the question and the solution by adding more details to enhance its clarity. I hope it is now easier to understand.
