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# If m, n, and m^n are nonzero integers, which of the following must be

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Manager
Joined: 10 Feb 2011
Posts: 113

Kudos [?]: 363 [0], given: 10

If m, n, and m^n are nonzero integers, which of the following must be [#permalink]

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18 Feb 2011, 11:33
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Difficulty:

55% (hard)

Question Stats:

42% (00:37) correct 58% (01:08) wrong based on 31 sessions

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If m, n, and m^n are nonzero integers, which of the following must be true?

I. m^n is positive
II. n^m is an integer
III. m^n is an integer

(A) None
(B) I only
(C) II only
(D) III only
(E) I and II only
[Reveal] Spoiler: OA

Kudos [?]: 363 [0], given: 10

Manager
Joined: 03 Jun 2010
Posts: 172

Kudos [?]: 71 [1], given: 40

Location: United States (MI)
Concentration: Marketing, General Management
WE: Business Development (Consumer Products)
Re: If m, n, and m^n are nonzero integers, which of the following must be [#permalink]

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18 Feb 2011, 11:44
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How m^n can be a non-integer, if it is given that it is an integer?

Kudos [?]: 71 [1], given: 40

Math Forum Moderator
Joined: 20 Dec 2010
Posts: 1964

Kudos [?]: 2049 [0], given: 376

Re: If m, n, and m^n are nonzero integers, which of the following must be [#permalink]

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18 Feb 2011, 11:55
ulm wrote:
How m^n can be a non-integer, if it is given that it is an integer?

I believe it is a typo; it should be "mn".

When m=-2; n=-1
m^n = 2^-1 = 1/2. Non integer

When n=2, m=-1
n^m = 2^-1 = 1/2. Non integer

When m=-2, n=3
m^n = (-2)^3=-8. Negative

Ans: "A"
_________________

Kudos [?]: 2049 [0], given: 376

Director
Joined: 14 Nov 2014
Posts: 598

Kudos [?]: 93 [0], given: 46

Re: If m, n, and m^n are nonzero integers, which of the following must be [#permalink]

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08 Oct 2017, 01:28
take m = -3 , n = -3
I , ii and iii all will fail ..

Kudos [?]: 93 [0], given: 46

Re: If m, n, and m^n are nonzero integers, which of the following must be   [#permalink] 08 Oct 2017, 01:28
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# If m, n, and m^n are nonzero integers, which of the following must be

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