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For how many pair(s) of positive integers m and n, such that n > m > 1

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Joined: 07 Jun 2017
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Location: India
Concentration: Technology, General Management
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For how many pair(s) of positive integers m and n, such that n > m > 1  [#permalink]

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New post 24 Oct 2017, 01:17
2
00:00
A
B
C
D
E

Difficulty:

  85% (hard)

Question Stats:

46% (00:53) correct 54% (01:30) wrong based on 61 sessions

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For how many pair(s) of positive integers \(m\) and \(n\), such that \(n > m > 1\), is \(m^n\) not greater than \(n^m\)?

A. 0
B. 1
C. 2
D. 3
E. 4

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Re: For how many pair(s) of positive integers m and n, such that n > m > 1  [#permalink]

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New post 24 Oct 2017, 06:59
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2
nkmungila wrote:
For how many pair(s) of positive integers \(m\) and \(n\), such that \(n > m > 1\), is \(m^n\) not greater than \(n^m\)?

A. 0
B. 1
C. 2
D. 3
E. 4


The question asks for how many pairs is \(m^n≤n^m\)

if \(m=2\) & \(n=3\), then \(m^n=2^3=8\) and \(n^m=3^2=9\), so this satisfies our condition

again if \(m=2\) & \(n=4\), then \(m^n=2^4=16\) and \(n^m=4^2=16\) this also satisfies our condition.

Hence there are two such pairs

Option C
Re: For how many pair(s) of positive integers m and n, such that n > m > 1 &nbs [#permalink] 24 Oct 2017, 06:59
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