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

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Manager
Joined: 10 Feb 2011
Posts: 113
Followers: 1

Kudos [?]: 294 [0], given: 10

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

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18 Feb 2011, 11:33
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55% (hard)

Question Stats:

45% (01:48) correct 55% (01:07) wrong based on 11 sessions

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195. 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
Manager
Joined: 03 Jun 2010
Posts: 181
Location: United States (MI)
Concentration: Marketing, General Management
Followers: 6

Kudos [?]: 69 [0], given: 40

Re: 195. If m, n, and mn are nonzero integers, which of the foll [#permalink]

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18 Feb 2011, 11:44
How m^n can be a non-integer, if it is given that it is an integer?
Math Forum Moderator
Joined: 20 Dec 2010
Posts: 2013
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Kudos [?]: 1822 [0], given: 376

Re: 195. If m, n, and mn are nonzero integers, which of the foll [#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"
_________________
Re: 195. If m, n, and mn are nonzero integers, which of the foll   [#permalink] 18 Feb 2011, 11:55
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