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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] New post 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] New post 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.

Answer: C.
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Re: If m and n are negative integers what is the value of m*n [#permalink] New post 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] New post 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] New post 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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COLLECTION OF QUESTIONS:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

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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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