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# If m and n are negative integers, what is the value of mn?

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Manager
Joined: 24 Nov 2010
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Location: United States (CA)
Concentration: Technology, Entrepreneurship
Schools: Ross '15, Duke '15
If m and n are negative integers, what is the value of mn? [#permalink]

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29 Dec 2011, 08:45
00:00

Difficulty:

55% (hard)

Question Stats:

48% (01:32) correct 52% (01:30) wrong based on 37 sessions

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If m and n are negative integers, what is the value of mn?

(1) m^n = 1/81
(2) n^m = - 1/64

OPEN DISCUSSION OF THIS QUESTION IS HERE: if-m-and-n-are-negative-integers-what-is-the-value-of-m-n-108394.html
[Reveal] Spoiler: OA

Last edited by Bunuel on 23 Feb 2016, 02:06, edited 1 time in total.
Renamed the topic and edited the question.
Manager
Joined: 20 Aug 2011
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Re: If m and n are negative integers, what is the value of mn? [#permalink]

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29 Dec 2011, 10:18
C

1.
m=-3,n=-4; m=-9, n=-2
mn=12; mn=18
2.
n=-64,m=-1; n=-4, m=-3 [m will always be odd]
nm=64; mn=12

1+2
nm=12
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Manager
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Re: If m and n are negative integers, what is the value of mn? [#permalink]

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29 Dec 2011, 19:49
no doubt. just double checking as the OA was B.
Intern
Joined: 27 Dec 2011
Posts: 6
Re: If m and n are negative integers, what is the value of mn? [#permalink]

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30 Dec 2011, 00:48

consider the first statement

u have m^n=1/81 cz both m and n are negative i.e. it should be (-ve)^(-ve) or in this case (-9)^(-2) or (-3) ^(-4) both of which satisfy the statement
thus Insufficient

consider the 2nd statement

we have n^m= -(1/64)

so the options can be (-8)^(-2) or (-4)^(-3)

cz minus sign is already there that means the exponent has to be odd (that is the only way we would get a negative sign out of the base.
thus we have only one solution (-4)^(-3) which give n=-4 and m=-3 or mn=12 hence
Sufficient
Manager
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Posts: 80
Re: If m and n are negative integers, what is the value of mn? [#permalink]

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30 Dec 2011, 01:34
puneetkr wrote:
consider the 2nd statement

we have n^m= -(1/64)

so the options can be (-8)^(-2) or (-4)^(-3)

there can one more solution: (-64)^(-1)
it should be C) imo
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Re: If m and n are negative integers, what is the value of mn? [#permalink]

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30 Dec 2011, 07:09
d3thknell wrote:
puneetkr wrote:
consider the 2nd statement

we have n^m= -(1/64)

so the options can be (-8)^(-2) or (-4)^(-3)

there can one more solution: (-64)^(-1)
it should be C) imo

Yes It should be C...
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Re: If m and n are negative integers, what is the value of mn? [#permalink]

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23 Feb 2016, 02:07
dreambeliever wrote:
If m and n are negative integers, what is the value of mn?

(1) m^n = 1/81
(2) 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.

OPEN DISCUSSION OF THIS QUESTION IS HERE: if-m-and-n-are-negative-integers-what-is-the-value-of-m-n-108394.html
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Re: If m and n are negative integers, what is the value of mn?   [#permalink] 23 Feb 2016, 02:07
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