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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, 23:48

the answer is B

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

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.

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