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Is A^B positive? (1) B^A is positive (2) B is negative

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Is A^B positive? (1) B^A is positive (2) B is negative [#permalink] New post 26 Feb 2012, 02:07
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Is A^B positive?

(1) B^A is positive
(2) B is negative

Hi, i could not find this question with the search function:

(1)
B = negative, then A even and positive
B = positive, then A even or odd and positive or negative
-->not sufficient

(2)
B = negative and if A positive, then A^B positive. But if A negative, then A^B negative
--> not sufficient

(1)+(2)
B = negative
A = must be even and positive
--> If A positive, then A^B is positive

Do i think wrong here? Cause the explanation states: Statements (1) and (2) combined are insufficient. Consider B = -2 , A = 2 (the answer is "yes") and B = -1 , A = -2 (the answer is "no").
[Reveal] Spoiler: OA
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Re: Hardest questions - Powers - Q10 [#permalink] New post 26 Feb 2012, 02:50
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MSoS wrote:
(1)
B = negative, then A even and positive
B = positive, then A even or odd and positive or negative
-->not sufficient

(1) B^A is positive
so when B = negative, then A could be even and positive or even and negative
what follows after or is that u have missed
consider an example
B = -1 , A = 2 or -2, so when A= 2 then B^A = 1 ( positive) and
when A = -2, B^A = 1( positive)
B=positive...u have done it correctly

(2) B is negative
when 1 and 2 combined
A^B is positive when A = 2 and B = -1
however A^B is negative when A = -2 and B = -1
hope this expl helps. :)

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Re: Is A^B positive? (1) B^A is positive (2) B is negative [#permalink] New post 26 Feb 2012, 03:38
Cheers - my assumption was that negative B can only be positive with an even and positive power (A). However, that helped!
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Re: Is A^B positive? (1) B^A is positive (2) B is negative [#permalink] New post 26 Feb 2012, 04:34
Expert's post
MSoS wrote:
Is A^B positive?

(1) B^A is positive
(2) B is negative

Hi, i could not find this question with the search function:

(1)
B = negative, then A even and positive
B = positive, then A even or odd and positive or negative
-->not sufficient

(2)
B = negative and if A positive, then A^B positive. But if A negative, then A^B negative
--> not sufficient

(1)+(2)
B = negative
A = must be even and positive
--> If A positive, then A^B is positive

Do i think wrong here? Cause the explanation states: Statements (1) and (2) combined are insufficient. Consider B = -2 , A = 2 (the answer is "yes") and B = -1 , A = -2 (the answer is "no").


Not a good question. First of all on the GMAT possibility of 0^0 wold be ruled out (for example by saying that AB doesn't equal to zero), also most likely A and B would be limited to integers only.

Anyway, the answer is E only: in you post there is perfectly OK example, which satisfies both statements and gives both an YES and NO answer to the question.

For more on exponents check this: math-number-theory-88376.html

Also check:
PS exponents and roots questions with solutions: tough-and-tricky-exponents-and-roots-questions-125956.html
DS exponents and roots questions with solutions: tough-and-tricky-exponents-and-roots-questions-125967.html

Hope it helps.

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Current Student
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Joined: 10 Jan 2010
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GMAT Tests User
Re: Is A^B positive? (1) B^A is positive (2) B is negative [#permalink] New post 26 Feb 2012, 06:07
Thanks, helped a lot. If the question is not a good one, you might consider to change the wording (or given information) in the gmatclub test (Hardest question, powers, question 10).

Anyway, thanks for the given information...
Re: Is A^B positive? (1) B^A is positive (2) B is negative   [#permalink] 26 Feb 2012, 06:07
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