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If m and n are negative integers what is the value of m*n

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If m and n are negative integers what is the value of m*n [#permalink]  28 Jan 2011, 04:57
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If m and n are negative integers what is the value of m*n

(1) m^n = 1/81
(2) n^m = -(1/64)
[Reveal] Spoiler: OA

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Last edited by Bunuel on 15 Oct 2013, 07:10, edited 1 time in total.
Edited the question.
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Re: Exponents ds [#permalink]  28 Jan 2011, 05:37
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rxs0005 wrote:
if m and n are negative inegers what is the value of m*n

S1 m^n = 1 / 81

S2 m^n = - (1 / 64)

There is something wrong with this question as statements contradict each other: (1) says m^n=1/81 and (2) says m^n=-(1/64). Guess (2) should read: n^m=-(1/64).

If m and n are negative inegers what is the value of m*n?

(1) m^n=1/81 --> as both m and n are negative integers then $$m^n=\frac{1}{81}=(-9)^{-2}=(-3)^{-4}$$ --> $$mn=18$$ or $$mn=12$$ (note that as negative integer in negative integer power gives positive number then the power must be negative even number). Not sufficient.

(2) n^m=-(1/64) --> as the result is negative then $$m$$ must be negative odd number --> $$n^m=-\frac{1}{64}=(-4)^{-3}=(-64)^{-1}$$ --> $$mn=12$$ or $$mn=64$$. Not sufficient.

(1)+(2) Only one pair of negative integers $$m$$ and $$n$$ satisfies both statements $$m=-3$$ and $$n=-4$$ --> $$mn=12$$. Sufficient.

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Re: If m and n are negative integers what is the value of m*n [#permalink]  25 Jun 2013, 03:46
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Bumping for review and further discussion*. Get a kudos point for an alternative solution!

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Re: If m and n are negative integers what is the value of m*n [#permalink]  27 Sep 2013, 21:07
Hi Bunuel,

Can you please explain how did you come to the conclusion that it should be n^m and not m ^ n in the second sentence.
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Re: If m and n are negative integers what is the value of m*n [#permalink]  28 Sep 2013, 03:46
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jakelong1 wrote:
Hi Bunuel,

Can you please explain how did you come to the conclusion that it should be n^m and not m ^ n in the second sentence.

Sure.

On the GMAT, two data sufficiency statements always provide TRUE information and these statements never contradict each other.

Now, if the statements were:
(1) m^n = 1/81
(2) m^n = -1/64

Then they would clearly contradict each other, thus I assumed that one of them must be different.

Does this make sense?
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Re: If m and n are negative integers what is the value of m*n   [#permalink] 28 Sep 2013, 03:46
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