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16 Sep 2014, 00:48
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If \(m\) and \(n\) are positive numbers, what is the value of \(m*n\)?
(1) \(m^n = 1\)
(2) \(n^m = 1\)
(1) \(m^n = 1\)
(2) \(n^m = 1\)
16 Sep 2014, 00:48
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Official Solution:
If \(m\) and \(n\) are positive numbers, what is the value of \(m*n\)?
(1) \(m^n=1\).
Since \(m\) and \(n\) are positive numbers, the above implies that \(m=1\) (this is because no other positive number can be raised to a positive power and still equal 1). However, \(n\) can be any positive number, resulting in different values of \(m*n\). Not sufficient.
(2) \(n^m=1\).
Since \(m\) and \(n\) are positive numbers, the above implies that \(n=1\) (this is because no other positive number can be raised to a positive power and still equal 1). However, \(m\) can be any positive number, resulting in different values of \(m*n\). Not sufficient.
(1)+(2) From the above information, we can deduce that both \(m=1\) and \(n=1\). Therefore, \(mn=1\). This information is sufficient.
Answer: C
If \(m\) and \(n\) are positive numbers, what is the value of \(m*n\)?
(1) \(m^n=1\).
Since \(m\) and \(n\) are positive numbers, the above implies that \(m=1\) (this is because no other positive number can be raised to a positive power and still equal 1). However, \(n\) can be any positive number, resulting in different values of \(m*n\). Not sufficient.
(2) \(n^m=1\).
Since \(m\) and \(n\) are positive numbers, the above implies that \(n=1\) (this is because no other positive number can be raised to a positive power and still equal 1). However, \(m\) can be any positive number, resulting in different values of \(m*n\). Not sufficient.
(1)+(2) From the above information, we can deduce that both \(m=1\) and \(n=1\). Therefore, \(mn=1\). This information is sufficient.
Answer: C
20 Apr 2023, 02:53
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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.
