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

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Manager
Joined: 07 Jun 2017
Posts: 177

Kudos [?]: 101 [0], given: 59

Location: India
Concentration: Technology, General Management
GMAT 1: 660 Q46 V38
GPA: 3.6
WE: Information Technology (Computer Software)
For how many pair(s) of positive integers m and n, such that n > m > 1 [#permalink]

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24 Oct 2017, 00:17
00:00

Difficulty:

95% (hard)

Question Stats:

39% (00:48) correct 61% (01:26) wrong based on 51 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
[Reveal] Spoiler: OA

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Regards,
Naveen
email: nkmungila@gmail.com
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Kudos [?]: 101 [0], given: 59

Director
Joined: 25 Feb 2013
Posts: 619

Kudos [?]: 304 [1], given: 39

Location: India
GPA: 3.82
Re: For how many pair(s) of positive integers m and n, such that n > m > 1 [#permalink]

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24 Oct 2017, 05:59
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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

Kudos [?]: 304 [1], given: 39

Re: For how many pair(s) of positive integers m and n, such that n > m > 1   [#permalink] 24 Oct 2017, 05:59
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For how many pair(s) of positive integers m and n, such that n > m > 1

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